List of top Mathematics Questions

If y=\(\frac{2\cos2\theta+\cos\theta}{\cos3\theta+\cos^2\theta+\cos\theta}\), Then value of y''+y'+y is
A line L is perpendicular to y = 2x + 10 such that it touches the parabola y2 = 4(x – g). Then the distance between point of contact and origin is equal to
Area bounded by y = -2|x| and y = x|x| is:
If |a| = 2, |b| = 3 and a = b × 2, then minimum value of \(|\hat{c} - a|^2\) is:
Consider the equation ax2 + bx + c = 0 . Find probability if a, b, c ∈ A where A = {1,2,3, ... , 8} that the equation has equal roots.
Consider a equation  P(x)= ax2 + bx + c =0. If a,b,c ∈ A, were A = {1, 2, 3, 4, 5, 6} . Then the probability that P(x) has real and distinct roots?
If S = {2, 4, 8, 16, ..., 512}. If S is broken in 3 equal subsets A, B and C such that A∩B = B∩C = C∩A = φ and A∪B∪C = S then maximum number of ways to break is
A=\(\begin{bmatrix}   \alpha & \alpha & \alpha \\   \beta & \alpha & -\beta \\   -\alpha & \alpha & \alpha  \end{bmatrix}\)B is formed by co-factor of A matrix, then find out determinant of AB.
\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.
Let image of point(8,5,7) with respect to line \(\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}\) is (α,β,γ). Then, α+β+γ is equal to______.
Carry out the multiplication of the expressions in each of the following pairs.
(i) 4p, q + r
(ii) ab, a – b
(iii) a + b, 7a²b²
(iv) a2 – 9, 4a
(v) pq + qr + rp, 0
Factorise 
  1. \(x^ 2 + xy + 8x + 8y\)
  2.  \(15xy - 6x + 5y - 2 \)
  3.  \(ax + bx - ay - by\) 
  4.  \(15pq + 15 + 9q + 25p\) 
  5.  \(z - 7 + 7xy - xyz\)
In Figure, if x + y = w + z, then prove that AOB is a line.
x + y = w + z
HCF of co-prime numbers 4 and 15 was found as follows by factorisation : 4 = 2 × 2 and 15 = 3 × 5 since there is no common prime factor, so HCF of 4 and 15 is 0. Is the answer correct? If not, what is the correct HCF?

Show that the relation R in the set R of real numbers, defined as
R = {(a, b): a ≤ b2 } is neither reflexive nor symmetric nor transitive.

In Fig, ∠ ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

ABC = 69°, ∠ ACB = 31°, find ∠ BDC.

If f (x) = 3x2+15x+5, then the approximate value of f (3.02) is

A wheel rotates making $20$ revolutions per second. If the radius of the wheel is $35\, cm$, what linear distance does a point of its rim traverse in three minutes? (take $\pi = 22/7$)
If the complex number (1 + 2i cosθ) / (1 - 3i cosθ) is purely imaginary, then find the number of values of θ in the interval [-2π, 2π].
A ray of light coming from (3, 1) incident on 2x + y = 6 and deflected ray passing through (7, 2). If equation of incident ray is ax + by + 1 = 0, then a2 + b2 + 3ab =
If \(\frac{1}{(1+d)(1+2d)}+\frac{1}{(1+2d)(1+3d)}+...+\frac{1}{(1+9d)(1+10d)}=1,\) then the value of 50d is____. (d > 0)
A ray of light passing through (1, 2) after reflecting on x-axis at point Q passes through R(3, 4). If S(h, k) is such that PQRS is a parallelogram, then find the value of hk2.
Use the figure to name : 
Line containing point E
(a) Line containing point E. 
(b) Line passing through A. 
(c) Line on which O lies 
(d) Two pairs of intersecting lines.
A line segment has length 63 and direction ratios, <3, -2, 6>. If the line makes an obtuse angle with x-axis, then the components of the line vector are

Classify each one of the following angles as right, straight, acute, obtuse or reflex:

angles as right, straight, acute, obtuse or reflex: