List of top Mathematics Questions

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:
The value of \( \lim_{x \to 0} \frac{ax^3 + bx^2 + cx}{3x^2} \), where \( a, b, c > 0 \), is:
Find the center and radius of the circle given by the equation \( 2x^2 + 2y^2 + 3x + 4y + 9 = 0 \).
What will be the equation of the circle whose center is \( (1, 2) \) and touches the X-axis?
Evaluate: \( 8^{\log_5 5} \)
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
If \(\cot \theta = \frac{b}{a}\) then \(\frac{\cos \theta + \sin \theta}{\cos \theta - \sin \theta}\)=
The value of \(\frac{1 - \tan^2 45^\circ}{1 + \tan^2 45^\circ}=\)
If \(\tan \theta = \cot \theta\) then the value of \(sec\ θ \)=
The ratio of volumes of two cones is 4:5 and the ratio of the radii of their bases is 2:3 then the ratio of their vertical height is
In the figure \(OB = 13\) cm, \(OP⊥AB\), \(OP=12\) cm then \(AB =\)
OB = 13 cm
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 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
The radius of a cone is 7 m and its height is 10 m. Then its slant height is______