List of top Questions asked in JEE Main

An emf of 20 V is applied at time t = 0 to a circuit containing in series 10 mH inductor and 5 \( \Omega \) resistor. The ratio of the currents at time t = \( \infty \) and at t = 40 s is close to : (Take e² = 7.389)

Let y = y(x) be a function of x satisfying

\( y\sqrt {1 - {x^2}} = k - x\sqrt {1 - {y^2}} \) where k is a constant and

\( y\left( {{1 \over 2}} \right) = - {1 \over 4} \). Then \( {{dy} \over {dx}} \) at x = \( {1 \over 2} \), is equal to :

Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A \( \subseteq \) B and B \( \subseteq \) D, then A \( \subseteq \) C" is :

If \( {{3 + i\sin \theta } \over {4 - i\cos \theta }} \), \( \theta \) \( \in \) [0, 2\( \theta \)], is a real number, then an argument of
sin\( \theta \) + icos\( \theta \) is :

Let A = [a_ij] and B = [b_ij] be two 3 × 3 real matrices such that b_ij = (3)^(i+j-2)a_ji, where i, j = 1, 2, 3. If the determinant of B is 81, then the determinant of A is:

Let \( \alpha \) and \( \beta \) be the roots of the equation x² - x - 1 = 0.
If p_k = \( {\left( \alpha \right)^k} + {\left( \beta \right)^k} \) , k \( \ge \) 1, then which one of the following statements is not true?

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is \( {{1 \over 4}} \) . If the probability that at most two machines will be out of service on the same day is \( {\left( {{3 \over 4}} \right)^3}k \), then k is equal to :

Let ƒ(x) be a polynomial of degree 5 such that x = ±1 are its critical points.

If \( \mathop {\lim }\limits_{x \to 0} \left( {2 + {{f\left( x \right)} \over {{x^3}}}} \right) = 4 \), then which one of the following is not true?

Let X = {n \( \in \) N : 1 \( \le \) n \( \le \) 50}. If
A = {n \( \in \) X: n is a multiple of 2} and
B = {n \( \in \) X: n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is ________.

If \( \theta \)₁ and \( \theta \)₂ be respectively the smallest and the largest values of \( \theta \) in (0, 2\( \pi \)) - {\( \pi \)} which satisfy the equation,
2cot²\( \theta \) - \( {5 \over {\sin \theta }} \) + 4 = 0, then
\( \int\limits_{{\theta _1}}^{{\theta _2}} {{{\cos }^2}3\theta d\theta } \) is equal to :

The value of \( \alpha \) for which
\( 4\alpha \int\limits_{ - 1}^2 {{e^{ - \alpha \left| x \right|}}dx} = 5 \), is:

If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (\( \alpha \), 7, 1) is \( \left( {{5 \over 3},{7 \over 3},{{17} \over 3}} \right) \), then \( \alpha \) is equal to______.

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to _______.

Let \( \overrightarrow a \) , \( \overrightarrow b \) and \( \overrightarrow c \) be three unit vectors such that
\( \overrightarrow a + \vec b + \overrightarrow c = \overrightarrow 0 \). If \( \lambda = \overrightarrow a .\vec b + \vec b.\overrightarrow c + \overrightarrow c .\overrightarrow a \) and
\( \overrightarrow d = \overrightarrow a \times \vec b + \vec b \times \overrightarrow c + \overrightarrow c \times \overrightarrow a \), then the ordered pair, \( \left( {\lambda ,\overrightarrow d } \right) \) is equal to :

The number of ordered pairs (r, k) for which
6.³⁵C_r = (k² - 3). ³⁶C_{r + 1}, where k is an integer, is :

If the system of linear equations,
x + y + z = 6
x + 2y + 3z = 10
3x + 2y + \( \lambda \)z = \( \mu \)
has more than two solutions, then \( \mu \) - \( \lambda \)² is equal to ______.

Let \( {a_1} \) , \( {a_2} \) , \( {a_3} \) ,....... be a G.P. such that
\( {a_1} \) < 0, \( {a_1} \) + \( {a_2} \) = 4 and \( {a_3} \) + \( {a_4} \) = 16.
If \( \sum\limits_{i = 1}^9 {{a_i}} = 4\lambda \), then \( \lambda \) is equal to:

Let y = y(x) be the solution curve of the differential equation,

\( \left( {{y^2} - x} \right){{dy} \over {dx}} = 1 \), satisfying y(0) = 1. This curve intersects the x-axis at a point whose abscissa is :

The refining method used when the metal and the impurities have low and high melting temperatures, respectively, is :

The area (in sq. units) of the region
{(x, y) \( \in \) R² | 4x² \( \le \) y \( \le \) 8x + 12} is :

If the function ƒ defined on \( \left( { - {1 \over 3},{1 \over 3}} \right) \) by

f(x) = \( \left\{ {\matrix{ {{1 \over x}{{\log }_e}\left( {{{1 + 3x} \over {1 - 2x}}} \right),} & {when\,x \ne 0} \cr {k,} & {when\,x = 0} \cr } } \right. \)

is continuous, then k is equal to_______.

Identify the correct labels of A,B and C in the following graph from the options given below :

Root mean square speed (V_rms); most probable speed (V_mp); Average speed (V_av)

In the following reaction, products (A) and (B) respectively, are :

NaOH + Cl₂ \( \to \) (A) + side products
(hot and conc.)

Ca(OH)₂ + Cl₂ \( \to \) (B) + side products (dry)

The number of sp² hybridised carbons present in "Aspartame" is

In the following reaction sequence,

The major product B is :