Mathematics questions
18011 published questions with worked solutions.
- n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct numbers can be...
- A box 'A' contains 2 white, 3 red and 2 black balls. Another box 'B' contains 4 white, 2 red and 3 black balls. If two balls are...
- Let f : A → B be a function defined as f(x) = x - 1 x - 2 , where A = R – 2 and B = R – 1 . Then f is -
- The coefficient of x^ 10 in the expansion of (1 + x)^2(1 + x^2)^3(1 + x^3)^4 is equal to -
- If the system of linear equations x + ay + z = 3 x + 2y + 2z = 6 x + 5y + 3z = b has no solution, then
- If f(x) is a quadratic expression such that f(1) + f(2) = 0, and –1 is a root of f(x) = 0, then the other root of f(x) = 0 is -
- The number of four letter words that can be formed using the letters of the word BARRACK is -
- The number of solutions of 3x = 2x, in the interval ( 2 , ) is -Not in JEE Main syllabus
- The curve satisfying the differential equation, (x^2 - y^2) ,dx + 2xy ,dy = 0 and passing through the point (1, 1) is -
- Consider the following two statements. Statement p : The value of sin 120° can be divided by taking θ = 240° in the equation 2 2...
- 2x + 5 7 - 6x - x^2 ,dx = A 7 - 6x - x^2 + B ^ -1 ( x + 3 4 ) + C (where C is a constant of integration), then the ordered pair...
- A plane bisects the line segment joining the points (1, 2, 3) and (–3, 4, 5) at right angles. Then this plane also passes through...
- If |z - 3 + 2i| 4 then the difference between the greatest value and the least value of |z| is -
- If the position vectors of the vertices A, B and C of a are respectively 4 i + 7 j + 8 k , 2 i + 3 j + 4 k and 2 i + 5 j + 7 k ,...
- If f(x) = ^ -1 ( 2 3^x 1 + 9^x ), then f' (- 1 2 ) equals
- Let A_n = ( 3 4 ) - ( 3 4 )^2 + ( 3 4 )^3 - + (-1)^ n-1 ( 3 4 )^n and B_n = 1 - A_n. Then, the least odd natural number p, so...
- A normal to the hyperbola, 4x^2 - 9y^2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram...
- Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If _ x 0 ( f(x) x^2 + 1 ) = 3 then f(–1) is equal...
- If the mean of the data : 7, 8, 9, 7, 8, 7, λ, 8 is 8, then the variance of this data is -
- An angle between the lines whose direction cosines are given by the equations, + 3m + 5n = 0 and 5 m - 2mn + 6n = 0, is -