Mathematics questions
18011 published questions with worked solutions.
- If _ n ((n + 1)^ k−1 /n^ k+1 )[(nk + 1) + (nk + 2) + ... + (nk + n)] = 33 _ n (1/n^ k+1 )[1^k + 2^k + 3^k + ... + n^k], then the...
- Let the equation of two diameters of a circle x^ 2 + y^ 2 - 2x + 2fy + 1 = 0 be 2px − y = 1 and 2x + py = 4p. Then the slope m...
- The sum of diameters of the circles that touch (i) the parabola 75x^ 2 = 64(5y - 3) at the point (8/5, 6/5) and (ii) the y-axis,...
- The line of shortest distance between the lines (x − 2)/0 = (y − 1)/1 = z/1 and (x − 3)/2 = (y − 5)/2 = (z − 1)/1 makes an angle...
- Let A = x ℝ : |x + 1| < 2 and B = x ℝ : |x − 1| 2 . Then which one of the following statements is NOT true ?
- Let a, b ℝ be such that the equation ax^ 2 - 2bx + 15 = 0 has a repeated root . If and are the roots of the equation x^ 2 - 2bx +...
- Let z_ 1 and z_ 2 be two complex numbers such that z̄_ 1 = i z̄_ 2 and (z_ 1 /z̄_ 2 ) = . Then-
- _ x 2 ^2x ((2 ^2x + 3 x + 4)^ 1/2 - ( ^2x + 6 x + 2)^ 1/2 ) is equal to-
- The area of the region enclosed between the parabolas y^ 2 = 2x - 1 and y^ 2 = 4x - 3 is-
- The sum 1 + 2·3 + 3 3^ 2 + …. + 10 3^ 9 is equal to-
- Let P be the plane passing through the intersection of the planes r ( i + 3 j - k ) = 5 and r (2 i - j + k ) = 3, and the point...
- A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is
- Water is being filled at the rate of 1 cm^ 3 / in a right circular conical vessel (vertex downwards) of height 35 cm and diameter...
- If b_ n = _ 0 ^ /2 ^ 2 nx/ x dx, n ℕ, then-
- If y = y(x) is the solution of the difference equation 2x^ 2 dy/dx − 2xy + 3y^ 2 = 0 such that y( ) = /3, then y(1) is equal to
- If the angle made by the tangent at the point (x_ 0 , y_ 0 ) on the curve x = 12(t + sin t cos t), y = 12(1 + sin t)^ 2 , 0 < t <...
- The value of 2 sin(12°) − sin(72°) is-
- A biased die is marked with numbers 2, 4, 8, 16, 32, 32 on its faces and the probability of getting a face with mark n is 1/n. If...
- If the line y = 4 + kx, k > 0, is the tangent to the parabola y = x - x^ 2 at the point P and V is the vertex of the parabola,...
- The value of ^ -1 ( 15 4 - 1 4 ) is equal to-