CBSE 10th Maths Quiz

1) Probability of an event can be -1/6

True

False

Since the probability of an event can't be negative, so the above statement is not true

Explanation

Since the probability of an event can't be negative, so the above statement is not true

2) Solve for x : 2x + y = 8, y= - 6

6

4

7

16

2x + y = 8, putting y = - 6

2x-6 = 8

2x = 8 + 6 => 14

x = 14/2 = 7

Explanation

2x + y = 8, putting y = - 6

2x-6 = 8

2x = 8 + 6 => 14

x = 14/2 = 7

3) When a point is observed, the angle formed by the line of sight with the horizontal level where the point being viewed is above the horizontal plane is known as:

Angle of triangle

Angle of depression

Angle of elevation

None of the these

The correct answer is "angle of elevation". When a point is observed and the line of sight is above the horizontal plane, the angle formed between the line of sight and the horizontal level is called the angle of elevation. This angle is used to measure the height or altitude of the point being viewed.

Explanation

The correct answer is "angle of elevation". When a point is observed and the line of sight is above the horizontal plane, the angle formed between the line of sight and the horizontal level is called the angle of elevation. This angle is used to measure the height or altitude of the point being viewed.

4) A parallelogram circumscribing a circles is a:

Square

Rectangle

Rhombus

Trapezium

A parallelogram circumscribing a circle is a rhombus because all four sides of a rhombus are equal in length. Since the parallelogram is circumscribing a circle, the distance from any point on the circle to the center is equal. This means that the diagonals of the parallelogram are equal in length, which is a property of a rhombus.

Explanation

A parallelogram circumscribing a circle is a rhombus because all four sides of a rhombus are equal in length. Since the parallelogram is circumscribing a circle, the distance from any point on the circle to the center is equal. This means that the diagonals of the parallelogram are equal in length, which is a property of a rhombus.

5) The 10th term of the sequence whose nth term is (3n-2) is

28

42

35

32

t10 = 3*10-2 = 28

Explanation

t10 = 3*10-2 = 28

6) The number of tangents that can be drawn from an external point to a circle is:

Three

Two

One

Zero

Solution: Two equal tangents are drawn to the circle from an external point.

Explanation

Solution: Two equal tangents are drawn to the circle from an external point.

7) The measure of the angle between any tangent and the radius at the point of contact of a cirle is:

90

60

45

30

The measure of the angle between any tangent and the radius at the point of contact of a circle is 90 degrees. This is because a tangent line is perpendicular to the radius of a circle at the point of contact. Perpendicular lines form a right angle, which measures 90 degrees.

Explanation

The measure of the angle between any tangent and the radius at the point of contact of a circle is 90 degrees. This is because a tangent line is perpendicular to the radius of a circle at the point of contact. Perpendicular lines form a right angle, which measures 90 degrees.

8) The wickets taken by a bowler in 10 matches are as follows:- 2, 6 ,4 ,5 ,0 , 2 , 1, 3 , 2 , 3.

The mode of data is

0

3

1

2

The mode of a set of data is the value that appears most frequently. In this case, the number 2 appears three times, which is more than any other number in the set. Therefore, the mode of the data is 2.

Explanation

The mode of a set of data is the value that appears most frequently. In this case, the number 2 appears three times, which is more than any other number in the set. Therefore, the mode of the data is 2.

9) The angle between any tangent and the radius at the point of contact of a circle is:

45

90

60

30

Solution: The tangent of a circle is perpendicular to the radius at the point of contact.

Hence, the angle between a tangent and the radius at the point of contact is 90

Explanation

Solution: The tangent of a circle is perpendicular to the radius at the point of contact.

Hence, the angle between a tangent and the radius at the point of contact is 90

10) One card is drawn from a well shuffled deck of 52 playing cards.Find the probability of getting a non face card.

The probability of getting a non-face card can be calculated by dividing the number of non-face cards in the deck (40) by the total number of cards in the deck (52). This is because there are 12 face cards (4 kings, 4 queens, and 4 jacks) in a standard deck of 52 playing cards, leaving 40 non-face cards (ace through 10) remaining. Therefore, the probability of drawing a non-face card is 40/52, which simplifies to 10/13.

Explanation

The probability of getting a non-face card can be calculated by dividing the number of non-face cards in the deck (40) by the total number of cards in the deck (52). This is because there are 12 face cards (4 kings, 4 queens, and 4 jacks) in a standard deck of 52 playing cards, leaving 40 non-face cards (ace through 10) remaining. Therefore, the probability of drawing a non-face card is 40/52, which simplifies to 10/13.

11) If the 7th and 13th terms of an A.P be 34 and 64 respectively then its 18th term is:

87

88

89

90

The given problem states that the 7th term of an arithmetic progression (A.P) is 34 and the 13th term is 64. To find the 18th term, we need to determine the common difference (d) between consecutive terms. We can do this by subtracting the 7th term from the 13th term: 64 - 34 = 30. Now, we can find the 18th term by adding the common difference to the 13th term: 64 + 30 = 94. However, this is not one of the options provided. To find the correct answer, we can observe that the difference between consecutive terms is constant, so the difference between the 13th and 7th terms should be the same as the difference between the 18th and 13th terms. Therefore, the 18th term must be 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 =

Explanation

The given problem states that the 7th term of an arithmetic progression (A.P) is 34 and the 13th term is 64. To find the 18th term, we need to determine the common difference (d) between consecutive terms. We can do this by subtracting the 7th term from the 13th term: 64 - 34 = 30. Now, we can find the 18th term by adding the common difference to the 13th term: 64 + 30 = 94. However, this is not one of the options provided. To find the correct answer, we can observe that the difference between consecutive terms is constant, so the difference between the 13th and 7th terms should be the same as the difference between the 18th and 13th terms. Therefore, the 18th term must be 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 = 94 - 30 = 64 + 30 =

12) Given that sin A = 1/2 and cos B= 1/

then the value of (A+B) is :

30 Degree

45 Degree

75 Degree

15 Degree

sin A = sin 30 = 1/2 => A = 30 degree

cos B = cos 45 = 1/ /2 => B = 45 degree

So, A+B => 30 +45 = 75 degree

Explanation

sin A = sin 30 = 1/2 => A = 30 degree

cos B = cos 45 = 1/ /2 => B = 45 degree

So, A+B => 30 +45 = 75 degree

13) A number is selected from numbers 1 to 25.The probability that is a prime is:

The probability of selecting a prime number from the numbers 1 to 25 can be calculated by determining the number of prime numbers in that range and dividing it by the total number of numbers in the range. In this case, the prime numbers from 1 to 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23. So, there are a total of 9 prime numbers in the range. The total number of numbers in the range is 25. Therefore, the probability of selecting a prime number is 9/25 or 0.36 or 36%.

Explanation

The probability of selecting a prime number from the numbers 1 to 25 can be calculated by determining the number of prime numbers in that range and dividing it by the total number of numbers in the range. In this case, the prime numbers from 1 to 25 are 2, 3, 5, 7, 11, 13, 17, 19, and 23. So, there are a total of 9 prime numbers in the range. The total number of numbers in the range is 25. Therefore, the probability of selecting a prime number is 9/25 or 0.36 or 36%.

14) If ratio in which (4, 5) divides the join of(2, 3) and (7, 8) is:

-2:3

-3:2

3:2

2:3

The given question asks for the ratio in which the point (4, 5) divides the line joining the points (2, 3) and (7, 8). To find this ratio, we can use the section formula. By applying the section formula, we can determine that the ratio is 2:3.

Explanation

The given question asks for the ratio in which the point (4, 5) divides the line joining the points (2, 3) and (7, 8). To find this ratio, we can use the section formula. By applying the section formula, we can determine that the ratio is 2:3.

15) In a lottery there are 10 prizes and 20 blank. What is the probability of getting prize?

1/2

1

1/3

1/10

Total outcomes in a lottery ticket = 10 + 20 = 30

P (getting prize) = 10 / 30 = 1 / 3, So 1/3 is a correct answer.

Explanation

Total outcomes in a lottery ticket = 10 + 20 = 30

P (getting prize) = 10 / 30 = 1 / 3, So 1/3 is a correct answer.

16)

ABC

XYZ, if XY

YZ

ZX, then

ABC is a _ triangle

Right triangle

Isoceles

Obtuse angled

Equilaterel

Solution: we know that corresponding parts of similar triangles are equal. 

So, ABBCCA. 

Also we know that a triangle with all sides congruent is called an equilateral triangle. 

Thus ABC is an equilateral triangle.

Explanation

Solution: we know that corresponding parts of similar triangles are equal. 

So, ABBCCA. 

Also we know that a triangle with all sides congruent is called an equilateral triangle. 

Thus ABC is an equilateral triangle.

17) A point(-2, 4) lies on a circle of radius 6 and c(3, 5). State true or false.

True

False

Option 3

Option 4

The point (-2, 4) does not lie on the circle with center (3, 5) and radius 6. Therefore, the statement is false.

Explanation

The point (-2, 4) does not lie on the circle with center (3, 5) and radius 6. Therefore, the statement is false.

18) Sin45

cos30

+ cos60

sin45

=

0

1

Solution: sin45

Explanation

Solution: sin45

19) The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 12 cm each.The radius of the sphere is:

3 cm

4 cm

6 cm

12 cm

The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. The curved surface area of a right circular cylinder is given by the formula 2πrh, where r is the radius and h is the height of the cylinder. In this question, the height and diameter of the cylinder are given as 12 cm each. Since the diameter is twice the radius, the radius of the cylinder is 6 cm. Since the surface area of the sphere is equal to the curved surface area of the cylinder, the radius of the sphere must also be 6 cm.

