Practice questions
88551 published questions with worked solutions.
- The value of _ x 0 _e ( (ex) (e^2x) (e^ 10 x) ) e^2 - e^ 2 x is equal to
- The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are 2,3,5,10,11,13,15,21, then...
- Let A,B and C be three 2 2 matrices with real entries such that B = (I+A)^ -1 and A+C = I. If BC = bmatrix 1 & -5 -1 & 2 bmatrix...
- The common difference of the A.P.: a_1,a_2, ,a_m is 13 more than the common difference of the A.P.: b_1,b_2, ,b_n. If b_ 31 =...
- If the distances of the point (1,2,a) from the line x-1 1 = y 2 = z-1 1 along the lines L_1: x-1 3 = y-2 4 = z-a b and L_2: x-1 1...
- For three unit vectors a , b , c satisfying | a - b |^2+| b - c |^2+| c - a |^2 = 9 and |2 a +k b +k c | = 3, the positive value...
- Let y=y(x) be the solution of the differential equation x dy dx - 2y = x^3(2-x^3) ^2 y, x 0. If y(2)=0, then (y(1)) is equal to
- In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms...
- For some (0, 2 ), let the eccentricity and the length of the latus rectum of the hyperbola x^2 - y^2 ^2 = 8 be e_1 and _1,...
- The value of _ r=1 ^ 20 ( ( _0^r x| x|dx ) ) is _____.
- Let PQR be a triangle such that PQ = -2 i - j +2 k and PR = a i +b j -4 k , a,b Z. Let S be the point on QR, which is equidistant...
- 10 kg of ice at -10°C is added to 100 kg of water to lower its temperature from 25°C. Consider no heat exchange to surroundings....
- Water drops fall from a tap on the floor, 5 m below, at regular intervals of time, the first drop strikes the floor when the...
- An atom ^8_3X is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9...
- The electric field of an electromagnetic wave travelling through a medium is given by E (x,t) = 25 (2.0 10^ 15 t - 10^7x) n then...
- For the two cells having same EMF E and internal resistance r, the current passing through the external resistor 6 is same when...
- Two wires A and B made of different materials of length 6.0 cm and 5.4 cm, respectively and area of cross sections 3.0 10^ -5 m^2...
- A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the horizontal. Friction coefficient between...
- Given below are two statements : Statement-I : A plane wave after passing through prism remains as plane wave but passing through...
- When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, 4^ th...