List of top Mathematics Questions

Factorise 
  1.  \(4p^ 2 - 9q ^2\) 
  2.  \(63a^ 2 - 112b ^2\) 
  3.  \(49x^ 2 - 36\) 
  4.  \(16x^ 5 - 144x^ 3\)
  5.  \((l + m)^ 2 - (l - m) ^2\) 
  6.  \(9x^ 2 y^ 2 - 16 \)
  7.  \((x^ 2 - 2xy + y^ 2 ) - z^ 2\) 
  8.  \(25a ^2 - 4b^ 2 + 28bc - 49c ^2\)
Convert each part of the ratio to percentage: 
  1.  3:1 
  2.  2:3:5 
  3.  1:4 
  4.  1:2:5
If A is n $\times$ n matrix, then adj (adj A) =
The interval in which \(y=x^2e^{-x}\) is increasing is
Let f: R→R be defined as f(x) = 3x. Choose the correct answer.
When a die is thrown, list the outcomes of an event of getting 
  1. (a) a prime number (b) not a prime number. 
  2. (a) a number greater than 5 (b) a number not greater than 5.
In a city, 30% are females, 40% are males and remaining are children. What per cent are children?
If \( y = 5\cos x - 3\sin x \), then \( \frac{d^2y}{dx^2} + y \) equals:
The integral of \( \sec^{2/3}x \csc^{4/3}x \, dx \) from \( \pi/6 \) to \( \pi/3 \) is equal to:
The value of \( \sin(\cot^{-1}(x)) \) is:
A function \( f : \mathbb{R}_+ \to \mathbb{R} \) (where \( \mathbb{R}_+ \) is the set of all non-negative real numbers) defined by \( f(x) = 4x + 3 \) is:
Find: \[ \int \frac{x^2}{(x^2 + 4)(x^2 + 9)} \, dx. \]
If \( P(A | B) = P(A' | B) \), then which of the following statements is true?
Write seven consecutive composite numbers less than 100 so that there is no prime number between them.

Find the value of :

  1. 9.756 – 6.28
  2. 21.05 – 15.27
  3. 18.5 – 6.79
  4. 11.6 – 9.847
Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\
Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\
All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is: \\ \\
If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.
Let A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} and D = {5, 6, 7, 8}. Verify that
  1. A x (B ∩C) = (A x B) ∩(A x C)
  2. A x C is a subset of B x D

∆ABC is an isosceles triangle in which AB = AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that ∠ BCD is a right angle.

∆ABC is an isosceles triangle in which AB = AC.

Find: 
  1.  15% of 250 
  2.  1% of 1 hour 
  3.  20% of Rs 2500 
  4.  75% of 1 kg
Find the integrals of the function: \(cos\, 2x\, cos\, 4x\, cos\, 6x\)
Aakash bought vegetables weighing 10 kg. Out of this, 3 kg 500 g is onions, 2 kg 75 g is tomatoes and the rest is potatoes. What is the weight of the potatoes?
The following table gives the lifetimes of 400 neon lamps: 

Length (in hours) 

Number of lamps 

300 − 400     

14

400 − 500

56

500 − 600

60

600 − 700

86

700 − 800

74

 800 − 900

62

900 − 1000

48


(i) Represent the given information with the help of a histogram. 
(ii) How many lamps have a lifetime of more than 700 hours?