1.
Find the [HCF X LCM] for the numbers 100 and 190.
2.
If the diameter of a semi-circular protractor is 14 cm, then find its perimeter
3.
If sec^{2}θ (1 + sin θ)(1 – sin θ) = k, then find the value of k.
4.
Which measure of central tendency is given by the x-coordinate of the point of
intersection of the "more than ogive " and "less than ogive” ?
5.
From a well shuffled pack of cards, a card is drawn at random. Find the probability of getting a balck queen
6.
Which term of the progression 4,9,14,…. Is 109 ?
Correct Answer
D. 22
Explanation
tn= a+(n-1)d
109=4+(n-1)5
n=22
7.
If 1+2+….+k=55, then the value of k is
Correct Answer
A. 10
Explanation
Sn = n(n+1)/2
55=k(k+1)/2. then k=10
8.
The 10th term of the sequence whose nth term is (3n-2) is
Correct Answer
A. 28
Explanation
t10 = 3*10-2 = 28
9.
If cot A = 12/5, then the value of (sin A + cos A) x cosec A is :
Correct Answer
B. 17/5
Explanation
(sin A + cos A) x cosec A = 1 + cot A = 1 + 12/5 = 17/5
10.
Given that sin A = 1/2 and cos B= 1/ then the value of (A+B) is :
Correct Answer
C. 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
11.
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:
Correct Answer
C. 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.
12.
The HCF of two numbers a and b is 30, while their LCM is 45. What is the value of (a x b) ?
Correct Answer
C. 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
13.
Solve for x : 2x + y = 8, y= - 6
Correct Answer
C. 7
Explanation
2x + y = 8, putting y = - 6
2x-6 = 8
2x = 8 + 6 => 14
x = 14/2 = 7
14.
Probability of an event can be -1/6
Correct Answer
B. False
Explanation
Since the probability of an event can't be negative, so the above statement is not true
15.
In a lottery there are 10 prizes and 20 blank. What is the probability of getting prize?
Correct Answer
C. 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.
16.
The sum of exponents of prime factors of number 72072 is divisible by _
Correct Answer
B. 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.
17.
The quadratic polynomial whose sum and product of zeroes are -3 and 4 respectively, among the following is _
Correct Answer
D. + 3x +4
Explanation
Solution: The standard form of the quardratic polynomial is -(sum of zeroes)x + (product of zeroes) - (- 3) x + (4) = 0+ 3x + 4 = 0
18.
The point of intersection of the lines 2x - y = 6 and x + 2y = -2 is
Correct Answer
A. (2, -2)
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.
19.
If the corresponding sides of two similar triangles are in the ratio 16:9, then the ratio of thier areas is
Correct Answer
C. 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 ==
20.
If the median and mode of an ungrouped data are 25.6 and 21.4 respectively, then the mean of the data is
Correct Answer
D. 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
21.
If tan = cot , then =
Correct Answer
B. 45
Explanation
Solution:tan = tan(90-)<br>
=90-<br>
2=90 <br>
=45<br>
(or)
tan 45=cot 45 =1
22.
X = 2 cosec, y = 2 cot then -=
Correct Answer
D. -4
Explanation
Solution:-=- <br>
=4 - 4 <br>
=4=4(-1)=-4
23.
+ =
Correct Answer
A. .
Explanation
Solution:<br>
+ =+= <br>
== .
24.
If the HCF of 612 and 1314 is 18, then thier LCM is
Correct Answer
A. 44676
Explanation
Solution:We know that , HCF (a,b) x LCM(a,b)= axb<br>
18x LCM= <br>
LCM=44676<br>
Hence th LCM is 44676.
25.
The form 0f 0. is
Correct Answer
C.
Explanation
Solution: Let x=0.<br>
x= 0.36363636363... (i)<br>
Multiplying both the sides by 100, we get<br>
100x = 36.3636363... (ii)<br>
suubtract(i)from(ii), we get<br>
99x=36<br>
x=<br>
x=<br>
Thus 0.=.
26.
