CBSE 10th Maths Quiz

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Probability of an event can be -1/6
- True
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2.

Solve for x : 2x + y = 8, y= - 6
- 6
- 4
- 7
- 16
Correct Answer

A. 7

Explanation

2x + y = 8, putting y = - 6
2x-6 = 8
2x = 8 + 6 => 14
x = 14/2 = 7

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2
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
Correct Answer

A. Angle of elevation

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.

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4.

A parallelogram circumscribing a circles is a:
- Square
- Rectangle
- Rhombus
- Trapezium
Correct Answer

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.

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2
5.

The 10th term of the sequence whose nth term is (3n-2) is
- 28
- 42
- 35
- 32
Correct Answer

A. 28

Explanation

t10 = 3*10-2 = 28

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6.

The angle between any tangent and the radius at the point of contact of a circle is:
- 45
- 90
- 60
- 30
Correct Answer

A. 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

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7.

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
Correct Answer

A. 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.

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8.

The number of tangents that can be drawn from an external point to a circle is:
- Three
- Two
- One
- Zero
Correct Answer

A. Two

Explanation

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

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9.

The measure of the angle between any tangent and the radius at the point of contact of a cirle is:
- 90
- 60
- 45
- 30
Correct Answer

A. 90

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.

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10.

If the 7th and 13th terms of an A.P be 34 and 64 respectively then its 18th term is:
- 87
- 88
- 89
- 90
Correct Answer

A. 89

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 =

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11.

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

A.

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.

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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
Correct Answer

A. 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

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13.

In a lottery there are 10 prizes and 20 blank. What is the probability of getting prize?
- 1/2
- 1
- 1/3
- 1/10
Correct Answer

A. 1/3

Explanation

Total outcomes in a lottery ticket = 10 + 20 = 30
P (getting prize) = 10 / 30 = 1 / 3, So 1/3 is a correct answer.

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14.

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
Correct Answer

A. 256:81

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 ==

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15.

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
Correct Answer

A. 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.

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1
16.

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
Correct Answer

A. False

Explanation

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

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17.

ABCXYZ, if XYYZZX, then ABC is a _ triangle
- Right triangle
- Isoceles
- Obtuse angled
- Equilaterel
Correct Answer

A. Equilaterel

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.

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18.

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:
Correct Answer

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)==.

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0
19.

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
Correct Answer

A. 7cm

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.

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20.

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

A. 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.

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21.

Sin45cos30+ cos60sin45=
- 0
- 1
Correct Answer

A.

Explanation

Solution: sin45

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1
22.

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
Correct Answer

A. 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.

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23.

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

A.

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%.

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24.

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.
Correct Answer

A.

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.

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25.

Which term of the progression 4,9,14,…. Is 109 ?
- 12
- 18
- 20
- 22
Correct Answer

A. 22

Explanation

tn= a+(n-1)d

109=4+(n-1)5

n=22

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2
26.

The distance between the point: ( cos + b sin ,0) and (0, sin - b cos )
- A+b
Correct Answer

A.

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).

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27.

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

A.

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.

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28.

A coin s tossed two times. Find the probability of getting the least one head.
Correct Answer

A.

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.

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29.

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
Correct Answer

A. 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

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30.

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.
Correct Answer

A.

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.

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31.

A line segment that intersect a circle at two points is called a:
- Radius
- Diameter
- Tangent
- Secant
Correct Answer

A. Secant

Explanation

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

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32.

If the HCF of 612 and 1314 is 18, then thier LCM is
- 44676
- 44667
- 46674
- 46476
Correct Answer

A. 44676

Explanation

Solution:We know that , HCF (a,b) x LCM(a,b)= axb 
18x LCM= 
LCM=44676 
Hence th LCM is 44676.

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1
33.

If the circumference of a circle increases from 4 to 8, then its area is:
- Havled
- Doubled
- Tripled
- Quadrupled
Correct Answer

A. 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.

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34.

The probability that a non-leap year has 53 sundays:
Correct Answer

A.

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.

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35.

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
Correct Answer

A. 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.

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36.

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
Correct Answer

A. 3 abc

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.

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37.

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
Correct Answer

A. 45

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.

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38.

Th sum of the first 50 natural numbers is equal to:
- 1275
- 1450
- 1575
- 1625
Correct Answer

A. 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.

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39.

If 7th and 13th terms of an A.P be 34 and 64 respectively then its 18th term is:
- 87
- 88
- 89
- 90
Correct Answer

A. 89
40.

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.
Correct Answer

A.

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.

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41.

If tan = cot , then =
- 30
- 45
- 60
- 90
Correct Answer

A. 45

Explanation

Solution:tan = tan(90-) 
=90- 
2=90 
=45 
(or)

tan 45=cot 45 =1

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42.

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
Correct Answer

A. 55 ,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.

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43.

The area of a sector of a circle with radius 7 m and angle at center 60 is:
- 154
Correct Answer

A.

Explanation

Solution: r=7cm and =60 
area of sector=x 
x 7x7x 
22x7x 
=

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44.

If is a root of the equation +kx-=0, then the value of k is:
- 2
- -2
Correct Answer

A. 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.

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45.

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
Correct Answer

A. All chords are of 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.

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46.

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
Correct Answer

A. 3:4:5

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.

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47.

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
Correct Answer

A. 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."

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48.

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
Correct Answer

A. 70

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.

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49.

If cot A = 12/5, then the value of (sin A + cos A) x cosec A is :
- 13/5
- 17/5
- 14/5
- 1
Correct Answer

A. 17/5

Explanation

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

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2

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Probability of an event can be -1/6

Quiz Preview

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

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:

A parallelogram circumscribing a circles is a:

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

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

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

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

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

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

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

Given that sin A = 1/2 and cos B= 1/ then the value of (A+B) is :

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

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

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:

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

ABCXYZ, if XYYZZX, then ABC is a _ triangle

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:

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:

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

Sin45cos30+ cos60sin45=

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

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

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.

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

The distance between the point:<br> ( cos + b sin ,0) and (0, sin - b cos )

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

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

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

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.

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

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

If the circumference of a circle increases from 4 to 8, then its area is:

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

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

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

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

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

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

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.

If tan = cot , then =

If sum of two angles of a triangle is 80 and thier difference is 30 , then the angles of the triangle are

The area of a sector of a circle with radius 7 m and angle at center 60 is:

If is a root of the equation +kx-=0, then the value of k is:

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

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

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

TP and TQ are two tangents to a circle with center O s that POQ= 110 THEN PTQ is equal to:

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