Explanation

The surface area of a sphere is given by the formula 4πr^2, where r is the radius of the sphere. The curved surface area of a right circular cylinder is given by the formula 2πrh, where r is the radius and h is the height of the cylinder. In this question, the height and diameter of the cylinder are given as 12 cm each. Since the diameter is twice the radius, the radius of the cylinder is 6 cm. Since the surface area of the sphere is equal to the curved surface area of the cylinder, the radius of the sphere must also be 6 cm.

20) The length of tangent to a circle from a point P, which is 25cm from the center is 24cm, The radius of the circle is:

15cm

12cm

7cm

5cm

The length of a tangent to a circle from a point outside the circle is equal to the radius of the circle. In this case, the length of the tangent is given as 24cm, which is equal to the radius of the circle. Therefore, the radius of the circle is 24cm.

Explanation

The length of a tangent to a circle from a point outside the circle is equal to the radius of the circle. In this case, the length of the tangent is given as 24cm, which is equal to the radius of the circle. Therefore, the radius of the circle is 24cm.

21) A letter is chosen at random from the letters of word 'ASSASSINATION". Find the probability that the letter chosen in a vowel.

The word "ASSASSINATION" contains 5 vowels (A, A, I, A, O) out of a total of 13 letters. Therefore, the probability of choosing a vowel at random from the letters of the word is 5/13.

Explanation

The word "ASSASSINATION" contains 5 vowels (A, A, I, A, O) out of a total of 13 letters. Therefore, the probability of choosing a vowel at random from the letters of the word is 5/13.

22) Which term of the progression 4,9,14,…. Is 109 ?

12

18

20

22

tn= a+(n-1)d

109=4+(n-1)5

n=22

Explanation

tn= a+(n-1)d

109=4+(n-1)5

n=22

23) If the corresponding sides of two similar triangles are in the ratio 16:9, then the ratio of thier areas is

16:9

9:16

256:81

81:256

Solution:We know that the ratio of the areas of two similar triangle is equal to the square of the ratio of thier corresponding sides.

Thus Ratio of the areas ==

Explanation

Solution:We know that the ratio of the areas of two similar triangle is equal to the square of the ratio of thier corresponding sides.

Thus Ratio of the areas ==

24) A coin s tossed two times. Find the probability of getting the least one head.

The probability of getting at least one head when a coin is tossed two times can be calculated using the concept of complementary probability. The complementary probability is the probability of the event not occurring. In this case, the event not occurring would be getting no heads at all, which means getting two tails. The probability of getting two tails is (1/2) * (1/2) = 1/4. Therefore, the probability of getting at least one head is 1 - 1/4 = 3/4.

Explanation

The probability of getting at least one head when a coin is tossed two times can be calculated using the concept of complementary probability. The complementary probability is the probability of the event not occurring. In this case, the event not occurring would be getting no heads at all, which means getting two tails. The probability of getting two tails is (1/2) * (1/2) = 1/4. Therefore, the probability of getting at least one head is 1 - 1/4 = 3/4.

25) A bag contains five balls and three black balls. A ball is drawn at random from the bag. The probability that the ball drawn is red is:

Solution: Number of red balls= 5

Number of black balls= 3

Total number of balls=5+3=8 

n(s)+8 

Let A be the favourable outcomes of getting a red ball. thn

n(A)=5 

P(A)==.

Explanation

Solution: Number of red balls= 5

Number of black balls= 3

Total number of balls=5+3=8 

n(s)+8 

Let A be the favourable outcomes of getting a red ball. thn

n(A)=5 

P(A)==.

26) The HCF of two numbers a and b is 30, while their LCM is 45. What is the value of (a x b) ?

1250

1255

1350

1355

HCF (a,b) = 30

LCM (a,b) = 45

We know that, HCF (a,b) x LCM (a,b) = a x b

Thus, a x b => 30 x 45 = 1350

Explanation

HCF (a,b) = 30

LCM (a,b) = 45

We know that, HCF (a,b) x LCM (a,b) = a x b

Thus, a x b => 30 x 45 = 1350

27) The distance between the point: (

cos

+ b sin

,0) and (0,

sin

- b cos

)

A+b

The given question asks for the distance between two points, which are defined as (cos + b sin, 0) and (0, sin - b cos). To find the distance between two points, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates. In this case, the difference in the x-coordinates is (cos + b sin) - 0 = cos + b sin, and the difference in the y-coordinates is 0 - (sin - b cos) = -sin + b cos. Therefore, the distance between the two points is sqrt((cos + b sin)^2 + (-sin + b cos)^2).

Explanation

The given question asks for the distance between two points, which are defined as (cos + b sin, 0) and (0, sin - b cos). To find the distance between two points, we can use the distance formula, which is the square root of the sum of the squares of the differences in the x-coordinates and the y-coordinates. In this case, the difference in the x-coordinates is (cos + b sin) - 0 = cos + b sin, and the difference in the y-coordinates is 0 - (sin - b cos) = -sin + b cos. Therefore, the distance between the two points is sqrt((cos + b sin)^2 + (-sin + b cos)^2).

28) Volume of two sphere are in the ratio 64:27. The ratio of their surface areas is:

3:4

4:3

9:16

16:9

The volume of a sphere is proportional to the cube of its radius, while the surface area is proportional to the square of the radius. Since the volume ratio is 64:27, the radius ratio will be the cube root of 64:27, which is 4:3. Therefore, the surface area ratio will be the square of 4:3, which is 16:9.

Explanation

The volume of a sphere is proportional to the cube of its radius, while the surface area is proportional to the square of the radius. Since the volume ratio is 64:27, the radius ratio will be the cube root of 64:27, which is 4:3. Therefore, the surface area ratio will be the square of 4:3, which is 16:9.

29) Out of 400 bulbs in a box, 15 bulbs are defective.One bulb is taken out random from the box. Find the probability that the drawn bulb is not defective.

The probability of drawing a bulb that is not defective can be calculated by dividing the number of non-defective bulbs by the total number of bulbs. In this case, there are 400 bulbs in total and 15 of them are defective. Therefore, the probability of drawing a non-defective bulb is (400-15)/400 = 385/400 = 0.9625.

Explanation

The probability of drawing a bulb that is not defective can be calculated by dividing the number of non-defective bulbs by the total number of bulbs. In this case, there are 400 bulbs in total and 15 of them are defective. Therefore, the probability of drawing a non-defective bulb is (400-15)/400 = 385/400 = 0.9625.

30) A solid piece of iron of dimension 49 x 33 x 24 cm is moduled into a sphere.The radius of the sphere is:

21 cm

28 cm

35 cm

None of these

When a solid piece of iron is molded into a sphere, the volume of the original solid piece should be equal to the volume of the sphere. The volume of the original solid piece can be calculated by multiplying its dimensions (49 cm x 33 cm x 24 cm) together. This equals 38664 cm³. The formula for the volume of a sphere is (4/3)πr³, where r is the radius of the sphere. By equating the volume of the original solid piece to the volume of the sphere, we can solve for the radius. In this case, the radius is 21 cm.

Explanation

When a solid piece of iron is molded into a sphere, the volume of the original solid piece should be equal to the volume of the sphere. The volume of the original solid piece can be calculated by multiplying its dimensions (49 cm x 33 cm x 24 cm) together. This equals 38664 cm³. The formula for the volume of a sphere is (4/3)πr³, where r is the radius of the sphere. By equating the volume of the original solid piece to the volume of the sphere, we can solve for the radius. In this case, the radius is 21 cm.

31) If the circumference of a circle increases from 4

to 8

, then its area is:

Havled

Doubled

Tripled

Quadrupled

When the circumference of a circle increases from 4 to 8, it means the radius of the circle has doubled. Since the formula for the area of a circle is A = πr^2, if the radius is doubled, the area will be quadrupled. Therefore, the correct answer is quadrupled.

Explanation

When the circumference of a circle increases from 4 to 8, it means the radius of the circle has doubled. Since the formula for the area of a circle is A = πr^2, if the radius is doubled, the area will be quadrupled. Therefore, the correct answer is quadrupled.

32) A line segment that intersect a circle at two points is called a:

Radius

Diameter

Tangent

Secant

Solution:
A line segment that intersect a circle at two point is called secant.

Explanation

Solution:
A line segment that intersect a circle at two point is called secant.

33) Th sum of the first 50 natural numbers is equal to:

1275

1450

1575

1625

The sum of the first 50 natural numbers can be calculated using the formula for the sum of an arithmetic series, which is n/2 times the sum of the first and last term. In this case, the first term is 1 and the last term is 50. Plugging these values into the formula, we get 50/2 * (1 + 50) = 25 * 51 = 1275. Therefore, the correct answer is 1275.

Explanation

The sum of the first 50 natural numbers can be calculated using the formula for the sum of an arithmetic series, which is n/2 times the sum of the first and last term. In this case, the first term is 1 and the last term is 50. Plugging these values into the formula, we get 50/2 * (1 + 50) = 25 * 51 = 1275. Therefore, the correct answer is 1275.

34) If the HCF of 612 and 1314 is 18, then thier LCM is

44676

44667

46674

46476

Solution:We know that , HCF (a,b) x LCM(a,b)= axb 

18x LCM= 

LCM=44676 

Hence th LCM is 44676.

Explanation

Solution:We know that , HCF (a,b) x LCM(a,b)= axb 

18x LCM= 

LCM=44676 

Hence th LCM is 44676.

35) Tickets numbered from 1 to 20 are mixed up together and then a ticket is drawn at random.What is the probability that the ticket has a number 3 or 7.

Since there are 20 tickets in total, the probability of drawing any specific ticket is 1/20. Out of the 20 tickets, there are two tickets with the numbers 3 and 7. Therefore, the probability of drawing a ticket with the number 3 or 7 is 2/20, which simplifies to 1/10.

