Practice questions
88551 published questions with worked solutions.
- Let ^nC_ r-1 = 28, ^nC_r = 56 and ^nC_ r+1 = 70. Let A(4cost, 4sint), B(2sint, –2cost) and C(3r – n, r^2 – n – 1) be the vertices...
- Let O be the origin, the point A be z_1 = 3 + 2 2 i, the point B(z_2) be such that 3 |z_2| = |z_1| and arg (z_2) = (z_1) + 6 ....
- Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate...
- Let M denote the set of all real matrices of order 3 × 3 and let S = –3, –2, –1, 1, 2 . Let S_1 = A = [a_ ij ] M : A = A^T and a_...
- If = 1 + _ r=1 ^ 6 (-3)^ r-1 ^ 12 C_ 2r-1 , then the distance of the point (12, 3 ) from the line x - 3 y + 1 = 0 is
- Let a = i + j + k , b = 2 i +2 j + k and d = a b . If c is a vector such that a . c = | c |, | c -2 a |^2 = 8 and the angle...
- Let f(x) = cases 5, & x > 2 1+x+[x], x+2[x] , & 0 x 2 3x, & x < 0 cases where [.] denotes greatest integer function. If and are...
- Let E_1 : x^2 9 + y^2 4 = 1 be an ellipse. Ellipses E_i's are constructed such that their centres and eccentricities are same as...
- In the experiment for measurement of viscosity ' ' of given liquid with a ball having radius R, consider following statements. A....
- Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the...
- Three infinitely long wires with linear charge density are placed along the x-axis, y-axis and z-axis respectively. Which of the...
- A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines – engine E_1 works between...
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave...
- Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In a central...
- Choose the correct nuclear process from the below options [p: proton, n: neutron, e^-: electron, e^+: positron, : neutrino, :...
- A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance...
- Due to presence of an em-wave whose electric component is given by E = 100 sin( t–kx) NC^ -1 , a cylinder of length 200 cm holds...
- A proton of mass 'm_p' has same energy as that of a photon of wavelength ' '. If the proton is moving at non-relativistic speed,...
- A thin prism P_1 with angle 4° made of glass having refractive index 1.54, is combined with another thin prism P_2 made of glass...
- A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5mm, respectively. Using a specially designed screw gauge...