Practice questions
88551 published questions with worked solutions.
- Let a, b, c ∈ 1, 2, 3, 4 . If the probability, that ax² + 2√2 bx + c > 0 for all x ∈ ℝ, is mn, gcd(m, n) = 1, then m + n is equal...
- Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal...
- If = _0^ 2 3 _2(x^2 + 4) ,dx + _2^4 2^x - 4 ,dx, then α² is equal to _______.
- The dimensional formula of 12 _0E^2 (ε₀ = permittivity of vacuum and E = electric field) is MᵃLᵇTᶜ. The value of 2a − b + c =...
- The diameter of a wire measured by a screw gauge of least count 0.001 cm is 0.08 cm. The length measured by a scale of least...
- The velocity of a particle is given as v = -x i + 2y j - z k m/s. The magnitude of acceleration at point (1, 2, 4) is _______...
- The position of an object having mass 0.1 kg as a function of time t is given as r = (10t^2 i + 5t^3 j) m. At t = 1 s, which of...
- A planet (P₁) is moving around the star of mass 2M in the orbit of radius R. Another planet (P₂) is moving around another star of...
- A particle is rotating in a circular path and at any instant its motion can be described as = 5t^4 40 - t^3 3 . The angular...
- Two charged conducting spheres S₁ and S₂ of radii 8 cm and 18 cm are connected to each other by a wire. After equilibrium is...
- The equation of a plane progressive wave is given by y = 5 (200t - x 150 ) where x and y are in cm and t is in second. The...
- When a coil is placed in a time dependent magnetic field the power dissipated in it is P. The number of turns, area of the coil...
- For a certain metal, when monochromatic light of wavelength λ is incident, the stopping potential for photoelectrons is 3V₀. When...
- An electromagnetic wave travelling in x-direction is described by field equation E_y = 300 (t - xc ). If the electron is...
- A liquid drop of diameter 2 mm breaks into 512 droplets. The change in surface energy is α × 10⁻⁶ J. The value of α is _______....
- In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central...
- A vessel contains 0.15 m³ of a gas at pressure 8 bar and temperature 140°C with c_p = 3R and c_v = 2R. It is expanded...
- 1 μC charge moving with velocity v = ( i - 2 j + 3 k) m/s in the region of magnetic field B = (2 i + 3 j - 5 k) T. The magnitude...
- A uniform wire of length l of weight w is suspended from the roof with a weight of W at the other end. The stress in the wire at...
- A tub is filled with water and a wooden cube 10 cm × 10 cm × 10 cm is placed in the water. The wooden cube is found to float on...