Mathematics questions
18011 published questions with worked solutions.
- Let A = a_ ij be a 3 × 3 matrix, where a_ ij = cases (-1)^ j-i , & i<j 2, & i=j (-1)^ i+j , & i>j cases then det(3Adj(2A^ -1 ))...
- The number of solutions of the equation _ (x+1) (2x^2+7x+5)+ _ (2x+5) (x+1)^2-4=0, x > 0, is
- For p > 0, a vector v_2 =2 i +(p+1) j is obtained by rotating the vector v_1 = 3p i + j by an angle about origin in counter...
- Consider a triangle having vertices A(–2, 3), B(1, 9) and C(3, 8). If a line L passing through the circum-centre of triangle ABC,...
- If the point on the curve y^2=6x, nearest to the point (3, 3 2 ) is ( , ), then 2( + ) is equal to _____.
- Let a function g : [0, 4] R be defined as g(x)= cases _ 0 t x t^3-6t^2+9t-3 , & 0 x 3 4-x, & 3<x 4 cases then the number of...
- For k N, let 1 ( +1)( +2) ( +20) = _ k=0 ^ 20 A_k +k , where > 0. Then the value of 100 ( A_ 14 +A_ 15 A_ 13 )^2 is equal to...
- Let a_n _ n=1 ^ be a sequence such that a_1 = 1, a_2 = 1 and a_ n+2 =2a_ n+1 +a_n for all n 1. Then the value of 47 _ n=1 ^ a_n...
- If _ x 0 xe^x- _e(1+x)+ x^2e^ -x x ^2x =10, , , R then the value of + + is _____.
- The Boolean expression (P Q) (q p) is equivalent to :Not in JEE syllabus
- Let other two numbers be a, (21 – a). The mean of 6 distinct observations is 6.5 and their variance is 10.25. If 4 of the 6...
- The value of the integral _ -1 ^1 _e( 1-x + 1+x )dx is equal to :
- If and are the distinct roots of the equation x^2+(3)^ 1/4 x+3^ 1/2 =0, then the value of ^ 96 ( ^ 12 -1)+ ^ 96 ( ^ 12 -1) is...
- Let A= bmatrix 2&3 &0 bmatrix , a R be written as P + Q where P is symmetric matrix and Q is skew symmetric matrix. If det(Q) =...
- If z and are two complex numbers such that |z | = 1 and arg(z) – arg( ) = 3 2 , then ( 1-2 z 1+3 z ) is : (Here arg(z) denotes...
- If in triangle ABC, AB = 5 units, B= ^ -1 ( 3 5 ) and radius of circumcircle of is 5 units, then the area (in sq. units) of isNot in JEE syllabus
- Let a =2 i + j -2 k and b = i + j . If c is a vector such that a c =| c |, | c - a |=2 2 and the angle between ( a b ) and c is 6...
- Let [x] denote the greatest integer x, where x R. If the domain of the real valued function f(x)= |[x]|-2 |[x]|-3 is (- ,a) [b,c)...
- Let y = y(x) be the solution of the differential equation x ( y x )dy= (y ( y x )-x )dx, -1 x 1, y ( 1 2 )= 6 . Then the area...
- Let A=[a_ ij ] be a 3×3 matrix, where a_ ij = cases 1, & if i=j -x, & if |i-j|=1 2x+1, & otherwise cases . Let a function f : R R...