List of top Mathematics Questions

If | $x^2 - x - 6 | = x + 2$, then the values of $x$ are

If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :

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:

A light ray emerging from the point source placed at $P( 1,3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R (6, 7)$, then the abscissa of $Q$ is:

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

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

The term independent of $x$ in expansion of $\bigg(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\bigg)^{10}$ is

If the x-intercept of some line $L$ is double as that of the line, $3x+4y = 12$ and the $y$-intercept of $L$, is half as that of the same line, then the slope of $L$ is:

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:

If $f(x) = sin\, (sin\, x)$ and $f'' (x) + tan \,x\,f'(x)+ g(x) = 0,$ then $g(x) $ 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 $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of a for which the vectors $\vec{u}=\left(\alpha-2\right)\vec{a}+\vec{b}$ and $\vec{v}=\left(2+3\alpha\right)\vec{a}-3\vec{b}$ are collinear is :

A class has $175$ students. The following data shows the number of students obtaining one or more subjects. Mathematics $100$, Physics $70$, Chemistry $40$; Mathematics and Physics $30$, Mathematics and Chemistry $28$, Physics and Chemistry $23$; Mathematics, Physics and Chemistry $18$. How many students have offered Mathematics alone?

For the reaction $CO ( g )+\left(\frac{1}{2}\right) O _{2}( g ) \longrightarrow CO _{2}( g ), K _{ p } / K _{ c }$ is

The coefficient of the middle term in the expansion of $(2 + 3x)^4$ is :

A cylindrical tub of radius 12 cm contains water up to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. The radius of the ball is

There are two concentric circular track of radii 100m and 102m, respectively . A runs on the inner track and goes once round in 1 min 30 sec while B runs on the outer track in 1 min 32 sec. Who runs faster?

A conical tent is 5m high and the radius of the base of 12m find the slant height if the cost of 1m square canvas is rs 70 find thecost of canvas required to make the tent

In a medical certificate, by mistake a candidate gave his height as 25% more than actual. In the interview panel, he clarified that his height was 55 ft 5 inches. What is the percentage correction made by the candidate from his stated height to his actual height?

The fuel indicator in a car shows \(\frac{1}{5}\)th of the fuel tank as full. When 22 more litres of fuel are poured into the tank, the indicator rests at three-fourth of the full mark. What is the capacity of the fuel tank?

What per cent selling price would be 34% of the cost price if the gross profit is 26% of the selling price?

The present worth of a bill due 7 months hence is ₹1200. If the bill were due at the end of 2\(\frac{1}{2}\)yr, Its present worth would be Z ₹1016. What is the rate per cent of the bill?

If 7% of the total quantity of wheat is lost in grinding when a country has to import 12 million tonne but when only % is lost it can import 3 million tonne, then what is the quantity of wheat grown in the country?

A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by ₹ 20 and that for the first three years, by 61. What is the sum?

Out of 20 consecutive positive integers, two are chosen at random. The probability that their sum is odd is