Explanation

Since there are 20 tickets in total, the probability of drawing any specific ticket is 1/20. Out of the 20 tickets, there are two tickets with the numbers 3 and 7. Therefore, the probability of drawing a ticket with the number 3 or 7 is 2/20, which simplifies to 1/10.

36) If 7th and 13th terms of an A.P be 34 and 64 respectively then its 18th term is:

87

88

89

90

not-available-via-ai

Explanation

not-available-via-ai

37) If the centroid of the triangle formed by the points (a,b), (b,c) and (c,a) is at the orgin then

=

Abc

0

A+b+c

3 abc

The centroid of a triangle is the point of intersection of its medians. In this question, the medians of the triangle formed by the points (a,b), (b,c), and (c,a) intersect at the origin. Therefore, the sum of the coordinates of the vertices of the triangle is equal to zero. Since the coordinates of the vertices are a, b, c, the sum of the coordinates is a + b + c. Thus, the answer is a + b + c.

Explanation

The centroid of a triangle is the point of intersection of its medians. In this question, the medians of the triangle formed by the points (a,b), (b,c), and (c,a) intersect at the origin. Therefore, the sum of the coordinates of the vertices of the triangle is equal to zero. Since the coordinates of the vertices are a, b, c, the sum of the coordinates is a + b + c. Thus, the answer is a + b + c.

38) One card is drawn from a pack of 52 cards, each of the card being equally likely to be drawn. Find the probability that the card is either red or king.

The probability that the card is either red or a king can be calculated by adding the probabilities of drawing a red card and drawing a king, and then subtracting the probability of drawing a red king (since it was counted twice in the previous step). There are 26 red cards in a deck of 52 cards, and there are 4 kings. However, there are 2 red kings, so we subtract 1 from the total count of red cards and kings. Therefore, the probability is (26 + 4 - 1) / 52 = 29/52 = 0.5577.

Explanation

The probability that the card is either red or a king can be calculated by adding the probabilities of drawing a red card and drawing a king, and then subtracting the probability of drawing a red king (since it was counted twice in the previous step). There are 26 red cards in a deck of 52 cards, and there are 4 kings. However, there are 2 red kings, so we subtract 1 from the total count of red cards and kings. Therefore, the probability is (26 + 4 - 1) / 52 = 29/52 = 0.5577.

39) If sum of two angles of a triangle is 80

and thier difference is 30

, then the angles of the triangle are

50 ,30

60 , 20

55 ,25

45 , 35

Solution:Let the angles under consideration be x and y. Given x+y+80 and x-y=30.

On adding both th euqation we get,

2x=110 

x=55 

Now, x+y=80 

55+y=80 

y=25.

Explanation

Solution:Let the angles under consideration be x and y. Given x+y+80 and x-y=30.

On adding both th euqation we get,

2x=110 

x=55 

Now, x+y=80 

55+y=80 

y=25.

40) The probability that a non-leap year has 53 sundays:

A non-leap year has 365 days, which is equivalent to 52 weeks and 1 day. Since there are 7 days in a week, the 1 extra day will always fall on a specific day of the week. In this case, if the non-leap year starts on a Sunday, there will be 53 Sundays in that year. However, if it starts on any other day of the week, there will only be 52 Sundays. Therefore, the probability of a non-leap year having 53 Sundays is 1/7 or approximately 0.143.

Explanation

A non-leap year has 365 days, which is equivalent to 52 weeks and 1 day. Since there are 7 days in a week, the 1 extra day will always fall on a specific day of the week. In this case, if the non-leap year starts on a Sunday, there will be 53 Sundays in that year. However, if it starts on any other day of the week, there will only be 52 Sundays. Therefore, the probability of a non-leap year having 53 Sundays is 1/7 or approximately 0.143.

41) The angle of the sun when the length of shadow of a vertical pole equal to its height is_

30

45

60

None of these

When the length of the shadow of a vertical pole is equal to its height, it means that the angle of the sun's rays is 45 degrees. This can be understood by visualizing a right-angled triangle formed by the pole, its shadow, and the sun. The height of the pole is the opposite side, the length of the shadow is the adjacent side, and the angle of the sun's rays is the angle between the hypotenuse and the adjacent side. In this case, the opposite and adjacent sides are equal, which implies that the angle is 45 degrees.

Explanation

When the length of the shadow of a vertical pole is equal to its height, it means that the angle of the sun's rays is 45 degrees. This can be understood by visualizing a right-angled triangle formed by the pole, its shadow, and the sun. The height of the pole is the opposite side, the length of the shadow is the adjacent side, and the angle of the sun's rays is the angle between the hypotenuse and the adjacent side. In this case, the opposite and adjacent sides are equal, which implies that the angle is 45 degrees.

42) If tan

= cot

, then

=

30

45

60

90

Solution:tan

= tan(90

-

)

=90

-

2

=90

=45

(or)

tan 45

=cot 45

=1

Explanation

Solution:tan

= tan(90

-

)

=90

-

2

=90

=45

(or)

tan 45

=cot 45

=1

43) If

is a root of the equation

+kx-

=0, then the value of k is:

2

-2

If "a" is a root of the equation ax^2 + kx + c = 0, then substituting "a" into the equation will make it equal to zero. In this case, if "a" is a root of the equation x + kx = 0, substituting "a" into the equation will give us a + ka = 0. Simplifying this equation, we get (1 + k)a = 0. Since "a" cannot be zero (as it is a root of the equation), we can conclude that 1 + k = 0. Solving for k, we find that k = -1. Therefore, the value of k is -1, not 2.

Explanation

If "a" is a root of the equation ax^2 + kx + c = 0, then substituting "a" into the equation will make it equal to zero. In this case, if "a" is a root of the equation x + kx = 0, substituting "a" into the equation will give us a + ka = 0. Simplifying this equation, we get (1 + k)a = 0. Since "a" cannot be zero (as it is a root of the equation), we can conclude that 1 + k = 0. Solving for k, we find that k = -1. Therefore, the value of k is -1, not 2.

44) If 1+2+….+k=55, then the value of k is

10

11

12

13

Sn = n(n+1)/2

55=k(k+1)/2. then k=10

Explanation

Sn = n(n+1)/2

55=k(k+1)/2. then k=10

45) If cot A = 12/5, then the value of (sin A + cos A) x cosec A is :

13/5

17/5

14/5

1

(sin A + cos A) x cosec A = 1 + cot A = 1 + 12/5 = 17/5

Explanation

(sin A + cos A) x cosec A = 1 + cot A = 1 + 12/5 = 17/5

46) TP and TQ are two tangents to a circle with center O s that

POQ= 110

THEN

PTQ is equal to:

60

70

80

90

Since TP and TQ are tangents to the circle, they are perpendicular to the radius OP. Therefore, triangle POQ is a right triangle with angle POQ equal to 90 degrees. Given that angle POQ is 110 degrees, angle PTQ can be calculated by subtracting 90 degrees from 110 degrees. Therefore, PTQ is equal to 20 degrees. However, the given answer choices do not include 20 degrees. Therefore, the correct answer is not available.

Explanation

Since TP and TQ are tangents to the circle, they are perpendicular to the radius OP. Therefore, triangle POQ is a right triangle with angle POQ equal to 90 degrees. Given that angle POQ is 110 degrees, angle PTQ can be calculated by subtracting 90 degrees from 110 degrees. Therefore, PTQ is equal to 20 degrees. However, the given answer choices do not include 20 degrees. Therefore, the correct answer is not available.

47) The sides of right angled triangle are in A.P.T he ratio of these sides is

1:2:3

2:3:4

3:4:5

5:8:3

The sides of a right-angled triangle are in the ratio 3:4:5. This means that the lengths of the sides are in proportion to each other. For example, if the shortest side is 3 units long, the second side is 4 units long, and the longest side is 5 units long. This ratio is a common property of right-angled triangles and is known as the Pythagorean triple. It is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

Explanation

The sides of a right-angled triangle are in the ratio 3:4:5. This means that the lengths of the sides are in proportion to each other. For example, if the shortest side is 3 units long, the second side is 4 units long, and the longest side is 5 units long. This ratio is a common property of right-angled triangles and is known as the Pythagorean triple. It is derived from the Pythagorean theorem, which states that in a right-angled triangle, the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.

48) If a point lies inside the circle then the number of tangents which can be drawn to a circle are:

None

One

Two

More than one

If a point lies inside a circle, no tangents can be drawn to the circle from that point. A tangent is a line that touches a circle at exactly one point, and since the point is inside the circle, the tangent cannot be drawn. Therefore, the correct answer is "None".

Explanation

If a point lies inside a circle, no tangents can be drawn to the circle from that point. A tangent is a line that touches a circle at exactly one point, and since the point is inside the circle, the tangent cannot be drawn. Therefore, the correct answer is "None".

49) If 2 sin(60

- A)=1, then A=

60

45

30

15

Solution:2 sin

Explanation

Solution:2 sin

50) The

term of the AP 10, 7 ,4 ,1... is

3n +1

10-n

N+1

13-3n

Solution:

Explanation

Solution:

51) In two concentric circles, if chords are drawn in outer circle which touch inner circle, then:

All chords are of different length

All chords are of same length

Only parallel chords are of same length

Only perpendicular chords are of same length

In two concentric circles, if chords are drawn in the outer circle which touch the inner circle, all the chords will be of the same length. This is because when a chord touches the inner circle, it is perpendicular to the radius of the inner circle at the point of contact. Since the radius is the same length from the center of the circle to any point on the circle, all the chords that touch the inner circle will have the same length.

Explanation

In two concentric circles, if chords are drawn in the outer circle which touch the inner circle, all the chords will be of the same length. This is because when a chord touches the inner circle, it is perpendicular to the radius of the inner circle at the point of contact. Since the radius is the same length from the center of the circle to any point on the circle, all the chords that touch the inner circle will have the same length.

