Practice questions
88551 published questions with worked solutions.
- Let f be a real valued continuous function defined on the positive real axis such that g(x)= _0^x tf(t)dt. If g(x^3)=x^6+x^7,...
- The square of the distance of the point ( 15 7 , 32 7 ,7 ) from the line x+1 3 = y+3 5 = z+5 7 in the direction of the vector i...
- The area of the region bounded by the curves x(1+y^2)=1 and y^2=2x is :
- Let A= bmatrix 1 2 & -2 0 & 1 bmatrix and P= bmatrix & - & bmatrix , θ > 0. If B=PAP^T, C=P^TB^ 10 P and the sum of the diagonal...
- If f(x) = 1 x^ 1/4 (1+x^ 1/4 ) dx, f(0) = –6, then f(1) is equal to:
- Let f : R → R be a twice differentiable function such that f(2) = 1. If F(x) = xf(x) for all x ∈ R, _0^2 xF'(x)dx = 6 and _0^2...
- Let [x] denote the greatest integer less than or equal to x. Then domain of f(x)= ^ -1 (2[x]+1) is :
- If _ r=1 ^ 13 1 ( 4 +(r-1) 6 ) ( 4 + r 6 ) =a 3+b, a, b ∈ Z, then a^2+b^2 is equal to:
- Two equal sides of an isosceles triangle are along – x + 2y = 4 and x + y = 4. If m is the slope of its third side, then the sum,...
- Let the coefficients of three consecutive terms T_r, T_ r+1 and T_ r+2 in the binomial expansion of (a+b)^ 12 be in a G.P. and...
- If A and B are the points of intersection of the circle x^2+y^2-8x=0 and the hyperbola x^2 9 - y^2 4 =1 and a point P moves on...
- Let f(x)= _ n _ r=0 ^n ( (x/2^ r+1 )+ ^3(x/2^ r+1 ) 1- ^2(x/2^ r+1 ) ). Then _ x 0 e^x-e^ f(x) (x-f(x)) is equal to ____.
- The interior angles of a polygon with n sides, are in an A.P. with common difference 6°. If the largest interior angle of the...
- If y = y(x) is the solution of the differential equation, 4-x^2 dy dx = ( ( ^ -1 ( x 2 ) )^2-y ) ^ -1 ( x 2 ), -2 x 2, y(2)= (...
- A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform...
- A parallel plate capacitor of capacitance 1 μF is charged to a potential difference of 20 V. The distance between plates is 1 μm....
- Match List-I with List-II List-I: (A) Angular Impulse (B) Latent Heat (C) Electrical resistivity (D) Electromotive force List-II:...
- The ratio of vapour densities of two gases at the same temperature is 4 25 , then the ratio of r.m.s. velocities will be :
- The kinetic energy of translation of the molecules in 50g of CO2 gas at 17°C is:
- In a long glass tube, mixture of two liquids A and B with refractive indices 1.3 and 1.4 respectively, forms a convex refractive...