List of top Mathematics Questions

Write equations for the following statements:
(i) The sum of numbers x and 4 is 9.
(ii) 2 subtracted from y is 8.
(iii) Ten times a is 70.
(iv) The number b divided by 5 gives 6.
(v) Three-fourth of t is 15.
(vi) Seven times m plus 7 gets you 77.
(vii) One-fourth of a number x minus 4 gives 4.
(viii) If you take away 6 from 6 times y, you get 60.
(ix) If you add 3 to one-third of z, you get 30

2, b, c are in A.P. and the range of determinant $\begin{vmatrix}1&1&1\\ 2&b&c\\ 4&b^{2}&c^{2}\end{vmatrix}$ is [2, 16]. Then find range of c is
If \(3x^2-2ax+(a^2+2b^2+2c^2) = 2(ab+bc),\) then a,b,c can be in
Read the bar graph which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:
(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books sold? About 225 books sold?
(iii) In which years were fewer than 250 books sold?
(iv) Can you explain how you would estimate the number of books sold in 1989?
If $f(x) = \sqrt{2x} + \frac{4}{\sqrt{2x}}$ , then $f'(2) $ is equal to
In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?
If y=\(\frac{2\cos2\theta+\cos\theta}{\cos3\theta+\cos^2\theta+\cos\theta}\), Then value of y''+y'+y is
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:
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
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
\(\left( \frac{3^{\frac{1}{5}}}{x}+\frac{2x}{5^\frac{1}{3}} \right)^{12}\)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______.
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].