List of top Mathematics Questions asked in CBSE Class VII

Fill in the boxes with the correct symbol out of >, <, and =.
(i) -\(\frac{5}{7}\)__ \(\frac{2}{3}\) (ii) -\(\frac{4}{5}\)__-\(\frac{5}{7}\) (iii) -\(\frac{7}{8}\) __\(\frac{14}{-16}\) (iv) \(\frac{-8}{5}\) __\(\frac{-7}{4}\)(v) \(\frac{1}{-3}\) __\(\frac{-1}{4}\) (vi)\(\frac{5}{-11}\) __\(\frac{-5}{11}\) (vii) 0__ \(\frac{-7}{6}\)
Rewrite the following rational numbers in the simplest form:
(i) \(\frac{-8}{6}\) (ii) \(\frac{25}{45}\) (iii) \(\frac{-44}{72}\) (iv) \(\frac{-8}{10}\)
The points P, Q, R, S, T, U, A and B on the number line are such that, TR = RS = SU and AP = PQ = QB. Name the rational numbers represented by P, Q, R and S.
TR = RS = SU
Which of the following pairs represent the same rational number?
(i) \(\frac{-7}{21} \space and \frac{3}{9}\)

(ii) \(\frac{-16}{20}\space and\space  \frac{20}{-25}\)

(iii) \(\frac{-2}{-3}\space and \space \frac{2}{3}\)

(iv) \(\frac{-3}{5} \space and \space \frac{-12}{20}\)

(v) \(\frac{8}{-5}\space and \space \frac{-24}{15}\)

(vi) \(\frac{1}{3}\space and\space  \frac{-1}{9}\)

(vii) \(\frac{-5}{-9}\space and \space \frac{5}{-9}\)

Solve the following:
(i) Irfan says that he has 7 marbles more than five times the marbles Parmit has. Irfan has 37 marbles. How many marbles does Parmit have?
(ii)  Laxmi’s father is 49 years old. He is 4 years older than three times Laxmi’s age. What is Laxmi’s age?
(iii) People of Sundergram planted a total of 102 trees in the village garden. Some of the trees were fruit trees. The number of non-fruit trees was two more than three times the number of fruit trees. What was the number of fruit trees planted?

Solve the following:
(a) The teacher tells the class that the highest marks obtained by a student in her class are twice the lowest marks plus 7. The highest score is 87. What is the lowest score?
(b) In an isosceles triangle, the base angles are equal. The vertex angle is 40°. What are the base angles of the triangle? (Remember, the sum of three angles of a triangle is 180°.)
(c) Sachin scored twice as many runs as Rahul. Together, their runs fell two short of a double century. How many runs did each one score?

Give four rational numbers equivalent to:
(i)\(\frac{-2}{7}\)
(ii) \(\frac{5}{-3}\)
(iii) \(\frac{4}{9}\)
Write four more rational numbers in each of the following patterns:
(i) \(\frac{-3}{5},\frac{-6}{10},\frac{-9}{15},\frac{-12}{20}\)...

(ii) \(\frac{-1}{4},\frac{-2}{8},\frac{-3}{12},\)...

(iii) \(\frac{-1}{6},\frac{2}{-12},\frac{3}{-18},\frac{4}{-24}\),....

(iv)\(\frac{-2}{3},\frac{2}{-3},\frac{4}{-6},\frac{6}{-9}\),...
Give first the step you will use to separate the variable and then solve the equation: 
(a) 3l = 42 
(b) \(\frac{b}{2}\)= 6 
(c) \(\frac{p}{7}\) = 4 
(d) 4x = 25 
(e) 8y = 36 
(f) \(\frac{z}{3}\)=\(\frac{5}{4}\)
(g) \(\frac{a}{5}\)=\(\frac{7}{15}\)
(h) 20t = – 10
List five rational numbers between:
(i) –1 and 0
(ii) –2 and –1
(iii)\(\frac{-4}{5} \space and \frac{-2}{3}\)

(iv) \(\frac{-1}{2}\space and \frac{2}{3}\)
Give the steps you will use to separate the variable and then solve the equation:
(a) 3n – 2 = 46 
(b) 5m + 7 = 17 
(c) \(\frac{20p}{3}\) =40
(d) \(\frac{3p}{10}\)=6

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

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