List of top Mathematics Questions

$ \int \frac{\cos 2x}{\sin^2 x \cos^2 x} \, dx $ is equal to:

If $ \int_0^a \frac{1}{1 + 4x^2} \, dx = \frac{\pi}{8} $, then the value of $a$ is:

If $ \left| \begin{matrix} 2x & 5 \\ 12 & x \end{matrix} \right| = \left| \begin{matrix} 6 & -5 \\ 4 & 3 \end{matrix} \right| $, then the value of x is:

The principal value of $ \cot^{-1} \left( -\frac{1}{\sqrt{3}} \right) $ is:

If A and B are two square matrices of the same order, then (A + B)(A - B) is equal to:

A machine produces 0, 1 or 2 defective items in a day with probabilities of $ \frac{1}{4}, \frac{1}{2}, \frac{1}{4} $ respectively. Then, the standard deviation of the number of defective items produced by the machine in a day is ...........

Let $ A, B $ be two events and $ \overline{A} $ be the complement of $ A $. If $ P(\overline{A}) = 0.7 $, $ P(B) = 0.7 $, and $ P(B|A) = 0.5 $, then $ P(A \cup B) = $ ...........

If the Laplace transform of a function $ f(t) $ is given by $ \frac{2s + 1}{(s + 1)(s + 2)} $, then $ f(0) $ is equal to ...........

If $ y(x) $ satisfies the differential equation $ x \frac{dy}{dx} + (x - y) = 0 $ subject to the condition $ y(1) = 0 $, then $ y(e) $ is ...........

If the matrix $ A = \begin{pmatrix} 3 & -1 & 1 \\ -1 & 5 & -1 \\ 1 & -1 & 3 \end{pmatrix} $ has three distinct eigenvalues and one of its eigenvectors is $ \begin{pmatrix} 1 \\ 0 \\ -1 \end{pmatrix} $, then which of the following can be another eigenvector of $ A $?

Determine the value of $\lambda$ and $\mu$ for which such that the system of equations $x + 2y + z = 6$, $x + 4y + 3z = 10$, and $2x + 4y + \lambda z = \mu$ has infinite number of solutions.

Evaluate the sum: $$ \sum_{n=1}^{\infty} \frac{1}{n(n+1)(n+2)} $$

The equation of the circle passing through the points (1,2), (4,3), and (2,–1) is:

Let $ R $ be a relation defined by the teacher to plan the seating arrangement of students in pairs, where $ R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = 3x \} $. List the elements of $ R $. Is the relation $ R $ reflexive, symmetric, and transitive? Justify your answer.

Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
Give reasons to support your answer to (i).

Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
On the basis of the given information, answer the followingIs $ f $ a bijective function?

A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Find a relation between $ x $ and $ y $ such that the surface area $ S $ is minimum.

A carpenter needs to make a wooden cuboidal box, closed from all sides, which has a square base and fixed volume. Since he is short of the paint required to paint the box on completion, he wants the surface area to be minimum.
On the basis of the above information, answer the following questions :
Taking length = breadth = $ x $ m and height = $ y $ m, express the surface area $ S $ of the box in terms of $ x $ and its volume $ V $, which is constant.

A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant, and 8 seeds of radish plant. The shopkeeper assured him of germination probabilities of brinjal, cabbage, and radish to be 25%, 35%, and 40% respectively. But before he could plant the seeds, they got mixed up in the bag and he had to sow them randomly.

What is the probability that it is a cabbage seed, given that the chosen seed germinates?

A gardener wanted to plant vegetables in his garden. Hence he bought 10 seeds of brinjal plant, 12 seeds of cabbage plant, and 8 seeds of radish plant. The shopkeeper assured him of germination probabilities of brinjal, cabbage, and radish to be 25%, 35%, and 40% respectively. But before he could plant the seeds, they got mixed up in the bag and he had to sow them randomly.

Calculate the probability of a randomly chosen seed to germinate.

If \[ A = \begin{bmatrix} 5 & 0 \\ 0 & 5 \end{bmatrix}, \] then $ A^3 $ is:

Let $ R $ be a relation defined by $ R = \{(x, y) : x, y \text{ are Roll Numbers of students such that } y = x^3 \} $. List the elements of $ R $. Is $ R $ a function? Justify your answer.

If surface area $ S $ is constant, the volume $ V = \frac{1}{4}(Sx - 2x^3) $, $ x $ being the edge of the base. Show that the volume $ V $ is maximum for $ x = \frac{\sqrt{6}}{6} $.

Find $ \frac{dy}{dx} $ if $ x^3 + y^3 + x^2 = a^b $, where $ a $ and $ b $ are constants.

Find the point on the line $ \frac{x-1}{3} = \frac{y+1}{2} = \frac{z-4}{3} $ at a distance of $ \sqrt{2} $ units from the point $ (-1, -1, 2) $.