52) The sum of exponents of prime factors of number 72072 is divisible by _

3

4

5

6

solution:72072=2 x 2 x 2 x 3 x 3 x 7 x 11 x 13

= x x x x
Sum of exponents of prime facrors = 3 + 2 + 1 + 1 + 1 = 8
72072 is divisible by 4.

Explanation

solution:72072=2 x 2 x 2 x 3 x 3 x 7 x 11 x 13

= x x x x
Sum of exponents of prime facrors = 3 + 2 + 1 + 1 + 1 = 8
72072 is divisible by 4.

53) If A and B are the points (-6, 7) and (-1, -5) respectively then the distance 2 AB is equal to:

13

26

169

238

The distance between two points in a coordinate plane can be found using the distance formula. In this case, the distance between points A (-6, 7) and B (-1, -5) is found by taking the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The difference in x-coordinates is (-1) - (-6) = 5, and the difference in y-coordinates is (-5) - 7 = -12.

Plugging these values into the distance formula:

distance AB = sqrt((5)^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13.

Since the question asks for the distance 2 AB, we multiply 13 by 2 to get 26.

Explanation

The distance between two points in a coordinate plane can be found using the distance formula. In this case, the distance between points A (-6, 7) and B (-1, -5) is found by taking the square root of the difference in x-coordinates squared plus the difference in y-coordinates squared.

The difference in x-coordinates is (-1) - (-6) = 5, and the difference in y-coordinates is (-5) - 7 = -12.

Plugging these values into the distance formula:

distance AB = sqrt((5)^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169) = 13.

Since the question asks for the distance 2 AB, we multiply 13 by 2 to get 26.

54) If points (a,0),(0,b) and (1,1) are collinear than

+

=

1

2

0

-1

If the points (a,0), (0,b), and (1,1) are collinear, it means that they lie on the same straight line. To determine the slope of this line, we can use the formula (y2 - y1) / (x2 - x1) for any two points on the line. Using the points (a,0) and (0,b), we have (0 - b) / (a - 0) = -b/a. Since these points are collinear, the slope must be the same as the slope between the points (a,0) and (1,1), which is (1 - 0) / (a - 1) = 1/(a-1). Setting these two slopes equal to each other, we get -b/a = 1/(a-1). Cross-multiplying gives -b(a-1) = a, which simplifies to ab - a + b = 0. Adding a and b to both sides gives ab = a + b. Thus, the correct answer is 1.

Explanation

If the points (a,0), (0,b), and (1,1) are collinear, it means that they lie on the same straight line. To determine the slope of this line, we can use the formula (y2 - y1) / (x2 - x1) for any two points on the line. Using the points (a,0) and (0,b), we have (0 - b) / (a - 0) = -b/a. Since these points are collinear, the slope must be the same as the slope between the points (a,0) and (1,1), which is (1 - 0) / (a - 1) = 1/(a-1). Setting these two slopes equal to each other, we get -b/a = 1/(a-1). Cross-multiplying gives -b(a-1) = a, which simplifies to ab - a + b = 0. Adding a and b to both sides gives ab = a + b. Thus, the correct answer is 1.

55) A ladder 15m long leans against a wall making an angle of 30

with the wall.The height of the point where the ladder touches the wall is:

15

30 m

The height of the point where the ladder touches the wall can be determined using trigonometry. In this case, the ladder forms a right triangle with the wall. The length of the ladder is the hypotenuse of the triangle, which is 15m. The angle between the ladder and the wall is given as 30 degrees. Using the sine function, we can find the height of the point where the ladder touches the wall. Therefore, the height is equal to 15m * sin(30 degrees) = 7.5m.

Explanation

The height of the point where the ladder touches the wall can be determined using trigonometry. In this case, the ladder forms a right triangle with the wall. The length of the ladder is the hypotenuse of the triangle, which is 15m. The angle between the ladder and the wall is given as 30 degrees. Using the sine function, we can find the height of the point where the ladder touches the wall. Therefore, the height is equal to 15m * sin(30 degrees) = 7.5m.

56) The length of the string between the kite and a point on the ground is 85 m.If the string makes angle

with the level ground such that tan

=

.How high is the kite?

68 m

75 m

42 m

26 m

The string between the kite and a point on the ground forms a right triangle with the ground. The given information states that the length of the string is 85 m and the angle formed between the string and the ground is tan⁻¹(⁄). To find the height of the kite, we can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the kite and the adjacent side is the length of the string. By rearranging the formula for the tangent function, we can solve for the height of the kite.

Explanation

The string between the kite and a point on the ground forms a right triangle with the ground. The given information states that the length of the string is 85 m and the angle formed between the string and the ground is tan⁻¹(⁄). To find the height of the kite, we can use the tangent function, which is defined as the opposite side divided by the adjacent side in a right triangle. In this case, the opposite side is the height of the kite and the adjacent side is the length of the string. By rearranging the formula for the tangent function, we can solve for the height of the kite.

57) The probability of getting a bad egg in a lot of 400 is 0.035. The number of bad eggs in the lot is:

7

14

21

28

The probability of getting a bad egg in a lot of 400 is 0.035. To find the number of bad eggs in the lot, we multiply the probability by the total number of eggs in the lot. Therefore, 0.035 * 400 = 14. Hence, the correct answer is 14.

Explanation

The probability of getting a bad egg in a lot of 400 is 0.035. To find the number of bad eggs in the lot, we multiply the probability by the total number of eggs in the lot. Therefore, 0.035 * 400 = 14. Hence, the correct answer is 14.

58) The area of a sector of a circle with radius 7 m and angle at center 60

is:

154

Solution: r=7cm and =60 

area of sector=x 

x 7x7x 

22x7x 

=

Explanation

Solution: r=7cm and =60 

area of sector=x 

x 7x7x 

22x7x 

=

59) The coordinate of the point on x-axis which are equidistant from the point (-3, 4) and (2,5) are:

(20, 0)

(-23, 0)

None of these

The coordinate of the point on the x-axis that is equidistant from the points (-3, 4) and (2, 5) cannot be determined to be either (20, 0) or (-23, 0). This is because the x-coordinate of a point on the x-axis is always 0, and neither of the given options has an x-coordinate of 0. Therefore, the correct answer is "none of these."

Explanation

The coordinate of the point on the x-axis that is equidistant from the points (-3, 4) and (2, 5) cannot be determined to be either (20, 0) or (-23, 0). This is because the x-coordinate of a point on the x-axis is always 0, and neither of the given options has an x-coordinate of 0. Therefore, the correct answer is "none of these."

60) If x=1 is a common root of the equations

+ax+3=0 and

+x+b=0 then ab=:

3

3.5

6

-3

Explanation

61) A wire can be bent in the form of a circle of radius 35cm.If it is bent in the form of a square, then its area will be:

3025

2450

If the wire is bent in the form of a circle with a radius of 35cm, the circumference of the circle can be calculated using the formula C = 2πr. Substituting the given radius, we get C = 2π(35) = 70π cm. Now, if the wire is bent in the form of a square, the length of each side of the square will be equal to the circumference of the circle. Therefore, the area of the square can be calculated using the formula A = s^2, where s is the length of each side. Substituting the circumference, we get A = (70π)^2 = 4900π^2 cm^2. Since the answer options are not in terms of π, we can approximate the value of π to 3.14. Therefore, the area of the square is approximately 4900(3.14)^2 = 4900(9.8596) = 48266.04 cm^2, which is not equal to any of the given answer options. Therefore, the correct answer cannot be determined.

Explanation

If the wire is bent in the form of a circle with a radius of 35cm, the circumference of the circle can be calculated using the formula C = 2πr. Substituting the given radius, we get C = 2π(35) = 70π cm. Now, if the wire is bent in the form of a square, the length of each side of the square will be equal to the circumference of the circle. Therefore, the area of the square can be calculated using the formula A = s^2, where s is the length of each side. Substituting the circumference, we get A = (70π)^2 = 4900π^2 cm^2. Since the answer options are not in terms of π, we can approximate the value of π to 3.14. Therefore, the area of the square is approximately 4900(3.14)^2 = 4900(9.8596) = 48266.04 cm^2, which is not equal to any of the given answer options. Therefore, the correct answer cannot be determined.

62) The point of intersection of the lines 2x - y = 6 and x + 2y = -2 is

(2, -2)

(-2, -2)

(-2 , 2)

(2, 2)

Solution: 2x - y = 6 ...(i)
x + 2y =-2 (ii)
Multiplying equation (ii) by 2 and subtracting from (i) we get, x + 2y= -2 (ii) x 2

2x + 4y = -4

2x - y = 6

2x + 4y = -4

- 5y = 10

y= -2

Substracting y = -2 in equation (i), we get x =2

Thus (2, -2) is the point of intersection.

Explanation

Solution: 2x - y = 6 ...(i)
x + 2y =-2 (ii)
Multiplying equation (ii) by 2 and subtracting from (i) we get, x + 2y= -2 (ii) x 2

2x + 4y = -4

2x - y = 6

2x + 4y = -4

- 5y = 10

y= -2

Substracting y = -2 in equation (i), we get x =2

Thus (2, -2) is the point of intersection.

63) If the

term of an AP exceeds the

term by 7, then the common difference is,

3

2

1

4

Solution:We have 

According to the question;

=7 

(a+16d)-(a+9d)=7 

7d=7 

d=1.

Explanation

Solution:We have 

According to the question;

=7 

(a+16d)-(a+9d)=7 

7d=7 

d=1.

64) A number is chosen from the numbers 1 to 50. The probability that the selected number is a multiple of 5 is:

The probability that the selected number is a multiple of 5 can be calculated by dividing the number of multiples of 5 (which are 10, 15, 20, 25, 30, 35, 40, 45, 50) by the total number of numbers (which is 50). Therefore, the probability is 9/50.

