List of top Mathematics Questions

The minimum value of \( f(x) = x + \frac{4}{x + 2} \) is
If \( f(x) = \max \{3 - x, 3 + x, 6\} \) is not differentiable at \( x = a \) and \( x = b \), then \( |a| + |b| = \)
At any point \( (x, y) \) on a curve, if the length of the subnormal is \( (x - 1) \) and the curve passes through \( (1, 2) \), then the curve is a conic. A vertex of the curve is:
The function \( y = Ae^x + Be^{-2x} \) satisfies which of the following differential equations?
\( \int_0^{\pi} x \left( \sin^2(\sin x) + \cos^2(\cos x) \right) dx = \)
Let \( \alpha \) and \( \beta \) (\( \alpha<\beta \)) be roots of \( 18x^2 - 9\pi x + \pi^2 = 0 \), \( f(x) = x^2, g(x) = \cos x \). Then
\[ \int_{\alpha}^{\beta} x (g \circ f(x)) \, dx = ? \]
The parametric form of a curve is \( x = \frac{t^3}{t^2 - 1},\ y = \frac{t}{t^2 - 1} \), then \( \int \frac{dx}{x - 3y} = \)
If \( I_n = \int \tan^n x \, dx \), and \( I_0 + I_1 + 2I_2 + 2I_3 + 2I_4 + I_5 + I_6 = \sum_{k=1}^n \frac{\tan^k x}{k} \), then \( n = \)
The x-intercept of a plane $\pi$ passing through the point $(1, 1, 1)$ is $\dfrac{5}{2}$ and the perpendicular distance from the origin to the plane $\pi$ is $\dfrac{5}{7}$. If the y-intercept of the plane $\pi$ is negative and the z-intercept is positive, then its y-intercept is
If $\displaystyle \lim_{x \to \infty} x^n \log_e x = 0$, then $\log_e 12 =$
Let origin be the centre, $(\pm 3, 0)$ the foci and $\dfrac{3}{2}$ be the eccentricity of a hyperbola. Then the line $2x - y - 1 = 0$
The locus of a variable point whose chord of contact w.r.t. the hyperbola $\dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ subtends a right angle at the origin is
If the tangent at the point $P$ on the circle $x^2 + y^2 + 6x + 6y = 2$ meets the straight line $5x - 2y + 6 = 0$ at a point $Q$ on the y-axis, then the length of $PQ$ is
The pole of the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ with respect to the circle $x^2 + y^2 = c^2$ is
The locus of centers of the circles, possessing the same area and having $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as their common tangent, is
Starting from the point $A(-3,4)$, a moving object touches $2x + y - 7 = 0$ at $B$ and reaches $C(0,1)$. If the object travels along the shortest path, the distance between $A$ and $B$ is
A box contains 100 balls, numbered from 1 to 100. If 3 balls are selected one after the other at random with replacement from the box, then the probability that the sum of the three numbers on the balls selected from the box is an odd number, is
If 6 is the mean of a Poisson distribution, then $P(X \geq 3) =$
In a lottery containing 35 tickets, exactly 10 tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is
The mean deviation about the mean for the following data:
5, 6, 7, 8, 6.9, 13, 12, 15
If the angles of a triangle ABC are in the ratio 1:2:3, then the corresponding sides are in the ratio:
The point of intersection of the lines \[ \vec{r} = 2\vec{b} + t(6\vec{c} - \vec{a}) \quad \text{and} \quad \vec{r} = \vec{a} + s(\vec{b} - 3\vec{c}) \text{ is:} \]
Given vectors $3\vec{a} - 5\vec{b}$ and $2\vec{a} + \vec{b}$ are mutually perpendicular, and so are $\vec{a} + 4\vec{b}$ and $-\vec{a} + \vec{b}$. Find the acute angle between $\vec{a}$ and $\vec{b}$:
Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of the vertices of a triangle $ABC$. Through the vertices, lines are drawn parallel to the sides to form the triangle $A'B'C'$. Then the centroid of $\Delta A'B'C'$ is
In a triangle ABC, $a = 2,\ b = 3,\ c = 4$, then $\tan\left(\dfrac{A}{2}\right) = $ ?