## Skill Check X: IITJEE Foundation Math

I) Arrange the following decimal fractions in ascending order:

(i) 68.95, 6.985, 9.685, 86.59, 8.695

(ii) 1.36, 1.29, 1.48, 1.26, 1.38

(iii) 5.689, 5.869, 5.896, 5.698, 5.986

(iv) 1.1001, 1.0011, 1.111, 1.0101, 1.1011

(v) 7.8899, 7.9898, 7.9889, 7.9988, 7.8998

II) Add the following decimal fractions:

(i) 7.8 +3.2

(ii) 8.91 + 1.89

(iii) 2.3 + 2.65

(iv) 1.721 + 1.892

(v) 5.867+6.719+3.0018

(vi) 3.468+2.12+1.34464

III) Subtract the following decimal fractions:

(i) 6.9-2.9

(ii) 3.41 – 2.21

(iii) 5.4 – 3.22

(iv) 5.216 – 3.162

(v) 2.0-0.9963

(vi) 8.016-2.98694

IV) Multiply the following decimal fractions:

(i) $5.8 \times 2.5$

(ii) $4.64 \times 0.5$

(iii) $9.5 \times 0.04$

(iv) $2.13 \times 1.65$

(v) $5.68 \times 0.145$

(vi) $2.94 \times 0.3215$

V) Divide the following decimal fractions:

(i) $14.5 \div 2.9$

(ii) $2.1 \div 1.4$

(iii) $14.5 \div 4$

(iv) $19.68 \div 6.15$

(v) $2.028 \div 3.12$

(vi) $1.7019 \div 5.49$

VI) Find the HCF of the following decimal fractions:

(i) 0.72 and 4.8

(ii) 1.092 and 1.176

(iii) 0.21, 0.1925, and 0.175

(iv) 0.286, 0.3718, and 0.3146

VII) Find the LCM of the following decimal fractions:

(i) 4.5 and 0.42

(ii) 0.18 and 0.144

(iii) 2.52, 0.189 and 0.168

(iv) 0.112, 0.8, and 0.48

VIII) Find the greatest decimal fractions that can be divided by 0.33, 0.495 and 0.297 leaving exactly 0.15 as remainder.

IX) Simplify the following expressions:

(a) $(1.52 \hspace{0.1in} of \hspace{0.1in} 3.5 \div 0.8 -4.4) \div 2.5 =0.1$

(b) $(5.025 \div 2.5 + 1.49) \times 1.5 - 1.5 \times 2.5 + 1.5$

(c) $[4.5 +0.4 \{ 7.31 - (2.45 + 3.68 -1.32)\}] +1.1$

(d) $\frac{3.27 \times 0.77}{3.85 \times 2.18}$

(e) $\frac{1.82 \times 2.5}{3.25} - \frac{2.22}{1.85}$

(f) $\frac{0.47 \times 0.81 \times 0.63}{1.62 \times 0.85 \times 2.35} \div \frac{8}{5}$

(g) $\frac{6.84 \times 4.52}{1.808 \times 2.85} - \frac{1.62 \times 8.26}{2.36 \times 2.025}$

(h) $0.3 \div 0.1 - [0.3 + \{ 0.1 \times 0.3 - (0.3 + \overline{0.3-0.1} \hspace{0.1in} of \hspace{0.1in} 0.3)\}]$

X) Simplify the following expressions:

(i) $3.865^{2}-1.135^{2}$

(ii) $1.481^{2} + 2 \times 1.481 \times 0.519 + 0.519^{2}$

(iii) $4.694^{2} - 2 \times 4.694 \times 3.494 +3.494^{2}$

XI) Juno buys 1.00 kg of plasticine at Rs. 35.50 per kg and 0.35 litres of paint at Rs. 142.80 per litre. If he gives the shopkeeper a 100 rupee note, how much change should he get back?

XII) 0.125 part of a peace keeping force are doctors, 0.09375 are engineers, 0.03125 parts are cooks, and the rest are armed soldiers. If the peace-keeping force has 1152 members, how many armed soldiers are in it?

XIII) Gitanjali read 0.25 part of a book on the first day, 0.35 part on the second day, and 160 pages to finish the book on the third day. How many pages were there in the book?

XIV) If i metre is equal to 3.28084 feet, how many feet will 15 metres equal to?

XV) If 2.54 cm made an inch, how many inches will 60.96 cm make?

XVI) 0.4 part of a 9.3 g ornamental chain is made of gold. If the chain is cut into 6 equal pieces how much gold will be there in each piece?

XVII) The perimeter of an isosceles trapezium is 7.07 cm. If its unequal sides measure 1.85 cm, 2.32 cm, how much do its equal sides measure?

XVIII) Mrs Rita gives 0.025 part of her salary as pocket money to her son Vinod every month. Vinod spends 0.8 part of his pocket money and saves the rest. If he saves Rs. 277.50 in three months, how much does Mrs. Rita earn in a month?

XIX) The average earning of three family members A, B and C is Rs. 11240.25. One member B leaves for another town and a new family member D starts earning. The new average earning of A, C and D is now Rs. 10520.50 . If D is earning Rs. 9886.25, how much was B earning?

XX) A petrol pump attendant lowers a 5 m long dip-stick to check the oil-level in an underground tank. For every 0.1 m in height of oil on the dip-stick, there is 1200 liters of oil in the tank. If ).38 part of the dip-stick is wet with oil, how many litres of oil are there in the tank?

Regards,

Nalin Pithwa.

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