Mathematics questions
18011 published questions with worked solutions.
- Let A = -2,-1,0,1,2,3,4 . Let R be a relation on A defined by xRy if and only if 2x+y 2. Let be the number of elements in R. Let...
- Let y=y(x) be the solution of the differential equation x^4 dy + (4x^3y + 2 x)dx = 0, x>0, y ( 2 )=0. Then ^4 y ( 3 ) is equal to...
- Let f(x) = cases ax^2+2ax+3 4x^2+4x-3 , & x - 3 2 , 1 2 b, & x=- 3 2 , 1 2 cases be continuous at x=- 3 2 . If fof(x)= 7 5 , then...
- The value of the integral _ /24 ^ 5 /24 dx 1+ [3] 2x is :
- Among the statements : I : If vmatrix 1 & & & 1 & & & 1 vmatrix = vmatrix 0 & & & 0 & & & 0 vmatrix , then ^2 + ^2 + ^2 = 3 2 ,...
- The value of ^ 100 C_ 50 51 + ^ 100 C_ 51 52 + + ^ 100 C_ 100 101 is :
- Let the mean and variance of 8 numbers -10,-7,-1,x,y,9,2,16 be 7 2 and 293 4 , respectively. Then the mean of 4 numbers x, y,...
- The sum of all possible values of n N, so that the coefficients of x, x^2 and x^3 in the expansion of (1+x^2)^2(1+x)^n, are in...
- The vertices B and C of a triangle ABC lie on the line x 1 = 1-y -2 = z-2 3 . The coordinates of A and B are (1,6,3) and (4,9, )...
- Number of solutions of 3 2 + 8 + 3 3 = 0, [-3 , 2 ] is:Not in JEE Main syllabus
- Let S = z: 3 |2z-3(1+i)| 7 be a set of complex numbers. Then Min _ z S |z+ 1 2 (5+3i) | is equal to :
- Let and respectively be the maximum and the minimum values of the function f( ) = 4 ( ^4 ( 7 2 - )+ ^4(11 + ) )-2 ( ^6 ( 3 2 - )+...
- Let the direction cosines of two lines satisfy the equations: 4 +m-n=0 and 2mn+10n +3 m=0. Then the cosine of the acute angle...
- Let |A|=6, where A is a 3 3 matrix. If | adj (3 adj (A^2. adj (2A)) ) | = 2^m 3^n, m,n N, then m+n is equal to ____.
- Let the area of the region bounded by the curve y = x, x , lines x=0, x= 3 2 , and the x-axis be A. Then, A+A^2 is equal to _____
- Let f be a twice differentiable non-negative function such that (f(x))^2 = 25 + _0^x ((f(t))^2+(f'(t))^2 )dt. Then the mean of f(...
- The number of 4-letter words, with or without meaning, which can be formed using the letters PQRPQRSTUVP, is _____。
- If f(x) = cases a|x| + x^2 - 2 |x|( |x|) x & , x 0 b & , x = 0 cases is continuous at x = 0, then a + b is equal to :
- Let 2 < < and = - 1 2 2 . Then the value of ( 150 2 )( 8 + 8 ) + ( 150 2 )( 8 - 8 ) is equal to :
- Let a = i - 2 j + 3 k , b = 2 i + j - k , c = i + j + k and v = a b . If v c = 11 and the length of the projection of b on c is...