Let `x=1+1/(1+1/(1+1/(1+\ ddotoo)))` . Which of the following is correct? `x^2+x+1=0` (b) `x^2-x+1=0` (c) `x^2+x-1=0` (d) `x^2-x-1=0`

If 0 < x < 1 , which of the following is greatest ? x (b) x^2 (c) 1/x (d) 1/(x^2)

Let alpha and beta be the roots of the equation x^2+x+1=0 . The equation whose roots are alpha^29, beta^17 is (A) x^2-x+1=0 (B) x^2+x+1=0 (C) x^2-x-1=0 (D) x^2+x-1=0

Consider the function g/defined by g(x) = {x^2 sin(pi/x) +(x-1)^2sin(pi/(x-1)),x!=0,1; 0, if x=0,1} then which of the following statement(s) is/are correct? (A) g (x) is differentiable AA in R. (B) g(x) is discontinuous at x=0 but continuous at x = 1 . C) g(x) is discontinuous at both x =0 and x = 1 D) Rolle's theorem is applicable for g(x) in [0, 1].

The equation of common tangent at the point of contact of two parabola y^(2)=x and 2y=2x^(2)-5x+1 is x+y+1=0 (B) x+2y+1=0( C) x-2y-1=0( D )-x+2y-1=0

Which of the following identities does not hold? (A) sin^-1 x = cot^-1[sqrt((1-x^2))/x],0ltxle1 (B) sin^-1 x = cot^-1[sqrt((1-x^2))/x],-1,=xlt0 (C) sin^-1 x = cos^-1 sqrt(1-x^2),0ltxle1 (D) sin^-1 x= 1-sin^-1 (-x), -1lexle1

If A is a square matrix of any order then |A-x|=0 is called the chracteristic equation of matrix A and every square matrix satisfies its chatacteristic equation. For example if A=[(1,2),(1,5)], Then [(A-xI)], = [(1,2),(1,5)]-[(x,0),(0,x)]=[(1-x,2),(1-0,5-x)]=[(1-x,2),(1,5-x)] Characteristic equation of matrix A is |(1-x,2),(1,5-x)|=0 or (1-x)(5-x)(0-2)=0 or x^2-6x+3=0 Matrix A will satisfy this equation ie. A^2-6A+3I=0 A^-1 can be determined by multiplying both sides of this equation let A=[(1,0,0),(0,1,1),(1,-2,4)] On the basis for above information answer the following questions:Sum of elements of A^-1 is (A) 2 (B) -2 (C) 6 (D) none of these

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

Which of the following is and determinate form (lim)_(xvec1)(x^3-1)/(x-1) b. (lim)_(xvec0)(1+x)^(1//x) c. (lim)_(xvec1)(1/(x^2-1)-1/(x-1)) d. (lim)_(xvec0)(|x|)^(s in R)

Let f(x)={a x^2+1,\ \ \ \ \ x >1 , \ \ \ \ x+1//2,\ \ \ \ \ xlt=1 Then, f(x) is derivable at x=1 , if a=2 (b) b=1 (c) a=0 (d) a=1//2

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1