If `sinx+cos e cx=2,` then `sin^n x+cos e c^n x` is equal to `2` (b) `2^n` (c) `2^(n-1)` (d) `2^(n-2)`

("lim")_(xvec0)(sin(x^2))/(1n(cos(2x^2-x)))is equal to 2 (b) -2 (c) 1 (d) -1

If the equation (4cos^(2)x -2 sinx -3 ) sin x, then x is equal to (n in Z)

If int_1^2e^(x^2)dx=a ,t h e nint_e^(e^4)sqrt(1n x)dx is equal to (a) 2e^4-2e-a (b) 2e^4-e-a (c) 2e^4-e-2a (d) e^4-e-a

If lim_(x->0)(x^n-sinx^n)/(x-sin^n x) is non-zero finite, then n must be equal to 4 (b) 1 (c) 2 (d) 3

If 2sec^2A-sec^4A-2cos e c^2A+cos e c^4A=(15)/4,t h e n tan A is equal 1//sqrt(2) (b) 1/2 (c) 1/2sqrt(2) (d) -1/(sqrt(2))

Matrix A such that A^2=2A-I ,w h e r eI is the identity matrix, the for ngeq2. A^n is equal to 2^(n-1)A-(n-1)l b. 2^(n-1)A-I c. n A-(n-1)l d. n A-I

If tanx=ntany ,n in R^+, then the maximum value of sec^2(x-y) is equal to (a) ((n+1)^2)/(2n) (b) ((n+1)^2)/n (c) ((n+1)^2)/2 (d) ((n+1)^2)/(4n)

Let int cos^(3)xdx = m sin x +(sin^(3)x)/n+c , then n+2m is equal to

int_0^x[sint]dt ,w h e r ex in (2npi,(2n+1)pi),n in N ,a n d[dot] denotes the greatest integer function is equal to -npi (b) -(n+1)pi 2npi (d) -(2n+1)pi

Two players P_1a n dP_2 play a series of 2n games. Each game can result in either a win or a loss for P_1dot the total number of ways in which P_1 can win the series of these games is equal to a. 1/2(2^(2n)-^ "^(2n)C_n) b. 1/2(2^(2n)-2xx^"^(2n)C_n) c. 1/2(2^n-^"^(2n)C_n) d. 1/2(2^n-2xx^"^(2n)C_n)