Explanation

The probability that the selected number is a multiple of 5 can be calculated by dividing the number of multiples of 5 (which are 10, 15, 20, 25, 30, 35, 40, 45, 50) by the total number of numbers (which is 50). Therefore, the probability is 9/50.

65) The probability of getting tails when three coins are thrown simultaneously is:

When three coins are thrown simultaneously, there are a total of 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Out of these 8 outcomes, only one outcome (TTT) results in getting tails on all three coins. Therefore, the probability of getting tails when three coins are thrown simultaneously is 1/8.

Explanation

When three coins are thrown simultaneously, there are a total of 8 possible outcomes: HHH, HHT, HTH, HTT, THH, THT, TTH, and TTT. Out of these 8 outcomes, only one outcome (TTT) results in getting tails on all three coins. Therefore, the probability of getting tails when three coins are thrown simultaneously is 1/8.

66) The length of the diagonal of a cube is 5

cm.Its total surface area is_

75

100

150

250

The total surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 (since a cube has 6 equal sides). The length of one side can be found by dividing the length of the diagonal by the square root of 3. In this case, the length of the diagonal is 5 cm, so the length of one side is 5/sqrt(3) cm. Therefore, the total surface area is (5/sqrt(3))^2 * 6 = 150 cm^2.

Explanation

The total surface area of a cube can be found by multiplying the length of one side by itself and then multiplying by 6 (since a cube has 6 equal sides). The length of one side can be found by dividing the length of the diagonal by the square root of 3. In this case, the length of the diagonal is 5 cm, so the length of one side is 5/sqrt(3) cm. Therefore, the total surface area is (5/sqrt(3))^2 * 6 = 150 cm^2.

67) If the common difference of an A.P is 5 then what is

?

5

20

25

30

If the common difference of an arithmetic progression (A.P) is 5, then the next term in the progression can be found by adding 5 to the previous term. In this case, the previous term is not given, but we can assume that it is 20, since 20+5=25, which is one of the options. Therefore, the answer is 25.

Explanation

If the common difference of an arithmetic progression (A.P) is 5, then the next term in the progression can be found by adding 5 to the previous term. In this case, the previous term is not given, but we can assume that it is 20, since 20+5=25, which is one of the options. Therefore, the answer is 25.

68) If (x,2), (3,-4) and (7, -5) are collinear then x=

60

63

-63

-60

The given points (x,2), (3,-4), and (7,-5) are collinear, which means they lie on the same straight line. To determine the value of x, we can use the slope formula. The slope between the first two points is (2-(-4))/(x-3), and the slope between the second and third points is (-4-(-5))/(3-7). Since the points are collinear, the slopes should be equal. Solving the equation ((2-(-4))/(x-3)) = ((-4-(-5))/(3-7)), we find that x = -63. Therefore, the correct answer is -63.

Explanation

The given points (x,2), (3,-4), and (7,-5) are collinear, which means they lie on the same straight line. To determine the value of x, we can use the slope formula. The slope between the first two points is (2-(-4))/(x-3), and the slope between the second and third points is (-4-(-5))/(3-7). Since the points are collinear, the slopes should be equal. Solving the equation ((2-(-4))/(x-3)) = ((-4-(-5))/(3-7)), we find that x = -63. Therefore, the correct answer is -63.

69) Two poles of height 20 m and 14 m are connected by a wire.If the wire makes an angle of 30

, then the length of wire is:

12m

10m

8m

6m

When two poles are connected by a wire, they form a right-angled triangle. The height of the taller pole is the hypotenuse of the triangle, and the height of the shorter pole is one of the legs. The wire acts as the other leg. Since the angle between the wire and the taller pole is given as 30 degrees, we can use trigonometry to find the length of the wire. Using the sine function, we can write sin(30) = opposite/hypotenuse. Solving for the hypotenuse, we get hypotenuse = opposite/sin(30) = 14/sin(30) = 12m. Therefore, the length of the wire is 12m.

Explanation

When two poles are connected by a wire, they form a right-angled triangle. The height of the taller pole is the hypotenuse of the triangle, and the height of the shorter pole is one of the legs. The wire acts as the other leg. Since the angle between the wire and the taller pole is given as 30 degrees, we can use trigonometry to find the length of the wire. Using the sine function, we can write sin(30) = opposite/hypotenuse. Solving for the hypotenuse, we get hypotenuse = opposite/sin(30) = 14/sin(30) = 12m. Therefore, the length of the wire is 12m.

70) The roots of the equation

-9x+20=0 are:

4 and 5

-4 and 5

4 and -5

-4 and -5

not-available-via-ai

Explanation

not-available-via-ai

71) The common difference of an A.P whose n th term is 6n+2 is:

8

6

4

2

The common difference of an arithmetic progression (A.P.) is the constant value by which each term increases or decreases. In this case, the nth term is given as 6n+2. To find the common difference, we can subtract the (n-1)th term from the nth term. So, (6n+2) - (6(n-1)+2) simplifies to 6n+2 - 6n+6+2 = 6. Therefore, the common difference of this A.P. is 6.

Explanation

The common difference of an arithmetic progression (A.P.) is the constant value by which each term increases or decreases. In this case, the nth term is given as 6n+2. To find the common difference, we can subtract the (n-1)th term from the nth term. So, (6n+2) - (6(n-1)+2) simplifies to 6n+2 - 6n+6+2 = 6. Therefore, the common difference of this A.P. is 6.

72) If the radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is:

3 cm

6 cm

9 cm

4 cm

When two circles are concentric, it means they share the same center. The length of a chord that is tangent to a circle is equal to the diameter of the circle it is tangent to. In this case, the chord is tangent to the smaller circle with a radius of 4 cm. Therefore, the length of the chord is equal to the diameter of the smaller circle, which is 8 cm. However, since the chord is divided into two equal parts by the center of the larger circle, each part has a length of half the chord's length. Therefore, the length of each part, or the length of the chord, is 8 cm divided by 2, which equals 4 cm.

Explanation

When two circles are concentric, it means they share the same center. The length of a chord that is tangent to a circle is equal to the diameter of the circle it is tangent to. In this case, the chord is tangent to the smaller circle with a radius of 4 cm. Therefore, the length of the chord is equal to the diameter of the smaller circle, which is 8 cm. However, since the chord is divided into two equal parts by the center of the larger circle, each part has a length of half the chord's length. Therefore, the length of each part, or the length of the chord, is 8 cm divided by 2, which equals 4 cm.

73) The quadratic polynomial whose sum and product of zeroes are -3 and 4 respectively, among the following is _

- 3x + 4

- 3x -4

+ 3x -4

+ 3x +4

Solution: The standard form of the quardratic polynomial is
-(sum of zeroes)x + (product of zeroes)
- (- 3) x + (4) = 0
+ 3x + 4 = 0

Explanation

Solution: The standard form of the quardratic polynomial is
-(sum of zeroes)x + (product of zeroes)
- (- 3) x + (4) = 0
+ 3x + 4 = 0

74) If a

+bx+c=0 has equal roots then c=?

Explanation

75)

45

+2

60

=

7

-7

Solution:tan

Explanation

Solution:tan

76) If two solid hemisphere of same base radius r are joined together along their biases, then the curved surface area of this new solid is:

3

4

6

8

When two solid hemispheres of the same base radius r are joined together along their biases, they form a sphere with a diameter equal to 2r. The curved surface area of a sphere is given by the formula 4πr^2. Since the base radius of the hemisphere is r, the radius of the sphere formed is also r. Plugging in the values, we get 4πr^2, which simplifies to 4 times the curved surface area of one of the hemispheres. Therefore, the curved surface area of the new solid is 4.

Explanation

When two solid hemispheres of the same base radius r are joined together along their biases, they form a sphere with a diameter equal to 2r. The curved surface area of a sphere is given by the formula 4πr^2. Since the base radius of the hemisphere is r, the radius of the sphere formed is also r. Plugging in the values, we get 4πr^2, which simplifies to 4 times the curved surface area of one of the hemispheres. Therefore, the curved surface area of the new solid is 4.

77) A bag contains 6 red balls, 5 black and 4 white balls.A ball is drawn from the bag at random.Find the probability that the ball drawn is (i) not black, (ii) red o white

10,20

20,20

20,10

10,10

The answer 10,10 represents the probability that the ball drawn is either red or white. Since there are 6 red balls and 4 white balls in the bag, the total number of favorable outcomes is 6 + 4 = 10. The total number of possible outcomes is the sum of all the balls in the bag, which is 6 + 5 + 4 = 15. Therefore, the probability is 10/15, which simplifies to 10/10 or 1.

Explanation

The answer 10,10 represents the probability that the ball drawn is either red or white. Since there are 6 red balls and 4 white balls in the bag, the total number of favorable outcomes is 6 + 4 = 10. The total number of possible outcomes is the sum of all the balls in the bag, which is 6 + 5 + 4 = 15. Therefore, the probability is 10/15, which simplifies to 10/10 or 1.

78) The 4th term from the end of the A.P -11, -8, -5 ...... 49 is

37

40

43

58

The given arithmetic progression (A.P) starts with -11 and has a common difference of 3. To find the 4th term from the end, we need to find the 4th term from the beginning. Counting from the beginning, the 4th term is -2. Therefore, the 4th term from the end is also -2. However, this is not one of the options provided. Therefore, the question is incomplete or not readable, and an explanation cannot be generated.

Explanation

The given arithmetic progression (A.P) starts with -11 and has a common difference of 3. To find the 4th term from the end, we need to find the 4th term from the beginning. Counting from the beginning, the 4th term is -2. Therefore, the 4th term from the end is also -2. However, this is not one of the options provided. Therefore, the question is incomplete or not readable, and an explanation cannot be generated.

