Practice questions
90156 published questions with worked solutions.
- Let the centre of the circle x²+y²+2gx+2fy+25=0 be in the first quadrant and lie on the line 2x−y=4. Let the area of an...
- If a= i+ j+ k, b= j- k and c are three vectors such that a c= b and a c=3, then c ( a-2 b) is equal to _______.
- For the functions f(θ)=α tan²θ+β cot²θ and g(θ)=α sin²θ+β cos²θ, α>β>0, let _ 0< < /2 f( )= _ 0< < g( ). If the first term of a...
- Let y=y(x) be the solution of the differential equation (x^2-x x^2-1 )dy+(y(x- x^2-1 )-x)dx=0, x≥1. If y(1)=1, then the greatest...
- The density ρ of a uniform cylinder is determined by measuring its mass m, length l and diameter d. The measured values of m, l...
- The rain drop of mass 1 g, starts with zero velocity from a height of 1 km. It hits the ground with a speed of 5 m/s. The work...
- A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an...
- The two wires A and B of equal cross-section but of different materials are joined together. The ratio of Young's modulus of wire...
- Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure 90 kPa and...
- In interference experiment the path difference between two interfering waves at a point A on the screen is λ/3, where λ is the...
- A particle is executing simple harmonic motion. Its amplitude is A and time period is 5 sec. The time required by it to move from...
- A thin half ring of radius 35 cm is uniformly charged with a total charge of Q coulomb. If the magnitude of the electric field at...
- A point light source emits E.M. waves in free space. A detector, placed at a distance of L m, measures the intensity as I₀. The...
- The ratio of momentum of the photons of the 1st and 2nd line of Balmer series of Hydrogen atoms is α/β. The possible values of α...
- A LCR series circuit driven with E_rms=90 V at frequency f_d=30 Hz has resistance R=80 Ω, an inductance with inductive reactance...
- An unpolarized light of intensity I₀ passes through polarizer and then through a certain optically active solution and finally it...
- The energy released when (7/17.13) kg of ⁷₃Li is converted into ⁴₂He by proton bombardment is α×10³² eV. The value of α is...
- A three coulomb charge moves from the point (0,−2,−5) to the point (5,1,2) in an electric field expressed as E=2x i+3y^2 j+4 k...
- A certain gas is isothermally compressed to (1/3)ʳᵈ of its initial volume (V₀=3 litre) by applying required pressure. If the bulk...
- An oxide of iron contains 69.9% iron, its empirical formula, is: (Given: Molar mass of Fe and O are 56 and 16 g mol⁻¹...