If `x^3+3x^2-9x+c` is of the form `(x-alpha)^2(x-beta)` , then `c` is equal to a.`27` b. `-27` c. `5` d. `-5`

If tanalpha is equal to the integral solution of the inequality 4x^2-16 x+15<0 and cosbeta is equal to the slope of the bisector of the first quadrant, then sin(alpha+beta)sin(alpha-beta) is equal to (a) 3/5 (b) 3/5 (c) 2/(sqrt(5)) (d) 4/5

If x+4y=14 is a normal to the curve y^2=alphax^3-beta at (2,3), then the value of alpha+beta is 9 (b) -5 (c) 7 (d) -7

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0. Then the roots of the equation (x-alpha)(x-beta)+c=0 are a , c b. b , c c. a , b d. a+c , b+c

If alpha, beta in C are distinct roots of the equation x^2-x+1=0 then alpha^(101)+beta^(107) is equal to

If I=intx^(27)(6x^(2)+5x+4)(x^(2)+x+1)^(6)dx=f(x)+C , then f(x) is equal to

If alpha" and "beta are the roots of the equation x^(2)+3x-4=0 , then (1)/(alpha)+(1)/(beta) is equal to

If alpha and beta are the zeros of the polynomials x^(2) -5x+6 then (1)/(alpha) + ( 1)/(beta) is equal to .........

If alpha,beta,gamma,delta are the roots of the equation x^4+4x^3-6x^2+7x-9=0, then he value of (1+alpha^2)(1+beta^2)(1+gamma^2)(1+sigma^2) is a. 9 b. 11 c. 13 d. 5

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

27 x^(2) e^(3x)