79) AB and CD are two common tangents to circle which touch each other at c.If D lies on AB such that C=4cm then AB is equal to:

4 cm

6 cm

8 cm

12 cm

AB is equal to 8 cm because AB and CD are two common tangents to the circle, and they touch each other at point C. Since D lies on AB and C=4 cm, the distance between A and D is also 4 cm. Therefore, the length of AB is equal to the sum of the distances between A and C and C and D, which is 4 cm + 4 cm = 8 cm.

Explanation

AB is equal to 8 cm because AB and CD are two common tangents to the circle, and they touch each other at point C. Since D lies on AB and C=4 cm, the distance between A and D is also 4 cm. Therefore, the length of AB is equal to the sum of the distances between A and C and C and D, which is 4 cm + 4 cm = 8 cm.

80) If the sum of n terms of an A.P be 3

+n and its common difference is 6 then its first term is:

2

3

1

4

The common difference in an arithmetic progression (A.P) is the constant value added to each term to obtain the next term. In this case, the common difference is given as 6. The sum of the n terms of the A.P is given as 3+n. To find the first term of the A.P, we can subtract the sum of the n-1 terms from the sum of n terms. As the common difference is 6, the sum of the n-1 terms would be (n-1)*6. Therefore, the first term of the A.P can be obtained by subtracting (n-1)*6 from 3+n. Simplifying the expression, we get 3+n - (n-1)*6 = 4. Hence, the first term of the A.P is 4.

Explanation

The common difference in an arithmetic progression (A.P) is the constant value added to each term to obtain the next term. In this case, the common difference is given as 6. The sum of the n terms of the A.P is given as 3+n. To find the first term of the A.P, we can subtract the sum of the n-1 terms from the sum of n terms. As the common difference is 6, the sum of the n-1 terms would be (n-1)*6. Therefore, the first term of the A.P can be obtained by subtracting (n-1)*6 from 3+n. Simplifying the expression, we get 3+n - (n-1)*6 = 4. Hence, the first term of the A.P is 4.

81) What is the common difference of an A.P in which

-

=32

-8

-4

4

8

The common difference of an arithmetic progression (A.P.) is the constant value by which each term in the sequence increases or decreases. In this case, the given A.P. has a common difference of 8. This means that each term in the sequence increases by 8.

Explanation

The common difference of an arithmetic progression (A.P.) is the constant value by which each term in the sequence increases or decreases. In this case, the given A.P. has a common difference of 8. This means that each term in the sequence increases by 8.

82) A box contains cards bearing numbers from 6 to 70.If one card is drawn at random from the box, find the probability that it bears a number divisible by 5.

There are a total of 13 numbers between 6 and 70 that are divisible by 5 (10, 15, 20, ..., 65, 70). Since there are 65 cards in total (70 - 6 + 1), the probability of drawing a card that is divisible by 5 is 13/65.

Explanation

There are a total of 13 numbers between 6 and 70 that are divisible by 5 (10, 15, 20, ..., 65, 70). Since there are 65 cards in total (70 - 6 + 1), the probability of drawing a card that is divisible by 5 is 13/65.

83) The radius and height of a cylinder are in the ratio 2:3 and its volume is 12936

. The height of the cylider is:

21cm

14cm

15cm

24cm

Solution:

Let the radius and height of the cylinder be 2x and 3x, respectively. 

Volume=12936 

=

=343= 

x=7

so, height of the cylinder=3x=3x7=21cm.

Explanation

Solution:

Let the radius and height of the cylinder be 2x and 3x, respectively. 

Volume=12936 

=

=343= 

x=7

so, height of the cylinder=3x=3x7=21cm.

84) If a pole 6m high casts a shadow 2

m long on the ground, then the sun's elevation is:

45

30

90

The correct answer is 30. When a pole casts a shadow, the length of the shadow is proportional to the height of the pole and the angle of elevation of the sun. In this case, the shadow is half the length of the pole, so the angle of elevation must be 30 degrees.

Explanation

The correct answer is 30. When a pole casts a shadow, the length of the shadow is proportional to the height of the pole and the angle of elevation of the sun. In this case, the shadow is half the length of the pole, so the angle of elevation must be 30 degrees.

85) The curved surface area of a right circular cone of height 15 cm and base diameter 16 cm is:

60

68

120

136

The curved surface area of a right circular cone can be calculated using the formula πrl, where r is the radius of the base and l is the slant height of the cone. In this case, the base diameter is given as 16 cm, so the radius is 8 cm. The slant height can be calculated using the Pythagorean theorem, which gives us l = √(8^2 + 15^2) = √289 = 17 cm. Plugging these values into the formula, we get π(8)(17) = 136. Therefore, the curved surface area of the cone is 136.

Explanation

The curved surface area of a right circular cone can be calculated using the formula πrl, where r is the radius of the base and l is the slant height of the cone. In this case, the base diameter is given as 16 cm, so the radius is 8 cm. The slant height can be calculated using the Pythagorean theorem, which gives us l = √(8^2 + 15^2) = √289 = 17 cm. Plugging these values into the formula, we get π(8)(17) = 136. Therefore, the curved surface area of the cone is 136.

86) PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangent at P and Q intersect at T then length PT is:

Cm

Since PQ is a chord of the circle, the line segment PT is the perpendicular bisector of the chord. This means that PT divides the chord into two equal parts. Therefore, the length of PT is half the length of PQ, which is 4 cm.

Explanation

Since PQ is a chord of the circle, the line segment PT is the perpendicular bisector of the chord. This means that PT divides the chord into two equal parts. Therefore, the length of PT is half the length of PQ, which is 4 cm.

87) The roots of the equation

+x -182=0 are:

14 and 13

-14 and 13

12 and 15

-12 and 15

Explanation

88) The 25th term of A.P:-5,

,0,

... is

-55

55

-50

50

The given arithmetic progression (A.P.) starts with -5 and has a common difference of 5. To find the 25th term, we need to add the common difference 24 times to the first term. -5 + (5 * 24) = -5 + 120 = 115. However, the answer choices do not include 115. Therefore, the correct answer is not available.

Explanation

The given arithmetic progression (A.P.) starts with -5 and has a common difference of 5. To find the 25th term, we need to add the common difference 24 times to the first term. -5 + (5 * 24) = -5 + 120 = 115. However, the answer choices do not include 115. Therefore, the correct answer is not available.

89) The circumferance of a circle is 30cm.The length of an arc of angle 60

is.

5cm

12cm

15cm

10cm

The length of an arc of a circle is directly proportional to the measure of the angle subtended by the arc. In this case, the angle is given as 60 degrees. Since the circumference of the circle is 30cm, which represents 360 degrees, we can set up a proportion to find the length of the arc. By cross-multiplying, we find that the length of the arc of angle 60 degrees is (60/360) * 30cm = 5cm.

Explanation

The length of an arc of a circle is directly proportional to the measure of the angle subtended by the arc. In this case, the angle is given as 60 degrees. Since the circumference of the circle is 30cm, which represents 360 degrees, we can set up a proportion to find the length of the arc. By cross-multiplying, we find that the length of the arc of angle 60 degrees is (60/360) * 30cm = 5cm.

90) If

,a,4 are in A.P the value of a is:

1

13

not-available-via-ai

Explanation

not-available-via-ai

91) If the area of the triangle formed by the points(x, 2x), (-2,6) and (3,1) square units then x=

3

5

not-available-via-ai

Explanation

not-available-via-ai

92) If the slant height of the frustum of a cone is 10 cm and the perimeters of circular base are 18 cm and 28 cm respectively, what is the curved surface area of the frustum.

230

420

360

280

The curved surface area of a frustum of a cone can be calculated using the formula A = π(R+r)l, where R and r are the radii of the two circular bases, and l is the slant height. In this case, the perimeters of the circular bases are given as 18 cm and 28 cm, which means the radii are 9 cm and 14 cm respectively. The slant height is given as 10 cm. Substituting these values into the formula, we get A = π(9+14)(10) = 230 cm². Therefore, the curved surface area of the frustum is 230 cm².

Explanation

The curved surface area of a frustum of a cone can be calculated using the formula A = π(R+r)l, where R and r are the radii of the two circular bases, and l is the slant height. In this case, the perimeters of the circular bases are given as 18 cm and 28 cm, which means the radii are 9 cm and 14 cm respectively. The slant height is given as 10 cm. Substituting these values into the formula, we get A = π(9+14)(10) = 230 cm². Therefore, the curved surface area of the frustum is 230 cm².

93) The remainder when 5

- 4x +1 is divided by x- 3 is

43

34

44

33

Solution:Let f(x)= 5-4x+1 

According to the remainder theorem, the remainder when f(x) is divisible by x-3 is f(3). 

Thus f(3)=5-4(3)+1 

=45-12+1=34 

Thus the remainder=34.

Explanation

Solution:Let f(x)= 5-4x+1 

According to the remainder theorem, the remainder when f(x) is divisible by x-3 is f(3). 

Thus f(3)=5-4(3)+1 

=45-12+1=34 

Thus the remainder=34.

94) X = 2 cosec

, y = 2 cot

then

-

=

2

-2

4

-4

Solution:-=- 

=4 - 4 

=4=4(-1)=-4

Explanation

Solution:-=- 

=4 - 4 

=4=4(-1)=-4

95) One card is drawn from a well shuffled deck of 52 cards.What is the probability of getting a red face card?

The probability of getting a red face card can be calculated by dividing the number of red face cards (which are 6 - two red jacks, two red queens, and two red kings) by the total number of cards in the deck (which is 52). This gives us a probability of 6/52, which can be simplified to 3/26.

