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- Question 1 of 20
##### 1. Question

**SECTION – 1 : (Only One Option Correct Type)****This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE option is correct.**Question:

The quadratic equation p(x) = 0 with real coefficients has purely imaginary roots. Then the equation p(p(x)) = 0 has

CorrectIncorrect - Question 2 of 20
##### 2. Question

Three boys and two girls stand in a queue. The probability, that the number of boys ahead of every girl is at least one more than the number of girls ahead of her, is

CorrectIncorrect - Question 3 of 20
##### 3. Question

Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card numbered 1 is always placed in envelope numbered 2. Then the number of ways it can be done is

CorrectIncorrect - Question 4 of 20
##### 4. Question

In a triangle the sum of two sides is x and the product of the same two sides is y. If x

^{2}– c^{2}= y, where c is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle isCorrectIncorrect - Question 5 of 20
##### 5. Question

The common tangents to the circle x

^{2}+ y^{2}= 2 and the parabola y^{2}= 8x touch the circle at the points P, Q and the parabola at the points R, S. Then the area of the quadrilateral PQRS isCorrectIncorrect - Question 6 of 20
##### 6. Question

The function y = f(x) is the solution of the differential equation in (−1, 1) satisfying f(0) = 0. Then is

CorrectIncorrect - Question 7 of 20
##### 7. Question

Let f : [0, 2] → R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let for x ∈ [0, 2]. If F′(x) = for all x ∈ (0, 2), then F(2) equals

CorrectIncorrect - Question 8 of 20
##### 8. Question

Coefficient of x

^{11}in the expansion of (1 + x^{2})^{4}(1 + x^{3})^{7}(1 + x^{4})^{12}isCorrectIncorrect - Question 9 of 20
##### 9. Question

For x (0, π ), the equation sin x + 2 sin 2x – sin 3x = 3 has

CorrectIncorrect - Question 10 of 20
##### 10. Question

CorrectIncorrect - Question 11 of 20
##### 11. Question

**SECTION – 2 : Comprehension Type (Only One Option Correct)****This section contains 3 paragraphs, each describing theory, experiments, data etc. Six questions relate to the three paragraphs with two questions on each paragraph. Each question has only one correct answer among the four given options (A),(B),(C) and (D).**________________________________________________________________________________________________

**Paragraph For Questions 51 and 52**Box 1 contains three cards bearing numbers 1, 2, 3; box 2 contains five cards bearing numbers 1, 2, 3, 4, 5; and box 3 contains seven cards bearing numbers 1, 2, 3, 4, 5, 6, 7. A card is drawn from each of the boxes. Let xi be the number on the card drawn from the ith box, i = 1, 2, 3.

______________________________________________________________________________________________

The probability that x

_{1}+ x_{2}+ x_{3}is odd, isCorrectIncorrect - Question 12 of 20
##### 12. Question

The probability that x

_{1}, x_{2}, x_{3}are in an arithmetic progression, isCorrectIncorrect - Question 13 of 20
##### 13. Question

**Paragraph For Questions 53 and 54**Let a, r, s, t be nonzero real numbers. Let P(at

^{2}, 2at), Q, R (ar^{2}, 2ar) and (as^{2}, 2as) be distinct points on the parabola y^{2}= 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0)____________________________________________________________________________________________

The value of r is

CorrectIncorrect - Question 14 of 20
##### 14. Question

If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

CorrectIncorrect - Question 15 of 20
##### 15. Question

**Paragraph For Questions 55 and 56**Given that for each a ∈ (0, 1)

exists. Let this limit be g(a). In addition, it is given that the function g(a) is differentiable on (0, 1).

_______________________________________________________________________________________________

CorrectIncorrect - Question 16 of 20
##### 16. Question

CorrectIncorrect - Question 17 of 20
##### 17. Question

**SECTION – 3 : Matching List Type (Only One Option Correct)**This section contains four questions, each having two matching lists. Choices for the correct combination of elements from List-I and List-II are given as options (A),(B),(C) and (D), out of which ONE is correct.

_______________________________________________________________________________________________

**List I List-II**

P. The number of polynomials f(x) with non-negative 1. 8

integer coefficients of degree ≤ 2, satisfying f(0) = 0

Q. The number of points in the interval 2. 2

at which f(x) = sin(x

^{2}) + cos(x^{2})attains its maximum value, is

CorrectIncorrect - Question 18 of 20
##### 18. Question

**List-I****List-II**P. Let y(x) = cos(3cos

^{−1}x), x ∈ [−1, 1], 1. 1equals

Q. Let A

_{1}, A_{2}, ……, A_{n}(n > 2) be the vertices of a 2. 2regular polygon of n sides with its its centre at

the origin. Let be the position vector of the

point A

_{k}, k = 1, 2, ….. , n. IfR. If the normal from the point P(h, 1) on the ellipse 3. 8

is perpendicular to the line x + y = 8,

then the value of h is

S. Number of positive solutions satisfying the equation 4. 9

CorrectIncorrect - Question 19 of 20
##### 19. Question

Let f

_{1}: R → R, f_{2}: [0, ∞) → R, f_{3}: R → R and f_{4}: R → [0, ∞) be defined by**List – I List-II**P. f

_{4}is 1. onto but not one-oneQ. f

_{3}is 2. neither continuous nor one-oneR. f

_{2}o f_{1}is 3. differentiable but not one-oneS. f

_{2}is 4. continuous and one-oneCorrectIncorrect - Question 20 of 20
##### 20. Question

**List-I List-II**

P. For each z

_{k}there exists a z_{j}such 1. Truethat z

_{k}. z_{j}= 1Q. There exists a k ∈ {1, 2,……,9} such 2. False

that z

_{1}. z = z_{k}has no solution z in theset of complex numbers.

CorrectIncorrect