Mathematics questions
18011 published questions with worked solutions.
- Let f be any function continuous on [a, b] and twice differentiable on (a, b). If for all x (a, b), f'(x) > 0 and f''(x) < 0,...
- The number of real roots of the equation e^ 4x +e^ 3x -4e^ 2x +e^x+1=0 is
- Let z be a complex number such that | z-i z+2i |=1 and |z|= 5 2 . Then the value of |z+3i| is :
- The value of ^3 ( 8 ) ( 3 8 )+ ^3 ( 8 ) ( 3 8 ) is
- If e_1 and e_2 are the eccentricities of the ellipse, x^2 18 + y^2 4 =1 and the hyperbola, x^2 9 - y^2 4 =1 respectively and...
- If f'(x)= ^ -1 ( x+ x), - 2 <x< 2 , and f(0) = 0, then f(1) is equal to
- Let the observations x_i (1 i 10) satisfy the equations, _ i=1 ^ 10 (x_i-5)=10 and _ i=1 ^ 10 (x_i-5)^2=40. If and are the mean...
- Negation of the statement : ' 5 is an integer or 5 is irrational' isNot in JEE syllabus
- If the number of five digit numbers with distinct digits and 2 at the 10^ th place is 336 k, then k is equal to
- If for all real triplets (a, b, c), f(x)=a+bx+cx^2; then _0^1 f(x) ,dx is equal to :
- Let C be the centroid of the triangle with vertices (3, −1), (1, 3) and (2, 4). Let P be the point of intersection of the lines x...
- The projection of the line segment joining the points (1, −1, 3) and (2, −4, 11) on the line joining the points (−1, 2, 3) and...
- If for x 0, y = y(x) is the solution of the differential equation, (x+1)dy=((x+1)^2+y-3) ,dx, y(2) = 0, then y(3) is equal to...
- The coefficient of x^4 in the expansion of (1+x+x^2)^ 10 is _____
- The number of distinct solutions of the equation, _ 1/2 | x| = 2 - _ 1/2 | x| in the interval [0, 2 ], is _____
- If the vectors, p =(a+1) i +a j +a k , q =a i +(a+1) j +a k and r =a i +a j +(a+1) k (a R) are coplanar and 3( p q )^2- | r q...
- Let e_1 and e_2 be the eccentricities of the ellipse, x^2 25 + y^2 b^2 =1 (b < 5) and the hyperbola, x^2 16 - y^2 b^2 =1...
- Let the latus rectum of the parabola y^2=4x be the common chord to the circles C_1 and C_2 each of them having radius 2 5 . Then,...
- If the value of the integral _0^ 1/2 x^2 (1-x^2)^ 3/2 dx is k 6 , then k is equal to -
- Let x_i (1 i 10) be ten observations of a random variable X. If _ i=1 ^ 10 (x_i-p)=3 and _ i=1 ^ 10 (x_i-p)^2=9 where 0 p R, then...