List of top Mathematics Questions

The equation of a plane passing through the line of intersection of the planes \( x + 2y + 3z = 2 \) and \( x - y + z = 3 \) and at a distance \( \frac{2}{\sqrt{3}} \) from the point \( (3, 1, -1) \) is:
The point of intersection of the lines \( \frac{x - 1}{3} = \frac{y - 2}{-3} = \frac{z - 3}{4} \) and \( \frac{x - 4}{5} = \frac{y - 1}{2} = \frac{z - 1}{-2} \) is:
The angle between the lines \( 2x = 3y - z \) and \( 6x = -y - 4z \) is:
The integral of \( \int \frac{dx}{x^2[1 + x^4]^{3/4}} \) is:
The integral \( \int \frac{2^x}{\sqrt{1 - 4^x}} \, dx \) is equal to:
The integral \( \int_{\pi/2}^{-\pi/2} \sin x \, dx \) is:
What will be the equation of the circle whose center is \( (1, 2) \) and which passes through the point \( (4, 6) \)?
The line \( \frac{x - 2}{3} = \frac{y - 3}{4} = \frac{z - 4}{5} \) is parallel to the plane:
The approximate value of \( f(5.001) \), where \( f(x) = x^3 - 7x^2 + 15 \), is:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
Evaluate: \( 8^{\log_5 5} \)
What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?
The coefficients \( a, b, c \) of the quadratic equation \( ax^2 + bx + c = 0 \) are obtained by throwing a die three times. The probability that this equation has equal roots is:
If \( L = \lim_{x \to 0} \frac{a - \sqrt{a^2 - x^2}}{x^4} \), \( a > 0 \), then:
If \( |\mathbf{a}| = 8 \), \( |\mathbf{b}| = 3 \) and \( |\mathbf{a} \times \mathbf{b}| = 12 \), then find the angle between \( \mathbf{a} \) and \( \mathbf{b} \).
If for \(\vec{a} = 2\hat{i} + 3\hat{j} + \hat{k}\), \(\vec{b} = \hat{i} - 2\hat{j} + \hat{k}\), and \(\vec{c} = -3\hat{i} + \hat{j} + 2\hat{k}\), then find \([\vec{a} \, \vec{b} \, \vec{c}]\).
The maximum value of \( x + y \) subject to \[ 2x + 3y \leq 6, \quad x \geq 0, \quad y \geq 0 \] is:
Write the solution of the following LPP \[ \text{Maximize } Z = x + y \] Subject to \[ 3x + 4y \leq 12, \quad x \geq 0, \quad y \geq 0 \] Which point the value of \( Z \) is maximum?
The vector that must be added to \[ \mathbf{i} - 3\mathbf{j} + 2\mathbf{k} \quad \text{and} \quad 3\mathbf{i} + 6\mathbf{j} - 7\mathbf{k} \] so resultant vector is a unit vector along the X-axis is:
If a straight line is used to connect V 3, what will be the angle formed between the lines V3 and V1?
straight line
The base of two similar triangles are 24 cm and 18 cm. If one side of the first triangle is 8 cm then corresponding side of other triangle is
The perimeter of a rhombus is 52 cm, if its one diagonal is 24 cm then the length of its other diagonal is
In the figure \(OB = 13\) cm, \(OP⊥AB\), \(OP=12\) cm then \(AB =\)
OB = 13 cm
The angle of elevation of the top of a tower, whose height is 100 m, at a point whose distance from the base of the tower is 100 m is