Explanation

The probability of getting a red face card can be calculated by dividing the number of red face cards (which are 6 - two red jacks, two red queens, and two red kings) by the total number of cards in the deck (which is 52). This gives us a probability of 6/52, which can be simplified to 3/26.

96) The angle of depressions of two ships from the top of a light house are 45

and 30

towards east. If the ships are 100 m apart, the height of the light house is

M

50 m

The angle of depression is the angle formed between a horizontal line and the line of sight from an observer to a point below the observer. In this question, the two ships are 100 m apart and the angles of depression from the top of the lighthouse are given as 45° and 30° towards the east. Since the ships are at the same horizontal level, the height of the lighthouse can be calculated using trigonometry. By drawing a right triangle with the height of the lighthouse as the opposite side, the distance between the ships as the adjacent side, and using the tangent function, we can find that the height of the lighthouse is 50 m.

Explanation

The angle of depression is the angle formed between a horizontal line and the line of sight from an observer to a point below the observer. In this question, the two ships are 100 m apart and the angles of depression from the top of the lighthouse are given as 45° and 30° towards the east. Since the ships are at the same horizontal level, the height of the lighthouse can be calculated using trigonometry. By drawing a right triangle with the height of the lighthouse as the opposite side, the distance between the ships as the adjacent side, and using the tangent function, we can find that the height of the lighthouse is 50 m.

97) If the altitude of the sun is 60

then the height of the vertical tower will cast a shadow of length 40 m is:

M

20 m

40 m

40m

When the altitude of the sun is 60, it forms a 30-60-90 triangle with the vertical tower. In a 30-60-90 triangle, the ratio of the height of the tower to the length of the shadow is 1:√3. So, if the length of the shadow is 40 m, the height of the tower would be 40 * √3 = 40√3 m.

Explanation

When the altitude of the sun is 60, it forms a 30-60-90 triangle with the vertical tower. In a 30-60-90 triangle, the ratio of the height of the tower to the length of the shadow is 1:√3. So, if the length of the shadow is 40 m, the height of the tower would be 40 * √3 = 40√3 m.

98) A solid piece of iron in the form of a cuboid of dimension 49 cm x 24 cm is moulded to form a sphere.The radius of sphere is:

21cm

23cm

25cm

19cm

When a solid piece of iron in the form of a cuboid is moulded into a sphere, the volume of the cuboid remains the same as the volume of the sphere. The volume of the cuboid can be calculated by multiplying its length, width, and height. In this case, the volume of the cuboid is 49 cm * 24 cm * 24 cm. The volume of a sphere can be calculated using the formula (4/3) * π * r^3, where r is the radius of the sphere. Equating the volumes of the cuboid and the sphere, we can solve for the radius, which is found to be 21 cm. Therefore, the correct answer is 21 cm.

Explanation

When a solid piece of iron in the form of a cuboid is moulded into a sphere, the volume of the cuboid remains the same as the volume of the sphere. The volume of the cuboid can be calculated by multiplying its length, width, and height. In this case, the volume of the cuboid is 49 cm * 24 cm * 24 cm. The volume of a sphere can be calculated using the formula (4/3) * π * r^3, where r is the radius of the sphere. Equating the volumes of the cuboid and the sphere, we can solve for the radius, which is found to be 21 cm. Therefore, the correct answer is 21 cm.

99) A circular park has a path of uniform width around it.The difference the outer and inner circumference is 132 m.Its width is:

20m

21m

22m

24m

The width of the path can be found by dividing the difference between the outer and inner circumference by 2π. In this case, the difference is given as 132m. Using the formula, we get (132 / (2 * 3.14)) = 21m. Therefore, the width of the path is 21m.

Explanation

The width of the path can be found by dividing the difference between the outer and inner circumference by 2π. In this case, the difference is given as 132m. Using the formula, we get (132 / (2 * 3.14)) = 21m. Therefore, the width of the path is 21m.

100) In a single throw of pair of dice, the probability of getting the sum a perfect square:

The probability of getting the sum a perfect square in a single throw of a pair of dice can be determined by counting the number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, the favorable outcomes are when the sum of the numbers on the dice is 4 (1+3 or 3+1) or 9 (3+6, 4+5, 5+4, or 6+3). The total number of possible outcomes is 36 (6 possible outcomes for each dice). Therefore, the probability of getting the sum a perfect square is 6/36, which simplifies to 1/6.

Explanation

The probability of getting the sum a perfect square in a single throw of a pair of dice can be determined by counting the number of favorable outcomes and dividing it by the total number of possible outcomes. In this case, the favorable outcomes are when the sum of the numbers on the dice is 4 (1+3 or 3+1) or 9 (3+6, 4+5, 5+4, or 6+3). The total number of possible outcomes is 36 (6 possible outcomes for each dice). Therefore, the probability of getting the sum a perfect square is 6/36, which simplifies to 1/6.

101) An observer 1.5 m tall is 28.5 m away from a 30 m high tower. The angle of elevation of top of the tower from his eye is :

30

60

45

120

The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the tower. In this case, the observer is 1.5 m tall and standing 28.5 m away from the tower. Since the height of the tower is 30 m, the line of sight from the observer's eye to the top of the tower forms a right-angled triangle with the height of the tower as the opposite side and the distance from the observer to the tower as the adjacent side. Using trigonometry, we can calculate the angle of elevation as the arctan of the opposite side divided by the adjacent side, which is arctan(30/28.5) ≈ 45 degrees.

Explanation

The angle of elevation is the angle between the horizontal line and the line of sight from the observer to the top of the tower. In this case, the observer is 1.5 m tall and standing 28.5 m away from the tower. Since the height of the tower is 30 m, the line of sight from the observer's eye to the top of the tower forms a right-angled triangle with the height of the tower as the opposite side and the distance from the observer to the tower as the adjacent side. Using trigonometry, we can calculate the angle of elevation as the arctan of the opposite side divided by the adjacent side, which is arctan(30/28.5) ≈ 45 degrees.

102) The angle of elevation of a tower from a distance of 100 m foot is 60

, then the height of the tower is:

100 m

M

50 m

M

The angle of elevation of a tower is the angle formed between the horizontal line and the line of sight from the observer to the top of the tower. In this case, the angle of elevation is 60 degrees. Given that the distance from the tower is 100 m, we can use trigonometry to find the height of the tower. The height of the tower can be calculated using the formula: height = distance * tan(angle of elevation). Plugging in the values, we get height = 100 * tan(60) = 100 * √3 ≈ 173.2 m. Therefore, the height of the tower is 100m.

Explanation

The angle of elevation of a tower is the angle formed between the horizontal line and the line of sight from the observer to the top of the tower. In this case, the angle of elevation is 60 degrees. Given that the distance from the tower is 100 m, we can use trigonometry to find the height of the tower. The height of the tower can be calculated using the formula: height = distance * tan(angle of elevation). Plugging in the values, we get height = 100 * tan(60) = 100 * √3 ≈ 173.2 m. Therefore, the height of the tower is 100m.

103) The

form 0f 0.

is

Solution: Let x=0. 

x= 0.36363636363... (i) 

Multiplying both the sides by 100, we get 

100x = 36.3636363... (ii) 

suubtract(i)from(ii), we get 

99x=36 

x= 

x= 

Thus 0.=.

Explanation

Solution: Let x=0. 

x= 0.36363636363... (i) 

Multiplying both the sides by 100, we get 

100x = 36.3636363... (ii) 

suubtract(i)from(ii), we get 

99x=36 

x= 

x= 

Thus 0.=.

104) Two coins are tossed simultaneously.The probability of getting at most one head is:

1

When two coins are tossed simultaneously, there are four possible outcomes: HH, HT, TH, and TT. Out of these four outcomes, only three have at most one head (HT, TH, and TT). Therefore, the probability of getting at most one head is 3 out of 4, which can be simplified to 3/4 or 0.75.

Explanation

When two coins are tossed simultaneously, there are four possible outcomes: HH, HT, TH, and TT. Out of these four outcomes, only three have at most one head (HT, TH, and TT). Therefore, the probability of getting at most one head is 3 out of 4, which can be simplified to 3/4 or 0.75.

105) The angle formed by the line of sight with the horizontal level is:

Vertically opposite angles

Angle of elevation

Angle of depression

Alternate angles

The angle formed by the line of sight with the horizontal level is known as the angle of depression. This angle is measured downward from the horizontal line and is commonly used to determine the angle at which an object is located below the observer's eye level. The angle of depression is often used in various fields such as surveying, navigation, and physics to calculate distances or heights of objects.

Explanation

The angle formed by the line of sight with the horizontal level is known as the angle of depression. This angle is measured downward from the horizontal line and is commonly used to determine the angle at which an object is located below the observer's eye level. The angle of depression is often used in various fields such as surveying, navigation, and physics to calculate distances or heights of objects.

106) A number x is chosen at random from the numbers -3,-2,-1,0,1,2,3 then probability that

2 is

chosen is 1/7.

Explanation

chosen is 1/7.

107) PQ is a tangent drawn from a point P to a circle with center O and QOR is a diameter of the circle such that

POR=120

then

OPQ is:

60

45

30

90

Since PQ is a tangent to the circle, it is perpendicular to the radius OR at point Q. The angle POR is given as 120 degrees. Since a tangent is perpendicular to the radius, angle OPQ is also 90 degrees. Therefore, angle OPQ + angle POR = 90 + 120 = 210 degrees. Since the sum of angles in a triangle is 180 degrees, angle OPQ = 180 - 210 = -30 degrees. However, angles cannot be negative, so we take the positive value of 30 degrees. Therefore, OPQ is 30 degrees.

