Mathematics questions
18011 published questions with worked solutions.
- Let denote a curve y=y(x) which is in the first quadrant and let the point (1,0) lie on it. Let the tangent to at a point P...
- Let L_1 and L_2 denote the lines r = i + (- i +2 j +2 k ), R and r = (2 i - j +2 k ), R respectively. If L_3 is a line which is...
- Let 1 be a cube root of unity. Then the minimum of the set |a+b +c ^2|^2:a,b,c distinct non-zero integers equals _____
- Let AP(a;d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d>0. If...
- Let S be the sample space of all 3 3 matrices with entries from the set 0,1 . Let the events E_1 and E_2 be given by E_1= A S:...
- Let the point B be the reflection of the point A(2,3) with respect to the line 8x-6y-23=0. Let _A and _B be circles of radii 2...
- If I= 2 _ - /4 ^ /4 dx (1+e^ x )(2- 2x) then 27I^2 equals _____
- Three lines are given by r = i , R r = ( i + j ), R and r = ( i + j + k ), R . Let the lines cut the plane x+y+z=1 at the points...
- Let P_1=I= bmatrix 1&0&0 0&1&0 0&0&1 bmatrix , P_2= bmatrix 1&0&0 0&0&1 0&1&0 bmatrix , P_3= bmatrix 0&1&0 1&0&0 0&0&1 bmatrix ,...
- For non-negative integers n, let f(n)= _ k=0 ^ n ( k+1 n+2 ) ( k+2 n+2 ) _ k=0 ^ n ^2 ( k+1 n+2 ) Assuming ^ -1 x takes values in...
- Let f: R R be a function. We say that f has PROPERTY 1 if _ h 0 f(h)-f(0) |h| exists and is finite, and PROPERTY 2 if _ h 0...
- Let f(x)= x x^2 , x>0. Let x_1<x_2<x_3< <x_n< be all the points of local maximum of f and y_1<y_2<y_3< <y_n< be all the points of...
- For a R , |a|>1, let _ n ( 1+ [3] 2 + + [3] n n^ 7/3 ( 1 (an+1)^2 + 1 (an+2)^2 + + 1 (an+n)^2 ) )=54. Then the possible value(s)...
- Let f: R R be given by f(x)=(x-1)(x-2)(x-5). Define F(x)= _0^xf(t) ,dt, x>0. Then which of the following options is/are correct?
- Three lines L_1: r = i , R , L_2: r = k + j , R and L_3: r = i + j +v k , v R are given. For which point(s) Q on L_2 can we find...
- Suppose bmatrix _ k=0 ^ n k & _ k=0 ^ n ^nC_kk^2 _ k=0 ^ n ^nC_kk & _ k=0 ^ n ^nC_k3^k bmatrix =0 holds for some positive integer...
- Let |X| denote the number of elements in a set X. Let S= 1,2,3,4,5,6 be a sample space, where each element is equally likely to...
- The value of ^ -1 ( 1 4 _ k=0 ^ 10 ( 7 12 + k 2 ) ( 7 12 + (k+1) 2 ) ) in the interval [- 4 , 3 4 ] equals _____
- The value of the integral _0^ /2 3 ( + )^5 ,d equals _____
- Let a =2 i + j - k and b = i +2 j + k be two vectors. Consider a vector c = a + b , , R . If the projection of c on the vector (...