In a ` A B C ,ifA B=x , B C=x+1,/_C=pi/3` , then the least integer value of `x` is 6 (b) 7 (c) 8 (d) none of these

If cot^(-1)n/pi>pi/6,n in N , then the maximum value of n is 6 (b) 7 (c) 5 (d) none of these

The minimum value of 2^(x^2-3)^(3+27) is a) 2^(27) (b) 2 (c) 1 (d) none of these

The period of the function f(x)=(6x+7)+cospix-6x , where [dot] denotes the greatest integer function is: 3 (b) 2 pi (c) 2 (d) none of these

The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (where [.] represents the greatest integer function). -1 (b) 1 (c) 0 (d) none of these

In a A B C ,/_B=90^0 and b+a=4. The area of the triangle is maximum when /_C is (a) pi/4 (b) pi/6 (c) pi/3 (d) none of these

("lim")_(xvec0)(x^asin^b x)/(sin(x^c)) , where a , b , c in R ~{0},exists and has non-zero value. Then, (a) a+c (b) 1 (c) -1 (d) none of these

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

The right hand derivative of f(x)=[x]t a npix at x=7 is (where [.] denotes the greatest integer function) a. 0 b. 7pi c. -7pi d. none of these

The right hand derivative of f(x)=[x]t a npix a tx=7 is (where [.] denotes the greatest integer function) 0 b. 7pi c. -7pi d. none of these

The range of sin^(-1)[x^2+1/2]+cos^(-1)[x^2-1/2] , where [.] denotes the greatest integer function, is {pi/2,pi} (b) {pi} (c) {pi/2} (d) none of these