Practice questions
88551 published questions with worked solutions.
- Let a_1, a_2, a_3, be a G.P. of increasing positive terms such that a_2 a_3 a_4 = 64 and a_1 + a_3 + a_5 = 813 7 . Then a_3 + a_5...
- Let c and d be vectors such that | c + d | = 29 and c (2 i + 3 j + 4 k ) = (2 i + 3 j + 4 k ) d . If _1, _2 ( _1 > _2) are the...
- Let y = y(x) be the solution curve of the differential equation (1 + x^2)dy + (y - ^ -1 x)dx = 0, y(0) = 1. Then the value of...
- The number of strictly increasing functions f from the set 1, 2, 3, 4, 5, 6 to the set 1, 2, 3, , 9 such that f(i) i for 1 i 6,...
- Let f : R (0, ) be a twice differentiable function such that f(3) = 18, f'(3) = 0 and f''(3) = 4. Then _ x 1 ( _e ( f(2+x) f(3)...
- Let the foci of hyperbola coincide with the foci of the ellipse x^2 36 + y^2 16 = 1. If the eccentricity of the hyperbola is 5,...
- The value of _ - /6 ^ /6 ( + 4x^ 11 1 - (|x| + /6) )dx is equal to
- If the coefficient of x in the expansion of (ax^2 + bx + c)(1 - 2x)^ 26 is -56 and the coefficients of x^2 and x^3 are both zero,...
- If x^2 + x + 1 = 0, then the value of (x + 1 x )^4 + (x^2 + 1 x^2 )^4 + (x^3 + 1 x^3 )^4 + + (x^ 25 + 1 x^ 25 )^4 is :
- The value of 10° - 3 10° is equal to:
- The sum of all the roots of the equation (x-1)^2 - 5|x-1| + 6 = 0, is:
- Let a_1 = 1 and for n 1, a_ n+1 = 1 2 a_n + n^2 - 2n - 1 n^2(n+1)^2 . Then | _ n=1 ^ (a_n - 2 n^2 ) | is equal to
- For some , R, let A = bmatrix & 2 1 & 2 bmatrix and B = bmatrix 1 & 1 1 & bmatrix be such that A^2 - 4A + 2I = B^2 - 3B + I = O....
- 6 _0^ |( 3x + 2x + x)| ,dx is equal to _____
- A gas based geyser heats water flowing at the rate of 5.0 litres per minute from 27°C to 87°C. The rate of consumption of the gas...
- A conducting circular loop of area 1.0 m^2 is placed perpendicular to a magnetic field which varies as B = (100t) Tesla. If the...
- In an experiment the values of two spring constants were measured as k_1 = (10 0.2) N/m and k_2 = (20 0.3) N/m. If these springs...
- Consider a modified Bernoulli equation. (P + A Bt^2 ) + g(h + Bt) + 1 2 V^2 = constant If t has the dimension of time then the...
- The electric field a plane electromagnetic wave is given by : E_y = 69 [0.6 10^3 x - 1.8 10^ 11 t] V/m. The expression for...
- In a double slit experiment the distance between the slits is 0.1 cm and the screen is placed at 50 cm from the slits plane. When...