List of top Mathematics Questions

A student observes the following spinner. What is the probability of obtaining the red colour.

A dice is thrown twice. The probability that 5 will not come up either time is:
Which of the following cannot be the probability of an event?
One card is drawn from a well-shuffled deck of 52 cards. The probability of getting a face card is:
The empirical relationship among the three measures of central tendency (median, mode, and mean) is:
If the median of the series exceeds the mean by 3, then the number by which the mode exceeds its mean is:
If the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower is $30^\circ$, then the height of the tower is :
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q So that OQ=12 cm, height PQ is :

If tangents PA and PB from a point P to a circle with centre O are inclined to each other at angle of $80^\circ$ in the fig, then $\angle POA$ is equal to :

To draw a pair of tangents to a circle which are inclined to each other at an angle of $ 50^\circ $, it is required to draw tangents at end points of those two radii of the circle. What should be the angle between these two radii?
If a cone of height h and a sphere have same radii r and same volume, then r:h will be:
The angle of elevation of a 15 m high tower from a point 15 m away from its foot is:
If \(\sec(7^\circ - 2\alpha) = \csc(5\alpha - 7^\circ)\), then the value of \(\alpha\) is:
The temperature at 12 noon was 10°C above zero. If it decreases at the rate of 2°C per hour until midnight, at what time would the temperature be 8°C below zero? What would be the temperature at mid-night?
List all the elements of the following sets: 
(i) A = {x: x is an odd natural number} 
(ii) B = {x: x is an \(\frac{-1}{2} < x <\frac{ 9}{2}\)  integer,} 
(iii) C = {x: x is an \(x^2 ≤ 4 \) integer, 
(iv) D = {x: x is a letter in the word “LOYAL“} 
(v) E = {x: x is a month of a year not having 31 days} 
(vi) F = {x: x is a consonant in the English alphabet which proceeds k}.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.
If the angle between the hands of a clock be $54^{\circ}$ and the time it reads between $7$ and $8$, find the time indicated by the clock.
The integral part of $(8+3\sqrt{7})^n$ is
Find the.
  1. Probability of the pointer stopping on D in (Question 1-(a))?
  2. Probability of getting an ace from a well shuffled deck of \(52\) playing cards?
  3. Probability of getting a red apple. (See figure below)
Image of Red Apples
If $C_{0}$, $C_{1}$, $C_{2}$, $C_{3}$, $\cdots$ are binomial coefficients in the expansion of $(1 + x)^n$, then $\frac{C_{0}}{3}- \frac{C_{1}}{4}+ \frac{C_{2}}{5}- \frac{C_{3}}{6}+ \cdots$ is equal to
Four writers must write a book containing $17$ chapters. The first and third writer must write $5$ chapters each, the second writer must write $4$ chapters and fourth writer must write three chapters. The number of ways that can be found to divide the book between four writers, is
The sum of the first \( n \) terms of an arithmetic progression is \( S_n = 3n^2 + 2n \). Find the 5th term of the sequence.
If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
Evaluate \( \int_{1}^{2} \frac{1}{x^2} \, dx \).