Practice questions
88551 published questions with worked solutions.
- Let a = 2 i - 3 j + k , b = 3 i + 2 j + 5 k and a vector c be such that ( a - c ) b = -18 i - 3 j + 12 k and a c = 3. If b c = d...
- 4 _0^1 ( 1 3+x^2 + 1+x^2 )dx - 3 _e( 3 ) is equal to :
- The number of terms of an A.P. is even, the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term...
- If the system of equations 2x + λy + 3z = 5 3x + 2y – z = 7 4x + 5y + μz = 9 has infinitely many solutions, then ( ^2 + ^2) is...
- Let A be a 3 × 3 real matrix such that A^2(A - 2I) - 4(A - I) = 0, where I and O are the identity and null matrices,...
- If the sum of the first 10 terms of the series 4.1 1+4.1^4 + 4.2 1+4.2^4 + 4.3 1+4.3^4 + is m n , where gcd(m, n), then m + n is...
- If the set of all a R - 1 , for which the roots of the equation (1 - a)x^2 + 2(a - 3)x + 9 = 0 are positive is (- , - ] [ , ),...
- If y = ( 3 + ^ -1 x 2 ), then (x - y)^2 + 3y^2 is equal to
- Let y = y(x) be the solution of the differential equation dy dx + 2y ^2 x = 2 ^2 x + 3 x ^2 x such that y(0) = 5 4 . Then 12 (y (...
- Let A(4, –2), B(1, 1) and C(9, –3) be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed...
- Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net...
- Energy released when two deuterons (_1H^2) fuse to form a helium nucleus (_2He^4) is (Given: Binding energy per nucleon of _1H^2...
- Two water drops each of radius 'r' coalesce to form a bigger drop. If 'T' is the surface tension, the surface energy released in...
- A bi-convex lens has radius of curvature of both the surfaces same as 1/6 cm. If this lens is required to be replaced by another...
- An electron with mass 'm' with an initial velocity (t = 0) v = v_0 i (v_0 > 0) enters a magnetic field B = B_0 j . If the initial...
- Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm, at same...
- A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the x-direction in 0.3 sec. The crest P is at x = 0 at...
- Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the...
- The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is...
- The internal energy of air in 4 m × 4 m × 3 m sized room at 1 atmospheric pressure will be _____ × 10⁶ J. (Consider air as...