List of top Mathematics Questions

Simplify: 
  1.  \(2 × 10^3\) 
  2.  \(7^ 2 × 2^2\) 
  3.  \(2^ 3 × 5\) 
  4.  \(3 × 4^4\) 
  5.  \(0 × 10^2\) 
  6.  \(5^ 2 × 3^3\) 
  7.  \(2^ 4 × 3^2\) 
  8.  \(3^ 2 × 10^4\)
Express each of the following as product of powers of their prime factors: 
  1.  648 
  2.  405 
  3.  540 
  4.  3,600
Identify the greater number, wherever possible, in each of the following? 
  1. \(4 ^3\) or \(3^4\) 
  2.  \(5 ^3\) or \(3^5\) 
  3.  \(2 ^8\) or \(8^2\) 
  4.  \(100^2\) or \(2^{100}\) 
  5.  \(2 ^{10}\) or \(10^{2}\)
Express the following in exponential form:
  1. 6 × 6 × 6 × 6
  2.  t × t
  3.  b × b × b × b
  4.  5 × 5× 7 × 7 × 7
  5.  2 × 2 × a × a
  6.  a × a × a × c × c × c × c × d
Express each of the following numbers using exponential notation: 
  1.  512 
  2.  343 
  3.  729 
  4.  3125

Find the value of: 

  1.  \(2^6\) 
  2.  \(9 ^3\) 
  3.  \(11^2\) 
  4.  \(5 ^4\)
The diagonals of a rhombus measure \(16\) \(cm\) and \(30\) \(cm\). Find its perimeter.

Find the perimeter of the rectangle whose length is \(40\) \(cm\) and a diagonal is \(41\) \(cm\).

Angles \(Q\) and \(R\) of a \(Δ\) \(PQR\) are \(25°\) and \(65°\). Write which of the following is true: 
  1.  \(PQ^2 + QR^2= RP^2\) 
  2.  \(PQ^2 + RP^2= QR^2\) 
  3.  \(RP^2 + QR^2= PQ^2\)

triangle PQR

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the original height of the tree.
A tree is broken at a height of 5 m from the ground
Which of the following can be the sides of a right triangle? 
  1.  2.5 cm, 6.5 cm, 6 cm 
  2.  2 cm, 2 cm, 5 cm 
  3.  1.5 cm, 2 cm, 2.5 cm 

In the case of right-angled triangles, identify the right angles.

A 15 m long ladder reached a window 12 m high from the ground on placing it against a wall at a distance a. Find the distance of the foot of the ladder from the wall.
15 m long ladder
In a culture,the bacteria count is 1,00,000.The number is increased by \(10\%\) in 2 hours. In how many hours will the count reach 2,00,000,if the rate of growth of bacteria is proportional to the number present?
In a bank,principal increases continuously at the rate of \(5\%\) per year. An amount of Rs1000 is deposited with this bank,how much will it worth after 10years\((e^{0.5}=1.648)\).
In a bank principal increases continuously at the rate of \(r\%\) per year.Find the value of \(r\) is Rs100 doubles itself in 10years\((log_e2=0.6931).\)
At any point \((x,y)\) of a curve,the slope of a tangent is twice the slope of the line segment joining the point of contact to the point \((-4,-3)\).Find the equation of the curve given that it passes through \((-2,1)\).
Find the equation of a curve passing through the point \((0,-2)\) given that at any point \((x,y)\) on the curve,the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.

Find the equation of the curve passing through the point \((0,\frac \pi4) \)whose differential equation is, \(sin\ x cos \ y\ dx+cos\ xsin\  y\ dy=0\)

Find the equation of a curve passing through the point \((0,2)\) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5.
For the differential equations, find a particular solution satisfying the given condition:\(cos(\frac{dy}{dx})=α(α∈R);y=1\) when x=0
State whether the following statements are True or False:
  1. The sum of three odd numbers is even.
  2. The sum of two odd numbers and one even number is even.
  3. The product of three odd numbers is odd.
  4. If an even number is divided by 2, the quotient is always odd.
  5. All prime numbers are odd.
  6. Prime numbers do not have any factors.
  7. Sum of two prime numbers is always even.
  8. 2 is the only even prime number.
  9. All even numbers are composite numbers.
  10. The product of two even numbers is always even.
What is the sum of any two
  1. Odd numbers?
  2. Even numbers?
Find all the multiples of 9 upto 100.
Check whether the value given in the brackets is a solution to the given equation or not:
(a) n + 5 = 19 (n = 1)
(b) 7n + 5 = 19 (n = – 2)
(c) 7n + 5 = 19 (n = 2)
(d) 4p – 3 = 13 (p = 1)
(e) 4p – 3 = 13 (p = – 4)
(f) 4p – 3 = 13 (p = 0)
Consider this data collected from a survey of a colony.
ata collected from a survey of a colony
(i) Draw a double bar graph choosing an appropriate scale. What do you infer from the bar graph?
(ii) Which sport is most popular?
(iii) Which is more preferred, watching or participating in sports?