The remainder when 5 - 4x +1 is divided by x- 3 is
Correct Answer
B. 34
Explanation
Solution:Let f(x)= 5-4x+1<br>
According to the remainder theorem, the remainder when f(x) is divisible by x-3 is f(3).<br>
Thus f(3)=5-4(3)+1<br>
=45-12+1=34<br>
Thus the remainder=34.
27.
If sum of two angles of a triangle is 80 and thier difference is 30 , then the angles of the triangle are
Correct Answer
C. 55 ,25
Explanation
Solution:Let the angles under consideration be x and y.< br> Given x+y+80 and x-y=30.
On adding both th euqation we get,
2x=110<br>
x=55<br>
Now, x+y=80<br>
55+y=80<br>
y=25.
28.
ABCXYZ, if XYYZZX, then ABC is a _ triangle
Correct Answer
D. Equilaterel
Explanation
Solution: we know that corresponding parts of similar triangles are equal.<br>
So, ABBCCA.<br>
Also we know that a triangle with all sides congruent is called an equilateral triangle.<br>
Thus ABC is an equilateral triangle.
29.
45+2 60=
Correct Answer
A. 7
Explanation
Solution:tan
30.
Sin45cos30+ cos60sin45=
Correct Answer
B.
Explanation
Solution: sin45
31.
If 2 sin(60- A)=1, then A=
Correct Answer
C. 30
Explanation
Solution:2 sin
32.
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
Correct Answer
D. 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.
33.
The rots of the equation +x -182=0 are:
Correct Answer
A. 14 and 13
Explanation
Solution:
34.
The term of the AP 10, 7 ,4 ,1... is
Correct Answer
D. 13-3n
Explanation
Solution:
35.
The number of tangents that can be drawn from an external point to a circle is:
Correct Answer
B. Two
Explanation
Solution: Two equal tangents are drawn to the circle from an external point.
36.
The measure of the angle between any tangent and the radius at the point of contact of a cirle is:
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.
37.
The circumferance of a circle is 30cm.The length of an arc of angle 60 is.
Correct Answer
A. 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.
38.
If the term of an AP exceeds the term by 7, then the common difference is,
Correct Answer
C. 1
Explanation
Solution:We have<br>
According to the question;
=7<br>
(a+16d)-(a+9d)=7<br>
7d=7<br>
d=1.
39.
A line segment that intersect a circle at two points is called a:
Correct Answer
D. Secant
Explanation
Solution:
A line segment that intersect a circle at two point is called secant.
40.
The angle between any tangent and the radius at the point of contact of a circle is:
Correct Answer
B. 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
41.
The area of a sector of a circle with radius 7 m and angle at center 60 is:
Correct Answer
B.
Explanation
Solution: r=7cm and =60<br>
area of sector=x<br>
x 7x7x <br>
22x7x<br>
=
42.
The radius and height of a cylinder are in the ratio 2:3 and its volume is 12936. The height of the cylider is:
Correct Answer
A. 21cm
Explanation
Solution:
Let the radius and height of the cylinder be 2x and 3x, respectively.<br>
Volume=12936<br>
=
=343=<br>
x=7
so, height of the cylinder=3x=3x7=21cm.
43.
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<br>
n(s)+8<br>
Let A be the favourable outcomes of getting a red ball. thn
n(A)=5<br>
P(A)==.
44.
Two coins are tossed simultaneously.The probability of getting at most one head is:
Correct Answer
C.
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.
45.
The angle formed by the line of sight with the horizontal level is:
Correct Answer
C. Angle of depression
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.
46.
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:
Correct Answer
A. 21cm
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.
47.
The distance between the point:<br>
( cos + b sin ,0) and (0, sin - b cos )
Correct Answer
D.
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).
48.
The roots of the equation -9x+20=0 are:
Correct Answer
A. 4 and 5
49.
The common difference of an A.P whose n th term is 6n+2 is:
Correct Answer
B. 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.
50.
If the equation +4x+1=0 has real and distinct roots then the value of k is
Correct Answer
A. K
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.