- Equation of normal to the curve where it cuts x – axis; is

(A) x + y = 1

(B) x – y = 1

(C) x + y = 0

(D) None of these

- If y = a ln |x| + bx
^{2}+ x has its extreme values at x = -1 and x = 2 then P ≡ (a , b) is

(A) (2 , -1)

(B) (2 , -1/2)

(C) (-2 , 1/2)

(D) none of these

- f(x) = tan
^{-1}(sinx + cosx) is an increasing function in

(A) (–π/2, 0)

(B) (0, π/2)

(C) (-π/4, π/4)

(D) none of these.

- If the parabola y
^{2}= 4x meets a circle with centre at (6,5) orthogonally, then possible point (s) of intersection can be;

(A) (4, 4)

(B) (9, 4)

(C) (2, √8)

(D) (3, 2)

- If f (x) = x
^{a}log x and f(0) = 0, then the value of a for which Rolle’s theorem can be applied in [0, 1] is

(A) -2

(B) -1

(C) 0

(D) 1/2

- In [0, 1] Lagranges Mean Value theorem is NOT applicable to

(A) f(x) =

(B) f(x) =

(C) f(x) = x|x|

(D) f(x) = |x|

- For what value of ‘a’ does the curve f(x) = (a
^{2}-2a -2 ) + cosx is always strictly monotonic for all x ∈ R

(A) a ∈ R

(B) a > 0

(C) 1-√2 < a < 1 + √2

(D) None of these

- If the curves a x
^{2}+ b y^{2}= 1 and a_{1}x^{2}+ b_{1}y^{2}= 1 intersect orthogonally then

(A)1/a – 1/b = 1/a_{1} + 1/b_{1}

(B)1/a + 1/b = 1/a_{1} + 1/b_{1}

(C)1/a + 1/b = 1/a_{1} + 1/b_{1}

(D) none of these

- If the equation x
^{5}– 10a^{3}x^{2}+ b^{4}x + c^{5}= 0 has three equal roots, then

(A) 2b^{2} –10 a^{3}b^{2}+c^{5} = 0

(B) 6a^{5} + c^{5} = 0

(C) 2c^{5} –10 a^{3}b^{2}+ b^{4}c^{5} = 0

(D) b^{4} = 15 a^{5}

- The function f is a differentiable function and satisfies the functional equation f(x) + f(y) = f(x + y) – xy – 1for every pair x, y of real numbers. If f(1) = 1, then the number of integers n ≠ 1 for which f(n) = n is

(A) 0

(B) 1

(C) 2

(D) 3

**Answer:**

1. B 2. B 3. C

4. A 5. D 6. A

7. C 8. A 9. B

10. B