List of top Mathematics Questions

A variable plane $ \frac{x}{a}+ \frac{y}{b}+ \frac{z}{c} =1$ at a unit distance from origin cuts the coordinate axes at A. Band C. Centroid (x, y, z) satisfies the equation $ \frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2} =K.$ The value of K is
If $\int_{sin x}^1 \, t^2 f(t) dt =1-sin x, \forall x \in (0,\pi/2), \, then \, f\bigg(\frac{1}{\sqrt 3}\bigg)$ is
If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is
The number of ordered pairs $(\alpha, \beta), $ where $\alpha, \beta \in(-\pi, \pi)$ satisfying cos $(\alpha-\beta)=1 and cos (\alpha+\beta)=\frac{1}{e}$ is
In a $\triangle$ ABC, among the following which one is true?
Let $f (x) = ax^2 + bx + c, a \ne 0$ and $\Delta =b^2 -4ac.$ If $a+ \beta,$ $a^2+ \beta^2$ and $a^3+ \beta^3$ are in GP, then
The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is
The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by
The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is
If f (x) is continuous and differentiable function and f (1/n) = 0 $\forall$ n $\ge$ 1and n $\in$ I, then
The value of $Cos (270^\circ +\theta )Cos (90^\circ - \theta ) - Sin (270^\circ - \theta )Cos \theta$ is
In a class, 40% of the boys is same as 1/2 of the girls and there are 20 girls. Total number of students in the class is
A man bets on number 16 on a roulette wheel 14 times and loses each time. On the 15th spin, he does a quick calculation and finds out that the number 12 had appeared twice in the 14 spans and is therefore unable to decide whether to bet on 16 or 12 in the 15th spin Which will give him the best chance and what are the odds of winning on the bet that he takes? (Roulette has numbers 1 to 36).
The sum of two numbers is 462 and their highest common factor is 22. What is the maximum number of pairs that satisfy these conditions?
Ten points are marked on a straight line and eleven points are marked on another straight line. How many triangles can be constructed with vertices from among the above points?
The number of boys is more than the number of girls by 12% of the total strength of the class. The ratio of the number of boys to that of the girls is
If a% of x is equal to b% of y, then c% of y is what % of x?
A person has deposited Rs. 13,200 in a bank which pays 14% inferest. He withdraws the money and invests in Rs. 100 stock at Rs. 110 which pays a dividend of 15%. How much does he gain or lose?
The ages of the two persons differ by 20 years. If 5 years ago, the older one be 5 times as olas the younger one, then their present ages, in years, are
A mail-sorting clerk is given 4 envelopes addressed to different people and 4 letters. She has to carefully put the letters in the correct envelopes and then mail them. However, she carelessly puts any letter in any envelope, making sure that each envelope has precisely one of those 4 letters. What is the likelihood that all the letters are in the correct envelope?
If Dennis is 1/3rd the age of his father Keith now, and was 1/4th the age of his father 5 years ago, then how old will his father Keith be 5 years from now?
In the given diagram, two circles pass through each other's centre. If the radius of each circle is 2, then what is the perimeter of the region marked B?
Two Overlap Circles
Cloth Makers Inc. has p spindles, each of which can produce q metres of cloth on an average in r minutes. If the spindles are made to run with no interruption, then how many hours will it take for 20,000 meters of cloth to be produced?
A certain number of people were supposed to complete a work in 24 days. The work, however, took 32 days, since 9 people were absent throughout. How many people were supposed to be working originally?
The LCM of two numbers is 280 and their ratio is 7: 8. The two numbers are