Practice questions
88551 published questions with worked solutions.
- Let the function f(x) = cases -3ax^2-2, & x<1 a^2+bx & x 1 cases Be differentiable for all x ∈ R, where a > 1, b ∈R. If the area...
- If _ r=0 ^ 5 ^ 11 C_ 2r+1 2r+2 = m n , gcd (m, n) = 1, then m – n is equal to _______.
- Let A be a square matrix of order 3 such that det(A) = –2 and det(3adj(–6adj(3A))) = 2^ m+n .3^ mn , m > n. Then 4m + 2n is equal...
- Let L1 : x-1 3 = y-1 -1 = z+1 0 and L2 : x-2 2 = y 0 = z+4 , α ∈R, be two lines, which intersect at the point B. If P is the foot...
- Let c be the projection vector of b = i +4 k , λ > 0, on the vector a = i +2 j +2 k . If | a + c | = 7, then the area of the...
- Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main...
- Assertion (A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive...
- Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller...
- An amount of ice of mass 10⁻³ kg and temperature –10°C is transformed to vapour of temperature 110° by applying heat. The total...
- An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10⁻¹¹ m while that for the electron in third...
- A closed organ and an open organ tube filled by two different gases having same bulk modulus but different densities ρ1 and ρ2...
- The work functions of cesium (Cs) and lithium (Li) metals are 1.9 eV and 2.5 eV, respectively. If we incident a light of...
- If B is magnetic field and μ0 is permeability of free space, then the dimensions of (B/μ0) is
- Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs....
- A parallel-plate capacitor of capacitance 40μF is connected to a 100 V power supply. Now the intermediate space between the...
- Given is a thin convex lens of glass (refractive index μ) and each side having radius of curvature R. One side is polished for...
- Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common...
- The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which...
- The position vectors of two 1 kg particles, (A) and (B), are given by r _A = ( _1t^2 i + _2t j + _3t k ) m and r _B = ( _1t i +...
- A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2A. The amount of the aluminium deposited at...