List of top Mathematics Questions

A function f(x) is given by f(x) = $\frac{5^x}{5^x + 5}$, then the sum of the series $f(\frac{1}{20}) + f(\frac{2}{20}) + \dots + f(\frac{39}{20})$ is equal to:

If the curve $x^2+2y^2 = 2$ intersects the line $x+y=1$ at two points P and Q, then the angle subtended by the line segment PQ at the origin is :

Let A be a fixed point (0, 6) and B be a moving point (2t, 0). Let M be the mid-point of AB and the perpendicular bisector of AB meets the y-axis at C. The locus of the mid-point P of MC is :

Let $f:[0, \infty) \to [0, \infty)$ be defined as $f(x) = \int_0^x [y] dy$, where $[x]$ is the greatest integer less than or equal to $x$. Which of the following is true ?

Let us consider a curve, $y = f(x)$ passing through the point $(-2, 2)$ and the slope of the tangent to the curve at any point $(x, f(x))$ is given by $f(x) + x f'(x) = x^2$. Then :

If \((\sqrt{3} + i)^{100} = 2^{99}(p + iq)\), then p and q are roots of the equation :

If \( \frac{dy}{dx} = \frac{2^x y + 2^y \cdot 2^x}{2^x + 2^{x+y} \log_e 2}, y(0) = 0 \), then for \( y = 1 \), the value of \( x \) lies in the interval :

The area (in sq. units) of the region, given by the set $\{(x, y) \in R \times R \mid x \ge 0, 2x^2 \le y \le 4 - 2x\}$ is :

The equation of the plane passing through the line of intersection of the planes \( \vec{r} \cdot (\hat{i} + \hat{j} + \hat{k}) = 1 \) and \( \vec{r} \cdot (2\hat{i} + 3\hat{j} - \hat{k}) + 4 = 0 \) and parallel to the x-axis is :

Three numbers are in an increasing geometric progression with common ratio \( r \). If the middle number is doubled, then the new numbers are in an arithmetic progression with common difference \( d \). If the fourth term of GP is \( 3 r^2 \), then \( r^2 - d \) is equal to :

A hyperbola passes through the foci of the ellipse $\frac{x^2}{25} + \frac{y^2}{16} = 1$ and its transverse and conjugate axes coincide with major and minor axes of the ellipse, respectively. If the product of their eccentricities is one, then the equation of the hyperbola is:

The value of the integral \( \int_{0}^{1} \frac{\sqrt{x} dx}{(1+x)(1+3x)(3+x)} \) is :

The value of \(2 \sin(\frac{\pi}{8}) \sin(\frac{2\pi}{8}) \sin(\frac{3\pi}{8}) \sin(\frac{5\pi}{8}) \sin(\frac{6\pi}{8}) \sin(\frac{7\pi}{8})\) is :

The function \( f(x) = \dfrac{4x^3 - 3x^2}{6} - 2 \sin x + (2x - 1)\cos x \) :

The value of the integral, \[ \int_{1}^{3} \left[ x^{2} - 2x - 2 \right] \, dx, \] where \( [x] \) denotes the greatest integer less than or equal to \( x \), is:

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m - n = 0 and mn + nl + lm = 0, is :

Let the foot of perpendicular from a point $P(1, 2, -1)$ to the straight line $L: \frac{x}{1} = \frac{y}{0} = \frac{z}{-1}$ be $N$. Let a line be drawn from $P$ parallel to the plane $x + y + 2z = 0$ which meets $L$ at point $Q$. If $\alpha$ is the acute angle between the lines $PN$ and $PQ$, then $\cos \alpha$ is equal to ________.

Let \( f \) be any continuous function on \( [0, 2] \) and twice differentiable on \( (0, 2) \). If \( f(0) = 0, f(1) = 1 \) and \( f(2) = 2 \), then :

Marks: 10–20, 20–30, 30–40, 40–50, 50–60, 60–70, 70–80, 80–90, 90–100
No. of students: 2, 3, 4, 5, 6, 12, 14, 10, 4

X: 1, 2, 3, 4, 5, 6, 7, 8
P(X): 0.15, 0.23, 0.12, 0.10, 0.20, 0.08, 0.07, 0.05