List of top Mathematics Questions asked in CBSE Class VII

Give first the step you will use to separate the variable and then solve the equation:
(a) x – 1 = 0
(b) x + 1 = 0
(c) x – 1 = 5
(d) x + 6 = 2
(e) y – 4 = – 7
(f) y – 4 = 4
(g) y + 4 = 4
(h) y + 4 = – 4

Complete the last column of the table
S. No.EquationValueSay, whether the Equation No. is Satisfied. (Yes/ No)
(i)x + 3 = 0x = 3 
(ii)x + 3 = 0x = 0 
(iii)x + 3 = 0x = – 3 
(iv)x – 7 = 1x = 7 
(v)x – 7 = 1x = 8 
(vi)5x = 25x = 0 
(vii)5x = 25x = 5 
(viii)5x = 25x = – 5 
(ix)\(\frac{m}{3}=2\)m = – 6 
(x)\(\frac{m}{3}=2\)m = 0 
(xi)\(\frac{m}{3}=2\)m = 6 
Compare the following numbers: 
  1. \( 2.7 × 10^{12 }\); \(1.5 × 10^8\) 
  2.  \(4 × 10^{14}\) ; \(3 × 10^{17}\)
Simplify: 
  1.  \((– 4)^3\) 
  2. \((–3) × (–2)^3\) 
  3.  \((–3)^2 × (–5)^2\) 
  4.  \((–2)^3 × (–10)^3\)
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
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?

Number of children in six different classes are given below. Represent the data on a bar graph.

(a) How would you choose a scale?
(b) Answer the following questions:
(i) Which class has the maximum number of children? And the minimum?
(ii) Find the ratio of students of class sixth to the students of class eight.

Use the bar graph to answer the following questions.
(a) Which is the most popular pet?
(b) How many students have dog as a pet?
Find the mode and median of the data: 13, 16, 12, 14, 19, 12, 14, 13, 14
The weights (in kg.) of 15 students of a class are: 38, 42, 35, 37, 45, 50, 32, 43, 43, 40, 36, 38, 43, 38, 47
(i) Find the mode and median of this data.
(ii) Is there more than one mode?
The runs scored in a cricket match by 11 players is as follows: 6, 15, 120, 50, 100, 80, 10, 15, 8, 10, 15
Find the mean, mode and median of this data. Are the three same?
The scores in mathematics test (out of 25) of 15 students is as follows: 19, 25, 23, 20, 9, 20, 15, 10, 5, 16, 25, 20, 24, 12, 20 Find the mode and median of this data. Are they same?
A bulb is kept burning just right above the following solids. Name the shape of the shadows obtained in each case. Attempt to give a rough sketch of the shadow. (You may try to experiment first and then answer these questions).
(i)A ball (iI) A cylindrical(iii) pipe A book