Mathematics questions
18011 published questions with worked solutions.
- The number of real roots of the equation ^ -1 x(x+1) + ^ -1 x^2+x+1 = 4 isNot in JEE Main syllabus
- Let y = y(x) be the solution of the differential equation e^x 1-y^2 dx+ ( y x )dy=0, y(1) = –1. Then the value of (y(3))^2 is...
- Let 'a' be a real number such that the function f(x)=ax^2+6x-15, x R is increasing in (- , 3 4 ) and decreasing in ( 3 4 , )....
- Let a function f : R R be defined as f(x)= cases x-e^x, & x 0 +[-x], & 0<x<1 2x-b, & x 1 cases where [x] is the greatest integer...
- Let the tangent to the parabola S:y^2=2x at the point P(2, 2) meet the x-axis at Q and normal at it meet the parabola S at the...
- The probability of selecting integers a [–5,30] such that x^2+2(a+4)x-5a+64>0, for all x R is
- Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The probability that the letter M...
- Let a , b , c be three mutually perpendicular vectors of the same magnitude and equally inclined at an angle , with the vector a...
- Let A= pmatrix 1&-1&0 0&1&-1 0&0&1 pmatrix and B = 7A^ 20 -20A^7+2I, Where I is an identity matrix of order 3× 3. If B = [b_ ij...
- Let P be a plane passing through the points (1, 0, 1), (1, –2, 1) and (0, 1, –2). let a vector a = i + j + k be such that a is...
- The number of rational terms in the binomial expansion of (4^ 1/4 +5^ 1/6 )^ 120 is _____.
- If the shortest distance between the lines r_1 = i +2 j +2 k + ( i -2 j +2 k ), R, >0 and r_2 =-4 i - k + (3 i -2 j -2 k ), R is...
- Let T be the tangent to the ellipse E:x^2+4y^2=5 at the point P(1, 1). If the area of the region bounded by the tangent T,...
- Let a, b, c, d be in arithmetic progression with common difference . If vmatrix x+a-c&x+b&x+a -1&x+c&x+b -b+d&x+d&x+c vmatrix =2,...
- There are 15 players in a cricket team, out of which 6 are bowlers, 7 are batsman and 2 are wicket keepers. The number of ways, a...
- Let y = mx + c, m > 0 be the focal chord of y^2 = –64x, which is tangent to (x+10)^2+y^2=4. Then, the value of 4 2(m+c) is equal...
- If the value of _ x 0 (2- x 2x )^ ( x+2 x^2 ) is equal to e^a, then a is equal to _____.
- Let L be the line of intersection of planes r ( i - j +2 k )=2 and r (2 i + j - k )=2. If P( , , ) is the foot of perpendicular...
- Let S_n denote the sum of first n-terms of an arithmetic progression. If S_ 10 = 530, S_5 = 140, then S_ 20 -S_6 is equal to :
- let f : R R be defined as f(x)= cases - 4 3 x^3+2x^2+3x, & x>0 3xe^x, & x 0 cases Then f is increasing function in the interval