Mathematics questions
18011 published questions with worked solutions.
- Let in a series of 2n observations, half of them are equal to a and remaining half are equal to –a. Also by adding a constant b...
- Let a and b be two non-zero vector perpendicular to each other and | a |=| b |. If | a b |=| a |, then the angle between the...
- Let in a Binomial distribution, consisting of 5 independent trials, probabilities of exactly 1 and 2 successes be 0.4096 and...
- Let a tangent be drawn to the ellipse x^2 27 +y^2=1 at (3 3 , ) where (0, 2 ). Then the value of such that the sum of intercepts...
- Define a relation R over a class of n × n real matrices A and B as "ARB iff there exists a non-singular matrix P such that PAP^...
- A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the...Not in JEE syllabus
- If 15 ^4 +10 ^4 =6, for some R, then the value of 27 ^6 +8cosec^6 is equal to :
- The area bounded by the curve 4y^2=x^2(4-x)(x-2) is equal to :
- Let f : R R be a function defined as f(x)= cases (a+1)x+ 2x 2x , & x<0 , & x=0 x+bx^3 - x bx^ 5/2 , & x>0 cases . If f is...
- Let I be an identity matrix of order 2 × 2 and P = bmatrix 2&-1 5&-3 bmatrix . Then the value of n N for which P^n=51-8P is equal...
- If _ r=1 ^ 10 r!(r^3+6r^2+2r+5)= (11!), then the value of is equal to _________.
- Let P(x) be a real polynomial of degree 3 which vanishes at x = –3. Let P(x) have local minima at x = 1, local maxima at x = –1...
- Let the mirror image of the point (1, 3, a) with respect to the plane r (2 i - j + k )-b=0 be (–3, 5, 2). Then the value of |a +...
- Let f : R R satisfy the equation f(x + y) = f(x). f(y) for all x, y R and f(x) 0 for any x R. If the function f is differentiable...
- Let ^nC_r denote the binomial coefficient of x^r in the expansion of (1+x)^n. If _ k=0 ^ 10 (2^2+3k) ^nC_k= .3^ 10 + .2^ 10 , ,...
- Let P be a plane containing the line x-1 3 = y+6 4 = z+5 2 and parallel to the line x-3 4 = y-2 -3 = z+5 7 . If the point (1, –1,...
- Let y = y(x) be the solution of the differential equation xdy – ydx = (x^2-y^2) dx, x 1, with y(1) = 0. If the area bounded by...
- The differential equation satisfied by the system of parabolas y^2=4a(x+a) is :
- Let (1+x+2x^2)^ 20 =a_0+a_1x+a_2x^2+ +a_ 40 x^ 40 . Then a_1+a_3+a_5+ +a_ 37 is equal to :
- The solutions of the equation vmatrix 1+ ^2x& ^2x& ^2x ^2x&1+ ^2x& ^2x 4 2x&4 2x&1+4 2x vmatrix =0, (0<x< ) are :Not in JEE Main syllabus