List of top Mathematics Questions

Let $A (-3,2)$ and $B (-2,1)$ be the vertices of a triangle $ABC$. If the centroid of this triangle lies on the line $3x + 4y+2 = 0$, then the vertex $C$ lies on the line :

Let $a=Im\left(\frac{1+z^{2}}{2iz}\right),$ where $z$ is any non-zero complex number. The set $A=\left\{a:\left|z\right|=1\,and\,z\ne\pm1\right\}$ is equal to:

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

Let $x \in \left(0,1\right).$ The set of all x such that $sin^{-1} x >\, cos^{-1} x, $ is the interval:

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$

The integral $\int \frac{xdx}{2-x^{2}+\sqrt{2-x^{2}}}$ equals

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of $n$ is

The line $x - 2y = 2$ meets the parabola, $y^2 + 2x = 0$ only at the point $(- 2,-2)$. The line $ y=mx-\frac{1}{2m}\left(m\ne0\right)$ is tangent to the parabola, $y^{2} = - 2x$ at the point $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

The cost of running a bus from $A$ to $B$ , is $Rs.\left(av+\frac{b}{v}\right)$ where $v$ km/h is the average speed of the bus. When the bus travels at $30\, km/h$, the cost comes out to be $Rs.\, 75$ while at $40\, km/h$, it is $Rs. \,65$. Then the most economical speed (in $km/ h$) of the bus is :

The maximum area of a right angled triangle with hypotenuse $h$ is :

The real number $k$ for which the equation $2x^3 + 3x + k = 0$ has two distinct real roots in $[0, 1]$

On the sides $AB, BC, CA$ of a $\Delta ABC, 3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices a re :

Find the variance of the data given below \[ \text{Size of item:} \quad 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5 \\ \text{Frequency:} \quad 3, 7, 22, 60, 85, 32, 8 \]

The determinant \[ \left| \begin{matrix} 1 & x & x^2 \\ 1 & x^3 & x^4 \\ 1 & x^5 & x^6 \end{matrix} \right| \] vanishes for

If \( f(x) = \begin{cases} \frac{x^2 + 3x - 10}{x^2 + 2x - 15}, & x \neq -5 \\ a, & x = -5 \end{cases} \) is continuous at \( x = -5 \), then the value of \( a \) will be

A shopkeeper wants to purchase two articles A and B of cost price \( 4 \) and \( 3 \) respectively. He thought that he may earn 30 paise by selling article A and 10 paise by selling article B. He has not to purchase total articles worth more than \( 24 \). If he purchases the number of articles of A and B, \( x \) and \( y \) respectively, then linear constraints are

An object is observed from the points A, B and C lying in a horizontal straight line which passes directly underneath the object. The angular elevation at A is \( \theta \), at B is \( 2\theta \), and at C is \( 3\theta \). If AB = a, BC = b, and the height of the object is h, then the height of the object is

The probability of India winning a test match against West Indies is \( \frac{1}{2} \). Assuming independence from match to match, the probability that in a 5 match series India’s second win occurs at the third test is

The coordinates of the point where the line through the points \( A(3, 4, 1) \) and \( B(5, 1, 6) \) crosses the \( XY \)-plane are

If vectors \( 2i + j + k \), \( 2j - 3k \), and \( 3i + j + 5k \) are coplanar, then the value of \( a \) is

Find the angle between the two planes \( 2x + y - 2z = 5 \) and \( 3x - 6y - 2z = 7 \).