List of top Mathematics Questions

If log₁₀10=1, log₁₀100=2, what is the value of log₅125?

The curved surface area of a cylindrical pillar is \(264  m^2\)and its volume is \(924\)\( m^3\)Find the ratio of its diameter to its height

If a²-b² = 8 and a*b = 2, find a⁴+b⁴.

How many terms are in the Arithmetic Progression 20, 25, 30,..., 135, 140?

Area and perimeter of a rectangular field are 2000 sq.m. and 180 m respectively. What is the length and breadth?

If \(cos2\theta+sin\theta= \sqrt{2}cos \theta,Then \ cos\theta-sin \theta=? \)

Given an A.P. whose terms are all positive integers. The sum of its first nine terms is greater than 200 and less than 220. If the second term in it is 12, then its 4th term is :

f \(\int_0 ^a3x^2dx=8\) then find the value of a

A circle cuts a chord of length $4a$ on the x-axis and passes through a point on the y-axis, distant $2b$ from the origin. Then the locus of the centre of this circle, is :

Considering only the principal values of inverse functions, the set $A = \{ x \ge 0 : \tan^{-1} (2x) + \tan^{-1} (3x) = \frac{\pi}{4} \}$

If the angle of elevation of a cloud from a point $P$ which is $25\, m$ above a lake be $30^\circ$ and the angle of depression of reflection of the cloud in the lake from $P$ be $60^\circ$, then the height of the cloud (in meters) from the surface of the lake is :

The logical statement $[\sim (\sim p \vee q) \vee (p \wedge r) \wedge (\sim q \wedge r)]$ is equivalent to:

A student scores the following marks in five tests : $45,54,41,57,43$. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks in six tests is

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is :

The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :

The mean of five observations is $5$ and their variance is $9.20.$ If three of the given five observations are $1, 3$ and $8$, then a ratio of other two observations is :

Let the equations of two sides of a triangle be $3x - 2y + 6 = 0$ and $4x + 5y - 20 = 0$. If the orthocentre of this triangle is at $(1, 1)$, then the equation of its third side is :

The area of the region $A = [(x, y): 0 \leq y \leq x|x|+1$ and $-1 \leq x \leq 1]$ in s units is :

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to :

The pair of equations 2x+3y= 5 and 6x+ky = 12 has no solution if k=

Axis of a parabola lies along $x$-axis. If its vertex and focus are at distances $2$ and $4$ respectively from the origin, on the positive $x$-axis then which of the following points does not lie on it ?

The area (in s units) of the smaller of the two circles that touch the parabola, $y^2 = 4x$ at the point $(1, 2)$ and the x-axis is :