List of top Mathematics Questions asked in JEE Main

If the probability that the random variable X takes the value x is given by $ P(X = x) = k(x + 1)3^{-x} $, $ x = 0, 1, 2, 3, ... $, where k is a constant, then $ P(X \ge 3) $ is equal to

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability that A wins if A makes the first throw is:

Bag $ B_1 $ contains 6 white and 4 blue balls, Bag $ B_2 $ contains 4 white and 6 blue balls, and Bag $ B_3 $ contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability that the ball is drawn from Bag $ B_2 $ is:

If A and B are two events such that $ P(A \cap B) = 0.1 $, and $ P(A|B) $ and $ P(B|A) $ are the roots of the equation $ 12x^2 - 7x + 1 = 0 $, then the value of $\frac{P(A \cup B)}{P(A \cap B)}$

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability that the ball drawn is white is $\frac{29}{45}$, then n is equal to:

If $ A $ and $ B $ are two events such that $ P(A) = 0.7 $, $ P(B) = 0.4 $ and $ P\left( A \cap \overline{B} \right) = 0.5 $, where $\overline{B}$ denotes the complement of $ B $, then $ P\left( B | \left( A \cup \overline{B} \right) \right) $ is equal to

A board has 16 squares as shown in the figure. Out of these 16 squares, two squares are chosen at random. The probability that they have no side in common is:

Let $ S $ be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set $ S $, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

Three distinct numbers are selected randomly from the set $ \{1, 2, 3, \dots, 40\} $. If the probability, that the selected numbers are in an increasing G.P. is $ \frac{m}{n} $, where $ \gcd(m, n) = 1 $, then $ m + n $ is equal to:

Let a random variable X take values 0, 1, 2, 3 with $ P(X = 0) = P(X = 1) = p, \, P(X = 2) = P(X = 3), \, \text{and} \, F(X^2) = 2F(X). $ Then the value of $ 8p - 1 $ is:

If A and B are two events such that $ P(A \cap B) = 0.1 $, and $ P(A|B) $ and $ P(B|A) $ are the roots of the equation $ 12x^2 - 7x + 1 = 0 $, then the value of $ \frac{P(A \cup B)}{P(A \cap B)} $ is:

A card from a pack of 52 cards is lost. From the remaining 51 cards, n cards are drawn and are found to be spades. If the probability of the lost card to be a spade is $\frac{11}{50}, \text{ then } n \text{ is equal to}$ _______

What is the solution to the differential equation $ \frac{dy}{dx} = \frac{y}{x} $ with the initial condition $ y(1) = 2 $?

Let for some function $ y = f(x) $, $\int_0^x t f(t) \, dt = x^2 f(x), x>0$ and $ f(2) = 3 $. Then $ f(6) $ is equal to:

If $ x = f(y) $ is the solution of the differential equation \[ (1 + y^2) + (x - 2e^{\tan^{-1}y}) \frac{dy}{dx} = 0, \quad y \in \left( -\frac{\pi}{2}, \frac{\pi}{2} \right), \] with $ f(0) = 1 $, then $ f\left( \frac{1}{\sqrt{3}} \right) $ is equal to:

Let $ [x] $ denote the greatest integer function, and let $ m $ and $ n $ respectively be the numbers of the points, where the function $ f(x) = [x] + |x - 2| $, $ -2<x<3 $, is not continuous and not differentiable. Then $ m + n $ is equal to:

Let for some function $ y = f(x) $, $\int_0^x t f(t) \, dt = x^2 f(x), x>0$ and $ f(2) = 3 $. Then $ f(6) $ is equal to:

Let $ y = y(x) $ be the solution of the differential equation \[ \left( xy - 5x^2 \sqrt{1 + x^2} \right) dx + (1 + x^2) dy = 0, \quad y(0) = 0. \] Then $ y(\sqrt{3}) $ is equal to:

Let $ y = y(x) $ be the solution curve of the differential equation $ x(x^2 + e^x) \, dy + \left( e^x(x - 2) y - x^3 \right) \, dx = 0, \quad x>0, $ passing through the point $ (1, 0) $. Then $ y(2) $ is equal to:

Let a curve $ y = f(x) $ pass through the points $ (0,5) $ and $ (\log 2, k) $. If the curve satisfies the differential equation: \[ 2(3+y)e^{2x}dx - (7+e^{2x})dy = 0, \] then $ k $ is equal to:

Let $ y = y(x) $ be the solution of the differential equation $ \frac{dy}{dx} + 3(\tan^2 x) y + 3y = \sec^2 x $, with $ y(0) = \frac{1}{3} + e^3 $. Then $ y\left(\frac{\pi}{4}\right) $ is equal to