List of top Mathematics Questions

Two dice are numbered 1,2,3,4,5,6 and 1,1,2,2,3,3 respectively. They are thrown and the sum of the numbers on them is noted. The probability of getting a sum of 5 will be :
In a single throw of pair of dice, the probability of getting a multiple of 2 on one and a multiple of 3 on the other will be :
From the top of a tower \(h\) meter high, the angle of depression of two objects, which lie on either side of it are \( \alpha \) and \( \beta \). The distance between the two objects is :
Graphically, the two systems of equations \(x+7=0, y-2=0\) and \(x-2=0, y+7=0\) enclose a :
The circumference of a circle is 100 cm. The side of a square inscribed in the circle is :
The least numbers divisible by 2,3,7 and 9 is :
The exponent of 3 in the prime factorisation of 864 is :

In the given figure \( \angle CAB = 90^\circ \) and AD \(\perp\) BC. If AC = 25 cm, AB = 1m and BD = 96.08 cm, then find the value of AD

Visual shows triangle CAB with right angle at A. AD is perpendicular to BC, with D on BC. Labels: AC=25cm, AB=1m. BD=96.08cm is marked on the hypotenuse segment.

If \( \alpha \) and \( \beta \) are the roots of \( 2x^2 - 4x + 1 = 0 \). Then \( \frac{1}{\alpha^2\beta} + \frac{1}{\alpha\beta^2} = \)
If the sum of first \(n\) terms of an A.P. is \( \frac{3n^2}{2} + \frac{5n}{2} \) then its 25th term is :
Sum of all 3 digit natural numbers which are divisible by 13 :
If \( \sin A + \sin^2 A = 1 \), then the value of \( \cos^2 A + \cos^4 A \) is :
A cone, a hemisphere and a cylinder stands on equal bases and have the same height. What is the ratio of their volumes :
If the equation : \( (a^2+b^2)x^2 - 2(ac+bd)x + (c^2+d^2) = 0 \) has equal roots then :
If \(a\) and \(b\) can take values 1,2,3,4. Then the number of the equations of the form : \(ax^2+bx+1=0\) having real roots is :
\( \sin(60^\circ + \theta) - \cos(30^\circ - \theta) \) is equal to :
In figure : AD = 4 cm, BD = 3 cm, CB = 12 cm, then \( \cot\theta = \) Figure description: A composite figure. From options and typical problems, it implies: Triangle ABD is right-angled at D. Triangle ABC is right-angled at B. Angle C is \(\theta\).
If \( \sin 3\theta = \cos(\theta - 6^\circ) \), where \( (3\theta) \) and \( (\theta - 6^\circ) \) are both acute angles then the value of \( \theta \) is :
If \( \sin\alpha \) and \( \cos\alpha \) are the roots of equation : \( ax^2+bx+c=0 \) then \( b^2 = \)
What will be the sum of n terms of the following arithmetic progression if the arithmetic progression is: \( (x-y)^2, (x^2+y^2), (x+y)^2, \ldots\ldots\ldots \) up to n terms:
If \( \tan \theta = \frac{a}{b} \) then \( \frac{a\sin\theta + b\cos\theta}{a\sin\theta - b\cos\theta} = \)
If \( \alpha, \beta \) are the zeroes of the polynomial :
\( f(x) = x^2 - p(x+1) - C \) such that \( (\alpha+1)(\beta+1) = 0 \) then C=
In \( \triangle ABC \) and \( \triangle DEF \), \( \angle A = \angle E = 40^\circ \) and AB : ED = AC : EF and \( \angle F = 65^\circ \) then \( \angle B = ? \)
If \(n\) is any natural number then \(6^n - 5^n\) always ends with :
If \( \csc\theta = 2x \) and \( \cot\theta = \frac{2}{x} \) then \( 2\left(x^2 - \frac{1}{x^2}\right) = ? \)