Practice questions
88551 published questions with worked solutions.
- Consider an A.P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies...
- Let a = i + 2 j + k and b = 2 i + 7 j + 3 k . Let L_1 : r = (- i + 2 j + k ) + a , R and L_2 : r = ( j + k ) + b , R be two...
- The value of _ n ( _ k=1 ^ n k^3+6k^2+11k+5 (k+3)! ) is :
- Let L_1 : x-1 1 = y-2 -1 = z-1 2 and L_2 : x+1 -1 = y-2 2 = z 1 be two lines. Let L_3 be a line passing through the point ( , , )...
- Let x_1, x_2,......x_ 10 be ten observations such that _ i=1 ^ 10 (x_i-2)=30, _ i=1 ^ 10 (x_i- )^2=98, > 2 and their variance is...
- Let A = [a_ ij ] = bmatrix _5 128 & _4 5 _5 8 & _4 25 bmatrix . If A_ ij is the co-factor of a_ ij , C_ ij = _ k=1 ^ 2 a_ ik A_...
- Let f : (0, ) R be a twice differentiable function. If for some a 0, _0^1 f( x)d = af(x), f(1) = 1 and f(16) = 1 8 , then 16 - f'...
- Let S = m Z : A^ m^2 + A^m = 3I - A^ -6 , where A = bmatrix 2 & -1 1 & 0 bmatrix . Then n(S) is equal to …………….. .
- The number of 6-letter words, with or without meaning, that can be formed using the letters of the word 'MATHS' such that any...
- Let S = x : ^ -1 x = + ^ -1 x + ^ -1 (2x + 1) . Then _ x S (2x-1)^2 is equal to ………….. .
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke...
- Two projectiles are fired with same initial speed from same point on ground at angles of (45° – α) and (45° + α), respectively,...
- An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E_0 i . When the dipole is rotated...
- The pair of physical quantities not having same dimensions is :
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Time...
- The expression given below shows the variation of velocity (ν) with time (t), = At^2 + Bt C+t . The dimension of ABC is :
- Consider I_1 and I_2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L_1 = self inductance of...
- Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly...
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) :...
- A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field B about an axis perpendicular to B ....