Exams › JEE Main › General

Let f : R → R be a continuous function satisfying f(x) + f(x + k) = n, for all x ∈ R where k > 0 and n is a positive integer. If dx ) x ( f I nk 4 0 1 ∫ = and dx ) x ( f I k 3 k 2 ∫ − = then

1. I 1 + 2I 2 = 4nk
2. I 1 + 2I 2 = 2nk
3. I 1 + nI 2 = 4n 2 k
4. I 1 + nI 2 = 6n 2 k

Correct answer: I 1 + nI 2 = 4n 2 k

Related JEE Main General questions

• A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is - L A O L B
• A sonometer wire of length 1.5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7.7 × 10 3 kg/m 3 and 2.2 × 10 11 N/m 2 respectively ?
• A projectile is given an initial velocity of ) j ˆ 2 i ˆ ( + m/s, where i ˆ is along the ground and j ˆ is along the vertical. If g = 10 m/s 2 , the equation of its trajectory is -
• A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x 0 of the spring when it is in equilibrium is - (Here k is spring constant)
• The graph between angle of deviation ( δ ) and angle of incidence (i) for a triangular prism is represented by -
• Diameter of a plano-convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is 2 × 10 8 m/s, the focal length of the lens is -

⚔️ Practice JEE Main General free + battle 1v1 →