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List of top Mathematics Questions

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 :

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.

Probability of the pointer stopping on D in (Question 1-(a))?
Probability of getting an ace from a well shuffled deck of $52$ playing cards?
Probability of getting a red apple. (See figure below)

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 $.

Find the derivative of the function $f(x) = \sqrt{3x^2 + 2x + 1}$.

If $ \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} $, $ \vec{b} = \hat{i} + 2\hat{j} - \hat{k} $, then the angle $ \theta $ between $ \vec{a} $ and $ \vec{b} $ is:

Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:

If $ f(x) = 2x^3 - 3x^2 + 4 $, then the minimum value of $ f(x) $ in the interval $ [0, 3] $ is:

The sum of the first 20 terms of an arithmetic progression is 610. If the first term is 7, what is the common difference?

The integral $ \int (3x^2 - 2x + 1) \, dx $ is:

If $ \tan A + \tan B + \tan C = \tan A \tan B \tan C $ and $ A + B + C = \pi $, then which of the following is true?

Let a, b, c be three distinct positive real numbers such that (2a)^log_^e^a = (bc)^log_^e^b and b^log_^e²= a^log_^e^c. Then 6a + 5bc is equal to _____.

If the roots of the quadratic equation $ x^2 - 6x + k = 0 $ have a difference of 2, find the value of $ k $.

If $ z = 1 + i $, find the modulus of $ z^2 $.