List of top Mathematics Questions

The number of terms in the expansion of \( (2x + 3y + 5z)^5 \) is
From a group of 5 men and 7 women, five persons are to be selected to form a committee so that at least 3 men are there in the committee. The number of ways this can be done is
The number of 3 digit numbers that can be formed with \( S = \{0,1,2,3,\dots,8\} \) when repetitions are allowed is
The position vectors of the vertices of a triangle are \( 4\hat{i} + 5\hat{j} + \hat{k} \), \( 2\hat{i} + 4\hat{j} - \hat{k} \) and \( 3\hat{i} + 6\hat{j} - 3\hat{k} \). Then the triangle is
The standard deviation of the observations 1; 2; 3; 4; 4; 5; 5; 5; 8 is
The equation of the normal to the curve \( y = x + \frac{1}{x} \) at the point where \( x = 2 \) is
Local maximum and local minimum values of \( f(x) = (x-1)^2(x+2) \) are attained respectively at
The points on the curve \( y = 2x^3 + 3x^2 - 8x \) where the tangents are parallel to the line \( y = 4x + 3 \) are
The binary representation of the decimal number 125 is
The hexadecimal representation of the decimal number 2000 is
In a frequency distribution, the mean and median are 17 and 18 respectively. Then the mode of the distribution is
If \( \sin^{-1} x + \sin^{-1} y = \frac{\pi}{2} \), then \( x^2 \) is equal to
Two dice are thrown together. The probability of getting a sum more than 8 is
On a shelf, 2 books of History, 3 books of Philosophy, and 5 books of Economics are to be arranged in such a way that the books of any subject are kept together. The number of ways this can be done is
The value of \( k \) for which the system of equations \( x + ky + 3z = 0 \); \( 3x + ky + 2z = 0 \); \( 2x + 3y + 4z = 0 \) has a non-trivial solution is
The number of ways in which the letters of the word "BUSINESS" can be arranged so that the vowels always come together is
In a group of people it was observed that 86 persons know Odia, 64 know English, 42 know Hindi, 39 know Odia and English, 21 know English and Hindi, 17 know Odia and English, and 16 persons know all the three languages. How many persons in the group know at least one language?
The system of equations \( 3x + 5y = 4 \); \( 6x + ky = 8 \) has infinitely many solutions if \( k \) is equal to
Let \( A \) be a square matrix of order 3 and \( |A| \) denote the determinant of \( A \). If \( A = kB \), where \( k \) is a scalar, then \( |A| \) is equal to

In the given figure, the numbers associated with the rectangle, triangle, and ellipse are 1, 2, and 3, respectively. Which one among the given options is the most appropriate combination of \( P \), \( Q \), and \( R \)?


 

A rectangle has a length \(L\) and a width \(W\), where \(L > W\). If the width, \(W\), is increased by 10%, which one of the following statements is correct for all values of \(L\) and \(W\)? 
Select the most appropriate option to complete the above sentence.

Let \( \mathbf{a}_R \) be the unit radial vector in the spherical coordinate system. For which of the following value(s) of \( n \), the divergence of the radial vector field \( \mathbf{f}(R) = \mathbf{a}_R \frac{1}{R^n} \) is independent of \( R \)?
Consider the set \( S \) of points \( (x, y) \in \mathbb{R}^2 \) which minimize the real-valued function \( f(x, y) = (x + y - 1)^2 + (x + y)^2 \). Which of the following statements is true about the set \( S \)?
Consider discrete random variables \( X \) and \( Y \) with probabilities as follows:

\( P(X=0 \text{ and } Y=0) = \frac{1}{4}, \)
\( P(X=1 \text{ and } Y=0) = \frac{1}{8}, \)
\( P(X=0 \text{ and } Y=1) = \frac{1}{2}, \)
\( P(X=1 \text{ and } Y=1) = \frac{1}{8}. \)

Given \( X = 1 \), the expected value of \( Y \) is
Let \( X \) and \( Y \) be continuous random variables with probability density functions \( P_X(x) \) and \( P_Y(y) \), respectively. Further, let \( Y = X^2 \) and \[ P_X(x) = \begin{cases} 1, & x \in (0,1] \\ 0, & \text{otherwise} \end{cases} \] Which one of the following options is correct?