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

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

For every pair of continuous functions f, g:[0, 1] → R such that max {f(x) : x ∈ [0, 1]} = max {g(x) : x ∈ [0, 1}, the correct statement(s) is (are)

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

Let M be a 2 × 2 symmetric matrix with integer entries. Then M is invertible if

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

Let be three vectors each of magnitude √2 and the angle between each pair of them is π/3. If is a nonzero vector perpendicular to is a nonzero vector perpendicular to and then

CorrectIncorrect - Question 5 of 20
##### 5. Question

From a point P(λ, λ, λ), perpendiculars PQ and PR are drawn respectively on the lines y = x = z = 1 and y = −x, z = −1. If P is such that ∠QPR is a right angle, then the possible value(s) of λ is (are)

CorrectIncorrect - Question 6 of 20
##### 6. Question

Let M and N be two 3 × 3 matrices such that MN = NM. Further, if M ≠ N

^{2}and M^{2}= N^{4}, thenCorrectIncorrect - Question 7 of 20
##### 7. Question

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

CorrectIncorrect - Question 9 of 20
##### 9. Question

A circle S passes through the point (0, 1) and is orthogonal to the circles (x – 1)

^{2}+ y^{2}= 16 and x^{2}+ y^{2}= 1. ThenCorrectIncorrect - Question 10 of 20
##### 10. Question

Let a ∈ R and let f : R → R be given by f(x) = x

^{5}– 5x + a. ThenCorrectIncorrect - Question 11 of 20
##### 11. Question

**SECTION – 2 : (One Integer Value Correct Type)****This section contains 10 questions. Each question, when worked out will result in one integer from 0 to 9 (both inclusive).**_________________________________________________________________________________________________

The slope of the tangent to the curve (y – x

^{5})^{2}= x(1 + x^{2})^{2}at the point (1, 3) isCorrectIncorrect - Question 12 of 20
##### 12. Question

Let f : [0, 4π] → [0, π] be defined by f(x) = cos

^{−1}(cos x). The number of points x ∈ [0, 4π] satisfying the equationCorrectIncorrect - Question 13 of 20
##### 13. Question

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

Let f : R → R and g : R → R be respectively given by f(x) = |x| + 1 and g(x) = x

^{2}+ 1. Define h : R → R by The number of points at which h(x) is not differentiable isCorrectIncorrect - Question 15 of 20
##### 15. Question

For a point P in the plane, let d

_{1}(P) and d_{2}(P) be the distance of the point P from the lines x – y = 0 and x + y = 0 respectively. The area of the region R consisting of all points P lying in the first quadrant of the plane and satisfying 2 ≤ d_{1}(P) + d_{2}(P) ≤ 4, isCorrectIncorrect - Question 16 of 20
##### 16. Question

Let n

_{1}< n_{2}< n_{3}< n_{4}< n_{5}be positivie integers such that n_{1}+ n_{2}+ n_{3}+ n_{4}+ n_{5}= 20. Then the number of such distinct arrangements (n_{1}, n_{2}, n_{3}, n_{4}, n_{5}) isCorrectIncorrect - Question 17 of 20
##### 17. Question

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

Let be three non-coplanar unit vectors such that the angle between every pair of them is π/3. If where p, q and r are scalars, then the value of

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

Let a, b, c be positive integers such that b/a is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of is

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

Let n ≤ 2 be an integer. Take n distinct points on a circle and join each pair of points by a line segment. Color the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of n is

CorrectIncorrect