Mathematics questions
18011 published questions with worked solutions.
- The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged as in a...
- The largest value of n, for which 40^n divides 60!, is
- The sum of all values of , for which the shortest distance between the lines x+1 = y-2 -1 = z-4 - and x = y-1 2 = z-1 2 is 2 , is
- Let f( ) denote the area of the region in the first quadrant bounded by x=0, x=1, y^2=x and y = | x - 5|-|1- x|+ x^2. Then...
- If the domain of the function f(x) = ^ -1 ( 1 x^2-2x-2 ), is (- , ] [ , ] [ , ), then + + + is equal to
- Let X = x N : 1 x 19 and for some a,b R , Y = ax+b: x X . If the mean and variance of the elements of Y are 30 and 750,...
- Consider the following three statements for the function f: (0, ) R defined by f(x) = | _e x|-|x-1|: (I) f is differentiable for...
- Let y=y(x) be a differentiable function in the interval (0, ) such that y(1)=2. and _ t x ( t^2y(x)-x^2y(t) x-t ) = 3 for each...
- Let f be a function such that 3f(x)+2f ( m 19x )=5x, x 0, where m= _ i=1 ^ 9 (i)^2. Then f(5)-f(2) is equal to
- The smallest positive integral value of a, for which all the roots of x^4-ax^2+9=0 are real and distinct, is equal to
- Let a = 2 i -5 j +5 k and b = i - j +3 k . If c is a vector such that 2( a c )+3( b c )= 0 and ( a - b ) c =-97, then | c k |^2...
- Let (h,k) lie on the circle C: x^2+y^2=4 and the point (2h+1, 3k+2) lie on an ellipse with eccentricity e. Then the value of 5...
- Let z=(1+i)(1+2i)(1+3i) (1+ni), where i= -1 . If |z|^2=44200, then n is equal to -
- Let S be a set of 5 elements and P(S) denote the power set of S. Let E be an event of choosing an ordered pair (A, B) from the...
- The number of elements in the set x [0,180^ ]: (x+100^ ) = (x+50^ ) x (x-50^ ) is _____ .Not in JEE Main syllabus
- If g(x) = 3x^2 + 2x - 3, f(0) = -3 and 4g(f(x)) = 3x^2 - 32x + 72, then f(g(2)) is equal to:
- Let y = x be the equation of a chord of the circle C_1 (in the closed half-plane x 0) of diameter 10 passing through the origin....
- If (A-B) A + ^2 C ^2 A = 1, A, B, C (0, 2 ), then
- Let z be a complex number such that |z-6| = 5 and |z+2-6i| = 5. Then the value of z^3 + 3z^2 - 15z + 141 is equal to
- Let S = 1,2,3,4,5,6,7,8,9 . Let x be the number of 9-digit numbers formed using the digits of the set S such that only one digit...