List of top Mathematics Questions

If the fractional part of the number $\frac{2^{403}}{15}$ is $\frac{k}{15}$, then $k$ is equal to :

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =

A tangent is drawn from an external point P to a circle of 8 cm radius. If the length of the tangent is 15 cm then the distance between the centre of the circle and point P is

The number of integral values of m for which the equation $(1 + m^2)x^2 - 2(1 + 3m)x + (1 + 8m) = 0$ has no real root is :

The outcome of each of $30$ items was observed; $10$ items gave an outcome $\frac{1}{2} - d$ each, $10$ items gave outcome $\frac{1}{2}$ each and the remaining 10 items gave outcome $\frac{1}{2} + d$ each. If the variance of this outcome data is $\frac{4}{3}$ then |d| equals :

If the side of a square increases by 30% its area increases by:

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

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

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

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

If the points (2a, a),(a,2a), and (a, a) enclose a triangle of area 18 square units. Then the centroid of the triangle is:

A salesman has a 70% chance to sell a product to any customer. The behavior of successive customers is independent. If two customers A and B enter, what is the probability that the salesman will sell the product to customer A or B?

Find the value of log_y(x⁴) if log_x(y³) = 2

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

A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole workalone?

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

Sarthak bought 7 new trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 31 cards left. How many cards did Sarthak start with ?

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

If \(tan ^{-1}(sinx)=\frac{\pi}{4}\),then the value of \(x\) is: