If `f^(prime)(k)=l ,t h e nl=` 0 (b) `4/5` (c) `pi/2` (d) `(16)/5`

Let h(x) be differentiable for all x and let f(x)=(k x+e^x)h(x) , where k is some constant. If h(0)=5,h^(prime)(0)=-2,a n df^(prime)(0)=18 , then the value of k is (a)5 (b) 4 (c) 3 (d) 2.2.

Comprehension (for Q.No.1 to 3) Let f(x)=sin^(-1)(1-x^(2))/(1+x^(2))+tan^(-1)(2x)/(1-x^(2)). Then If f'(-2)=k, then k=0( b) (4)/(5)(c)(pi)/(2)(d)(16)/(5)

A function f: R->R satisfies sinxcosy(f(2x+2y)-f(2x-2y)=cosxsiny(f(2x+2y)+f(2x-2y))dot If f^(prime)(0)=1/2,t h e n (a)f^(prime)(x)=f(x)=0 (b)4f^(x)+f(x)=0 (c)f^(x)+f(x)=0 (d)4f^(x)-f(x)=0

f'(l+3)=0(b)(2)/(5)(c)-(2)/(5)(d)-(4)/(5)

If f(1)=3,f^(prime)(1)=2,f^(1)=4,t h e n(f^(-1))^()(3)= a. 1 b. -1/2 c. -2 d. none of these

If F(t)=int(x+y)dt then the value of F(pi/2)-F(0) is 1 (b) -1 (c) e^(pi//2) (d) 0

If A B C and D E F are two triangles such that (A B)/(D E)=(B C)/(E F)=(C A)/(F D)=2/5 , then A r e a( A B C): A r e a( D E F)= 2:5 (b) 4: 25 (c) 4: 15 (d) 8: 125

Let f:[0,2]->R be a function which is continuous on [0,2] and is differentiable on (0,2) with f(0)=1 L e t :F(x)=int_0^(x^2)f(sqrt(t))dtforx in [0,2]dotIfF^(prime)(x)=f^(prime)(x) . for all x in (0,2), then F(2) equals (a)e^2-1 (b) e^4-1 (c)e-1 (d) e^4

If two events A and B are such that P(A^c)=0. 3. P(B^c)=0. 4 a n d P(AnnB^c)=0. 5 , t h e n P(B/AuuB^c)= (a) 0. 9 (b). 0. 5 (c). 0. 6 (d). 0. 25

Suppose that f is differentiable for all x and that f^(prime)(x)lt=2fora l lxdot If f(1)=2a n df(4)=8,t h e nf(2) has the value equal to 3 (b) 4 (c) 6 (d) 8