List of top Mathematics Questions

Let [x] denote the greatest integer function. Then match List-I with List-II:

If \( \vec{a}, \vec{b} \) and \( \vec{c} \) are three vectors such that \( \vec{a} + \vec{b} + \vec{c} = 0 \), where \( \vec{a} \) and \( \vec{b} \) are unit vectors and \( |\vec{c}| = 2 \), then the angle between the vectors \( \vec{b} \) and \( \vec{c} \) is:

The value of the integral \( \int_{\ln 2}^{\ln 3} \frac{e^{2x} - 1}{e^{2x} + 1} \, dx \) is:

If \( A \) is a square matrix and \( I \) is an identity matrix such that \( A^2 = A \), then \( A(I - 2A)^3 + 2A^3 \) is equal to:

The area of the region bounded by the lines \( \frac{x}{7\sqrt{3a}} + \frac{y}{b} = 4 \), \( x = 0 \), and \( y = 0 \) is:

If A is a square matrix of order 4 and |A| = 4, then |2A| will be:

Two dice are thrown simultaneously. If $X$ denotes the number of fours, then the expectation of $X$ will be:

If $f(x) = x^2 + bx + 1$ is increasing in the interval $[1, 2]$, then the least value of $b$ is:

If \([A]_{3 \times 2} [B]_{x \times y} = [C]_{3 \times 1}\), then \( x \) and \( y \) are:

If $A$ and $B$ are symmetric matrices of the same order, then $AB - BA$ is:

The degree of the differential equation $\left(1 - \left(\frac{dy}{dx}\right)^2\right)^{3/2} = k \frac{d^2 y}{dx^2}$ is:

The second-order derivative of which of the following functions is $5^x$?

Evaluate the integral $\int \frac{\pi}{x^n + 1 - x} , dx$:

A die is rolled thrice. What is the probability of getting a number greater than $4$ in the first and second throws and a number less than $4$ in the third throw?

The area of the region bounded by the lines $x + 2y = 12$, $x = 2$, $x = 6$, and the $x$-axis is:

An objective function $Z = ax + by$ is maximum at points $(8, 2)$ and $(4, 6)$. If $a \geq 0$ and $b \geq 0$ and $ab = 25$, then the maximum value of the function is:

If $t = e^{2x}$ and $y = \ln(t^2)$, then $\frac{d^2 y}{dx^2}$ is:

The corner points of the feasible region determined by $x + y \leq 8$, $2x + y \geq 8$, $x \geq 0$, $y \geq 0$ are $A(0, 8)$, $B(4, 0)$, and $C(8, 0)$. If the objective function $Z = ax + by$ has its maximum value on the line segment $AB$, then the relation between $a$ and $b$ is:

\(\tan 3A - \tan 2A \cdot \tan A\) is equal to:

The volume of the cylinder is \( 448 \pi \, \text{cm}^3 \) and height 7 cm. Then its lateral surface area is:

Let the range of the function \[ f(x) = \frac{1}{2 + \sin 3x + \cos 3x}, \, x \in \mathbb{R} \, \text{be } [a, b]. \] If \( \alpha \) and \( \beta \) are respectively the arithmetic mean (A.M.) and the geometric mean (G.M.) of \( a \) and \( b \), then \( \frac{\alpha}{\beta} \) is equal to:

Let $A = \{1, 2, 3, 4, 5\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $4x \leq 5y$. Let $m$ be the number of elements in $R$ and $n$ be the minimum number of elements from $A \times A$ that are required to be added to $R$ to make it a symmetric relation. Then $m + n$ is equal to:

Let A= {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15} Let R be a relation on A × B define by (a, b)R(c, d) if and only if 3ad – 7bc is an even integer. Then the relation R is

If \( (2, -1) \) is the point of intersection of the pair of lines \[ 2x^2 + axy + 3y^2 + bx + cy - 3 = 0 \quad \text{then} \quad 3a + 2b + c = \]

Given below is the distribution of a random variable \(X\):
\[ \begin{array}{|c|c|} \hline X = x & P(X = x) \\ \hline 1 & \lambda \\ 2 & 2\lambda \\ 3 & 3\lambda \\ \hline \end{array} \] If \(\alpha = P(X<3)\) and \(\beta = P(X>2)\), then \(\alpha : \beta = \)