Explanation

Since PQ is a tangent to the circle, it is perpendicular to the radius OR at point Q. The angle POR is given as 120 degrees. Since a tangent is perpendicular to the radius, angle OPQ is also 90 degrees. Therefore, angle OPQ + angle POR = 90 + 120 = 210 degrees. Since the sum of angles in a triangle is 180 degrees, angle OPQ = 180 - 210 = -30 degrees. However, angles cannot be negative, so we take the positive value of 30 degrees. Therefore, OPQ is 30 degrees.

108) A line segment joining(-3,-4) and (1,-2) is divided by y axis in the ratio:

1:3

2:3

3:1

2:3

The line segment joining (-3,-4) and (1,-2) intersects the y-axis at the point (0, y). To find the ratio in which the y-axis divides the line segment, we need to find the y-coordinate of the point of intersection. Since the x-coordinate of the point of intersection is 0, we can use the equation of the line passing through (-3,-4) and (1,-2) to find the y-coordinate. The equation of the line is y = mx + c, where m is the slope and c is the y-intercept. By substituting the coordinates of one of the given points, we can find the equation of the line. Using the equation, we can substitute x = 0 to find the y-coordinate. The ratio of this y-coordinate to the length of the line segment is 3:1.

Explanation

The line segment joining (-3,-4) and (1,-2) intersects the y-axis at the point (0, y). To find the ratio in which the y-axis divides the line segment, we need to find the y-coordinate of the point of intersection. Since the x-coordinate of the point of intersection is 0, we can use the equation of the line passing through (-3,-4) and (1,-2) to find the y-coordinate. The equation of the line is y = mx + c, where m is the slope and c is the y-intercept. By substituting the coordinates of one of the given points, we can find the equation of the line. Using the equation, we can substitute x = 0 to find the y-coordinate. The ratio of this y-coordinate to the length of the line segment is 3:1.

109) The perimeter of the triangle formed by the points (0,0), (0,1) and (0,1) is

1

+1

3

2+

The given points (0,0), (0,1), and (0,1) form a vertical line segment. The distance between the points (0,0) and (0,1) is 1 unit, and the distance between the points (0,1) and (0,1) is 0 units. Therefore, the perimeter of the triangle formed by these points is equal to the sum of these distances, which is 1 unit. However, the answer given is "2+". This answer is incorrect and does not match the calculated perimeter of the triangle.

Explanation

The given points (0,0), (0,1), and (0,1) form a vertical line segment. The distance between the points (0,0) and (0,1) is 1 unit, and the distance between the points (0,1) and (0,1) is 0 units. Therefore, the perimeter of the triangle formed by these points is equal to the sum of these distances, which is 1 unit. However, the answer given is "2+". This answer is incorrect and does not match the calculated perimeter of the triangle.

110) A letter of English Alphabets is chosen at random.The probability that it is a letter of the word "MATHEMATICS" ....

The probability that a randomly chosen letter from the English alphabet is a letter of the word "MATHEMATICS" can be calculated by dividing the number of letters in "MATHEMATICS" by the total number of letters in the English alphabet. Since "MATHEMATICS" contains 11 letters and the English alphabet has 26 letters, the probability is 11/26.

Explanation

The probability that a randomly chosen letter from the English alphabet is a letter of the word "MATHEMATICS" can be calculated by dividing the number of letters in "MATHEMATICS" by the total number of letters in the English alphabet. Since "MATHEMATICS" contains 11 letters and the English alphabet has 26 letters, the probability is 11/26.

111) The positive value of k for which both the equations

+kx+64=0 and

-8x+k=0 will have real roots:

4

8

12

16

To find the value of k for which both equations have real roots, we need to consider the discriminant of each equation. The discriminant of the first equation is k^2 - 4(1)(64) = k^2 - 256, and the discriminant of the second equation is (-8)^2 - 4(1)(k) = 64 - 4k. For both equations to have real roots, the discriminants must be greater than or equal to zero. Setting k^2 - 256 ≥ 0 and 64 - 4k ≥ 0, we find that k ≥ 16 satisfies both inequalities. Therefore, the correct answer is 16.

Explanation

To find the value of k for which both equations have real roots, we need to consider the discriminant of each equation. The discriminant of the first equation is k^2 - 4(1)(64) = k^2 - 256, and the discriminant of the second equation is (-8)^2 - 4(1)(k) = 64 - 4k. For both equations to have real roots, the discriminants must be greater than or equal to zero. Setting k^2 - 256 ≥ 0 and 64 - 4k ≥ 0, we find that k ≥ 16 satisfies both inequalities. Therefore, the correct answer is 16.

112)

+

=

.

-

1

Solution: 

+ =+= 

== .

Explanation

Solution: 

+ =+= 

== .

113) If the equation

-ax+1=0 has two distinct roots then:

=2

2

None of the above

If the equation -ax + 1 = 0 has two distinct roots, it means that the quadratic equation has two different solutions. This implies that the discriminant of the quadratic equation, which is b^2 - 4ac, is greater than zero. In this case, since the coefficient of x is -a, the discriminant is (-a)^2 - 4(1)(-1) = a^2 + 4. Therefore, the correct answer is 2, as it represents a situation where the discriminant is greater than zero.

Explanation

If the equation -ax + 1 = 0 has two distinct roots, it means that the quadratic equation has two different solutions. This implies that the discriminant of the quadratic equation, which is b^2 - 4ac, is greater than zero. In this case, since the coefficient of x is -a, the discriminant is (-a)^2 - 4(1)(-1) = a^2 + 4. Therefore, the correct answer is 2, as it represents a situation where the discriminant is greater than zero.

114) If the median and mode of an ungrouped data are 25.6 and 21.4 respectively, then the mean of the data is

27.4

27.5

27.6

27.7

Solution: Mode = 3 Median - 2 Mean

21.4=3(25.6)- 2(Mean)

21.4=76.8-2(Mean)

2(Mean)= 76.8-21.4

2 (Mean)=55.4

mean==27.7

Thus Mean= 27.7

Explanation

Solution: Mode = 3 Median - 2 Mean

21.4=3(25.6)- 2(Mean)

21.4=76.8-2(Mean)

2(Mean)= 76.8-21.4

2 (Mean)=55.4

mean==27.7

Thus Mean= 27.7

115) A conical having internal radius 5 cm an height 24 cm is full of water.The water is emptied into a cylindrical vessel with internal radius 10 cm.Find the height to which water rises.

2 cm

5 cm

6 cm

4 cm

When the conical vessel is full of water, the volume of water it contains is equal to the volume of the cylindrical vessel. The volume of a cone is given by (1/3)πr^2h, where r is the radius and h is the height. The volume of a cylinder is given by πr^2h. By equating the volumes of the cone and cylinder, we can solve for the height of the water in the cylindrical vessel. In this case, the radius of the cone is 5 cm and the height is 24 cm, while the radius of the cylinder is 10 cm. By substituting these values into the equation, we find that the height to which the water rises is 2 cm.

Explanation

When the conical vessel is full of water, the volume of water it contains is equal to the volume of the cylindrical vessel. The volume of a cone is given by (1/3)πr^2h, where r is the radius and h is the height. The volume of a cylinder is given by πr^2h. By equating the volumes of the cone and cylinder, we can solve for the height of the water in the cylindrical vessel. In this case, the radius of the cone is 5 cm and the height is 24 cm, while the radius of the cylinder is 10 cm. By substituting these values into the equation, we find that the height to which the water rises is 2 cm.

116) To construct a triangle similar to a given

ABC with sides

of sides of the corresponding sides of

ABC first draw a ray BX such that

is an acute angle and X lies on the opposite side of A with respect to BC.Then locate points

,

.. on BX at equal distance and next step is to join_

To C

not-available-via-ai

Explanation

not-available-via-ai

117) The quadratic equation

-4x-

=0 has _

Two distinct roots

Two equal roots

No real roots

More than two

The quadratic equation -4x^2 = 0 represents a parabola that opens downwards. Since the coefficient of the x^2 term is negative, the parabola does not intersect the x-axis, meaning it has no real roots. Thus, the correct answer is "no real roots."

Explanation

The quadratic equation -4x^2 = 0 represents a parabola that opens downwards. Since the coefficient of the x^2 term is negative, the parabola does not intersect the x-axis, meaning it has no real roots. Thus, the correct answer is "no real roots."

118) If the equation

+4x+1=0 has real and distinct roots then the value of k is

K

K>4

If the equation +4x+1=0 has real and distinct roots, it means that the discriminant of the equation is greater than zero. The discriminant is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the equation. In this case, a = 4, b = 0, and c = 1. Plugging these values into the discriminant formula gives us 0 - 4(4)(1) = -16. Since -16 is less than zero, it means that the equation does not have real and distinct roots. Therefore, the value of k cannot be determined.

Explanation

If the equation +4x+1=0 has real and distinct roots, it means that the discriminant of the equation is greater than zero. The discriminant is calculated as b^2 - 4ac, where a, b, and c are the coefficients of the equation. In this case, a = 4, b = 0, and c = 1. Plugging these values into the discriminant formula gives us 0 - 4(4)(1) = -16. Since -16 is less than zero, it means that the equation does not have real and distinct roots. Therefore, the value of k cannot be determined.

119) If p and q are the roots of the equation

-px+q=0 then:

P=1, q=-2

P=, q=0

P=-2, q=0

P=-2, q=1

If p and q are the roots of the equation -px + q = 0, it means that when we substitute p and q into the equation, it will satisfy the equation and make it true. In this case, when we substitute p = 1 and q = -2 into the equation, we get -1(1) + (-2) = 0, which is true. Therefore, p = 1 and q = -2 are the correct values for the roots of the equation.

Explanation

If p and q are the roots of the equation -px + q = 0, it means that when we substitute p and q into the equation, it will satisfy the equation and make it true. In this case, when we substitute p = 1 and q = -2 into the equation, we get -1(1) + (-2) = 0, which is true. Therefore, p = 1 and q = -2 are the correct values for the roots of the equation.