List of top Mathematics Questions

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
\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)Find which term is constant.
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.
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______.
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:

Add without using number line :
(a) 11 + (– 7)
(b) (– 13) + (+ 18)
(c) (– 10) + (+ 19)
(d) (– 250) + (+ 150)
(e) (– 380) + (– 270)
(f) (– 217) + (– 100)
For 82x - 16.8x + 48 = 0, the sum of values of x is equal to:
Evaluate each of the following:
  1. (–30) ÷ 10
  2. 50 ÷ (–5)
  3. (–36) ÷ (–9)
  4. (– 49) ÷ (49)
  5. 13 ÷ [(–2) + 1]
  6. 0 ÷ (–12)
  7. (–31) ÷ [(–30) + (–1)]
  8. [(–36) ÷ 12] ÷ 3
  9. [(– 6) + 5)] ÷ [(–2) + 1]
Name the types of following triangles: 
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) \(∆ABC\) with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. 
(c) \(∆PQR\) such that PQ = QR = PR = 5 cm. 
(d) \( ∆DEF\) with m\(∠\) D = 90° 
(e) \(∆XYZ\) with m \(∠\)Y = 90° and XY = YZ. 
(f) \(∆LMN\) with m \(∠\)L = 30°, m \(∠\)M = 70° and m \(∠\)N = 80°.
Let,\(f(\theta)=\frac{sin^4\theta+3cos^2\theta}{sin^4\theta+cos^2\theta},\)then range of f(θ) ∈ [a, b]. The sum of infinite G.P., where first term is 64 and common ratio is a/b is equal to:
If $\begin{vmatrix}a&5x&p\\ b&10y&5\\ c&15z&15\end{vmatrix} = 125$, then find the value of $\begin{vmatrix}3a&3b&c\\ x&2y&z\\ p&5&5\end{vmatrix}$

The cost of 4 kg onion,3 kg wheat and 2kg rice is Rs 60.The cost of 2 kg onion,4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

Evaluate\(\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\1&x&x+y \end{vmatrix}\)