JEE Main questions
34495 published questions with worked solutions.
- Let a = 4 i - j + k, b = 11 i - j + k and c be a vector such that ( a + b) c = c (-2 a + 3 b). If (2 a + 3 b) c = 1670, then |...
- If the function f(x) = 2x³ − 9ax² + 12a²x + 1, a > 0 has a local maximum at x = α and a local minimum x = α², then α and α² are...
- There are three bags X, Y and Z. Bag X contains 5 one-rupee coins and 4 five-rupee coins; Bag Y contains 4 one-rupee coins and 5...
- Let _ ^ _e4 dx e^x - 1 = 6. Then eᵅ and e⁻ᵅ are the roots of the equation:
- Let A = 2, 3, 6, 8, 9, 11 and B = 1, 4, 5, 10, 15 . Let R be a relation on A × B define by (a, b) R (c, d) if and only if 3ad −...
- For a, b > 0, let f(x) = cases ((a + 1)x) + b x x , & x < 0 3, & x = 0 ax + b^2x^2 - ax b a ,x x , & x > 0 cases be a continuous...
- If the term independent of x in the expansion of ( a ,x^2 + 1 2x^3 )^ 10 is 105, then a² is equal to:
- Let A be the region enclosed by the parabola y² = 2x and the line x = 24. Then the maximum area of the rectangle inscribed in the...
- If α = _ x 0^+ ( e^ x - e^ x x - x ) and β = _ x 0 (1 + x)^ 12 x are the roots of the quadratic equation ax² + bx − √e = 0, then...
- Let S be the focus of the hyperbola x^2 3 - y^2 5 = 1, on the positive x-axis. Let C be the circle with its centre at A(√6, √5)...
- The number of distinct real roots of the equation |x + 1||x + 3| − 4|x + 2| + 5 = 0, is ________ .
- Let a ray of light passing through the point (3, 10) reflects on the line 2x + y = 6 and the reflected ray passes through the...
- Let a, b, c ∈ N and a < b < c. Let the mean, the mean deviation about the mean and the variance of the 5 observations 9, 25, a,...
- Let α|x| = |y|e^ xy − β , α, β ∈ N be the solution of the differential equation x dy − y dx + xy(x dy + y dx) = 0, y(1) = 2. Then...
- If 1 [5] (x - 1)^4(x + 3)^6 dx = A ( x - 1 x + 3 )^B + C, where C is the constant of integration, then the value of α + β + 20AB...
- Match the C_p/C_V ratio for ideal gases with different type of molecules : List-I: (A) Monatomic (B) Diatomic rigid molecules (C)...
- Particle A of mass m_A= m 2 moving along the x-axis with velocity v_0 collides elastically with another particle B at rest having...
- On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by Ax (x^2+a^2)^...
- A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm s ^ -2 . The density of water is 1 gm cm ^ -3 and water...
- Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum :