List of practice Questions

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹4989.60. If the cost of whitewashing is ₹20 per square meter, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome

Find:
(i) 4.8 ÷ 10
(ii) 52.5 ÷ 10
(iii) 0.7 ÷ 10
(iv) 33.1 ÷ 10
(v) 272.23 ÷ 10
(vi) 0.56 ÷ 10
(vii) 3.97 ÷ 10

Find:
(i) 2.7 ÷ 100
(ii) 0.3 ÷ 100
(iii) 0.78 ÷ 100
(iv) 432.6 ÷ 100
(v) 23.6 ÷ 100
(vi) 98.53 ÷ 100

Is it possible to have a triangle with the following sides? 

1.  2 cm, 3 cm, 5 cm 
2.  3 cm, 6 cm, 7 cm 
3.  6 cm, 3 cm, 2 cm

Find the value of the unknowns x and y in the following diagrams:

Find the value of the unknown x in the following diagrams:

Find:
(i) 0.4 ÷ 2
(ii) 0.35 ÷ 5
(iii) 2.48 ÷ 4
(iv) 65.4 ÷ 6
(v) 651.2 ÷ 4
(vi) 14.49 ÷ 7
(vii) 3.96 ÷ 4
(viii) 0.80 ÷ 5

Factorise the expressions 

1.  \(ax^2 + bx\) 
2.  \(7p^ 2 + 21q^ 2\) 
3.  \(2x^ 3 + 2xy^2 + 2xz^2\) 
4.  \(am^2 + bm^2 + bn^2 + an^2\) 
5.  \((lm + l) + m + 1\) 
6.  \(y(y + z) + 9(y + z)\) 
7.  \(5y^ 2 - 20y - 8z + 2yz\) 
8.  \(10ab + 4a + 5b + 2\) 
9.  \(6xy - 4y + 6 - 9x\)

A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?

Find the value of the unknown interior angle x in the following figures:

Find:
(i) \(\frac{2}{5}\) ÷ \(\frac{1}{2}\)
(ii) \(\frac{4}{9}\) ÷ \(\frac{2}{3}\)
(iii) \(\frac{3}{7}\) ÷ \(\frac{8}{7}\)
(iv) 2\(\frac{1}{3}\)÷ \(\frac{3}{5}\)
(v) 3 \(\frac{1}{2}\) ÷ \(\frac{8}{3}\)
(vi) \(\frac{2}{5}\) ÷ 1 \(\frac{1}{2}\)
(vii) 3 \(\frac{1}{5}\) ÷ 1 \(\frac{2}{3}\)
(viii) 2 \(\frac{1}{5}\) ÷ 1 \(\frac{1}{5}\)

Find:
(i) \(\frac{7}{3}\) ÷ 2
(ii)\(\frac{4}{9}\)÷ 5
(iii)\(\frac{6}{13}\) ÷ 7
(iv)4\(\frac{1}{3}\) ÷ 3
(v)3\(\frac{1}{2}\) ÷ 4
(vi)4\(\frac{3}{7}\) ÷ 7

Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.
(i) \(\frac{3}{7}\)
(ii) \(\frac{5}{8}\)
(iii) \(\frac{9}{7}\)
(iv) \(\frac{6}{5}\)
(v) \(\frac{12}{7}\)
(vi) \(\frac{1}{8}\)
(vii) \(\frac{1}{11}\)

Draw rough sketches for the following: 

1.  In Δ ABC, BE is a median. 
2.  In Δ PQR, PQ and PR are altitudes of the triangle. 
3.  In Δ XYZ, YL is an altitude in the exterior of the triangle.

In \(\triangle\) \(PQR\), \(D\) is the mid-point of \(\overline {QR}\) . 
\(\overline{PM}\) is _________________. 
\(\overline{PD}\) is _________________. 
Is \(QM\) = \(MR\) ?

What rate gives Rs 280 as interest on a sum of Rs 56,000 in 2 years?

Find the amount to be paid at the end of 3 years in each case: 

1. Principal = Rs 1,200 at 12% p.a. 
2.  Principal = Rs 7,500 at 5% p.a.

Amina buys a book for Rs 275 and sells it at a loss of 15%. How much does she sell it for?

Juhi sells a washing machine for Rs 13, 500. She loses 20% in the bargain. What was the price at which she bought it?

The population of a city decreased from 25,000 to 24,500. Find the percentage decrease.

Arun bought a car for Rs 3,50,000. The next year, the price went upto Rs 3,70,000. What was the percentage of price increase?

Tell what is the profit or loss in the following transactions. Also find profit percent or loss percent in each case. 

1.  Gardening shears bought for Rs 250 and sold for Rs 325. 
2.  A refrigerator bought for Rs 12,000 and sold at Rs 13,500. 
3.  A cupboard bought for Rs 2,500 and sold at Rs 3,000. 
4.  A skirt bought for Rs 250 and sold at Rs 150.

A local cricket team played 20 matches in one season. It won 25% of them. How many matches did they win?

Meeta saves Rs 400 from her salary. If this is 10% of her salary. What is her salary?