Practice questions
88551 published questions with worked solutions.
- The length of the perpendicular from the point (2, −1, 4) on the straight line, x+3 10 = y-2 -7 = z 1 is:
- Let f: [0, 2] R be a twice differentiable function such that f''(x) > 0, for all x ∈ (0, 2). If (x) = f(x) + f(2 - x), then φ is:
- The greatest value of c ∈ R for which the system of linear equations x - cy - cz = 0, cx - y + cz = 0, cx + cy - z = 0 has a...
- The magnitude of the projection of the vector 2 i + 3 j + k on the vector perpendicular to the plane containing the vectors i + j...
- The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2, 4, 10, 12, 14, then the...
- The area (in sq. units) of the region A = (x, y) R R 0 x 3, 0 y 4, y x^2 + 3x is:
- If = ^ -1 ( 3 5 ), = ^ -1 ( 1 3 ), where 0 < , < 2 , then α − β is equal to:
- If S_1 and S_2 are respectively the sets of local minimum and local maximum points of the function, f(x) = 9x^4 + 12x^3 - 36x^2 +...
- Let A = pmatrix & - & pmatrix , (α ∈ R) such that A^ 32 = pmatrix 0 & -1 1 & 0 pmatrix . Then a value of α is:
- If α and β be the roots of the equation x^2 - 2x + 2 = 0, then the least value of n for which ( )^n = 1 is:
- The contrapositive of the statement "If you are born in India, then you are a citizen of India", is:Not in JEE syllabus
- In a line of sight radio communication, a distance of about 50 km is kept between the transmitting and receiving antennas. If the...Not in JEE or NEET syllabus
- Young's moduli of two wires A and B are in the ratio 7 : 4. Wire A is 2 m long and has radius R. Wire B is 1.5 m long and has...
- The electric field in a region is given by E = (Ax + B) i, where E is in NC^ -1 and x is in metres. The value of constants are A...
- A rocket has to be launched from earth in such a way that it never returns. If E is the minimum energy delivered by the rocket...
- In a simple pendulum experiment for determination of acceleration due to gravity (g), time taken for 20 oscillations is measured...
- A nucleus A, with a finite de-Broglie wavelength _A, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies...
- The magnetic field of an electromagnetic wave is given by B = 1.6 10^ -6 (2 10^ 7 z + 6 10^ 15 t)(2 i + j) Wb m ^2 . The...
- A parallel plate capacitor has 1 μF capacitance. One of its two plates is given +2 μC charge and the other plate, +4 μC charge....
- A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm...