Practice questions
88551 published questions with worked solutions.
- If an angle between the line, x+1 2 = y-2 1 = z-3 -2 and the plane, x − 2y − kz = 3 is ^ -1 ( 2 2 3 ), then a value of k is:
- If a straight line passing through the point P(−3, 4) is such that its intercepted portion between the coordinate axes is...
- Let a, b and c be three unit vectors, out of which vectors b and c are non-parallel. If α and β are the angles which vector a...
- The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then...
- The tangent to the curve y = x^2 - 5x + 5, parallel to the line 2y = 4x + 1, also passes through the point:
- The set of all values of λ for which the system of linear equations x − 2y − 2z = λx, x + 2y + z = λy, −x − y = λz has a...
- The number of integral values of m for which the quadratic expression, (1 + 2m)x^2 - 2(1 + 3m)x + 4(1 + m), x ∈ R, is always...
- The total number of irrational terms in the binomial expansion of (7^ 1/5 - 3^ 1/10 )^ 60 is:
- A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But...
- A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of...
- A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass '4m' and...
- A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the...
- Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I....
- A travelling harmonic wave is represented by the equation y(x, t) = 10^ -3 (50t + 2x), where x and y are in meter and t is in...
- A simple pendulum, made of a string of length ℓ and a bob of mass m, is released from a small angle _0. It strikes a block of...
- The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to...
- A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling...
- A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if...
- A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?Not in JEE or NEET syllabus
- A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30...