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Q. 1. In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

1. 
2. 
3. 
4. 

Sol: Let geometric progression is a, ar, ar2,………….;(a, r > 0)

Correct choice: (4)

Q. 2. If sin then a value of x is.

1. 1
2. 3
3. 4
4. 5

Sol:

Correct choice: (2)

Q. 3. In the binomial expansion of

1. 
2. 
3. 
4. 

Sol:

orrect choice: (4)

Q. 4. The set S : = {1, 2, 3, ……, 12} is to be partitioned into three sets A, B, C of equal size. Thus, The number of ways to partition S is

1. 
2. 
3. 
4. 

Sol: 12 different objects are to be divided into 3 groups of equal size, which are named as set A, B and C. Correct choice: (3)

Q. 5. The largest interval lying in for which the function

1. 
2. 
3. 
4. 

1. 
   

Sol:

Correct choice: (4)

Q. 6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

1. 12 kg and 13 kg
2. 5 kg and 5 kg
3. 5kg and 12 kg
4. 5 kg and 13 kg

Sol:

So tension in the strings are 5 kg and 12 kg. Correct choice: (3)

Q. 7. A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

1. 
2. 
3. 
4. 

Sol: Probability of getting sum of nine in a single throw

Probability of getting sum nine exactly two times out of three draws .

orrect choice: (4)

Q. 8. Consider a family of circles which are passing through the point (- 1, 1) and are tangent to x-axis. If (h, k), are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

1. 
2. 
3. 
4. 

Sol: Centre of circle is (h, k) and x-axis is tangent. Radius of the family of circle
Also circle passes through

Correct choice: (2)

Q. 9. Let L be the line of intersection of the planes 2x + 3y +z = 1 and x + 3y +2z = 2. If L makes an angle with the positive x-axis, then equals

1. 
2. 
3. 1
4. 

Sol:

Correct choice: (1)

Q. 10. The differential equation of all circles passing through the origin and having their centres on the x-axis is

1. 
2. 
3. 
4. 

Sol: Equation of family of circles passing through origin and having their centres on x-axis is

Correct choice: (3)