List of top Mathematics Questions

The value of \( \sin(\cot^{-1}(x)) \) is:

If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:

The integral of \( \sec^{2/3}x \csc^{4/3}x \, dx \) from \( \pi/6 \) to \( \pi/3 \) is equal to:

A function \( f : \mathbb{R}_+ \to \mathbb{R} \) (where \( \mathbb{R}_+ \) is the set of all non-negative real numbers) defined by \( f(x) = 4x + 3 \) is:

If \( P(A | B) = P(A' | B) \), then which of the following statements is true?

Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is: \\ \\

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\

The following table gives the lifetimes of 400 neon lamps: 

Length (in hours)	Number of lamps
300 − 400	14
400 − 500	56
500 − 600	60
600 − 700	86
700 − 800	74
800 − 900	62
900 − 1000	48

(i) Represent the given information with the help of a histogram. 
(ii) How many lamps have a lifetime of more than 700 hours?

Let the solution curve $y=y(x)$ of the differential equation $\frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\}$ pass through the origin Then $y(1)$ is equal to :

An urn contains 7 green and 5 yellow balls. Two balls are drawn at a time. The probability that both balls are of the same colour is

R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.

Out of 1800 students in a school, 750 opted basketball, 800 opted cricket and remaining opted table tennis. If a student can opt only one game, find the ratio of
(a) Number of students who opted basketball to the number of students who opted table tennis.
(b) Number of students who opted cricket to the number of students opting basketball.
(c) Number of students who opted basketball to the total number of students

A piece of string is 30 cm long. What will be the length of each side if the string is used to form : 

1. a square? 
2.  an equilateral triangle? 
3.  a regular hexagon?

Fill in the blanks.
(a) (– 8) + _____ = 0
(b) 13 + _____ = 0
(c) 12 + (– 12) = ____
(d) (– 4) + ____ = – 12
(e) ____ – 15 = – 10

Find the area of each of the following triangles:

The total revenue in Rupees received from the sale of \(x\) units of a product is given by \(R(x)=13x^2+26x+15\).The marginal revenue, when \(x=7\) is

Find the multiplicative inverse of the complex number \(√5+3i\)\(\)

A pair of dice is thrown $200$ times. If getting a sum of $9$ is considered a success, then find the mean and the variance respectively of the number of successes.