Q11. (54 ÷ 3 × 16 ÷ 2) / (180 ÷ 5 × 6 ÷ 3) = ?
= (18 × 8) / (36 × 2)
= 144/72
= 2
Q12. किसी संख्या के (3/4) तथा (4/7) का अंतर 100 है वह संख्या क्या होगी ?
माना संख्या = y
(3/4)y – (4/7)y = 100
y(3/4 – 4/7) = 100
y(5/28) = 100
y = 560
Q13. (5/6) ÷ (6/7) × ? – (8/9) ÷ 1 \frac{3}{5} + (3/4) × 3 \frac{1}{3} = 2 \frac{7}{9}
(5/6) ÷ (6/7) × y – (8/9) ÷ (8/5) + (3/4) × (10/3) = 25/9
(35/36)y – (5/9) + (5/2) = 25/9
(35/36)y = 25/9 + (5/9) – (5/2)
(35/36)y = 5/6
y = 6/7
Q14. {[999 \frac{999}{1000} ] × 7} = ?
= (999999/1000) × 7
= 6999993/1000
= 6999.993
Q15. {999 \frac{1}{7} + 999 \frac{2}{7} + 999 \frac{3}{7} + 999 \frac{4}{7} + 999 \frac{5}{7} + 999 \frac{6}{7} = ?
= [999 + 999 + 999 + 999 + 999 + 999] + [1/7 + 2/7 + 3/7 + 4/7 + 5/7 + 6/7]
= 5994 + 3
= 5997
Q16. [2 - (1/3)][2 - (3/5)][2 - (5/7)].......................[2 - (997/999)] = ?
= [5/3][7/5][9/7].......................[999/997][1001/999]
= 1001/3
Q17. [{1 + 1/(10+1/10)} × {1 + 1/(10+1/10)} - {1 - 1/(10+1/10)} × {1 - 1/(10+1/10)} ÷ {1 + 1/(10+1/10)} + {1 - 1/(10+1/10)} = ?
माना a = {1 + 1/(10+1/10)} और b = {1 - 1/(10+1/10)
= [a2 - b2] / (a + b)
= [(a - b)(a + b)] / (a + b)
= (a - b)
= 20/101
Q18. [1 + 1/(x+1)][1 + 1/(x+2)][1 + 1/(x+3)][1 + 1/(x+4)] = ?
= [(x+2)/(x+1)][(x+3)/(x+2)][(x+4)/(x+3)][(x+5)/(x+4)]
= (x+5)/(x+1)
Q19. 1/2 + 1/6 + 1/12 + 1/20 + 1/30 + ................. + 1/n(n+1) = ?
= 1/2 + (1/2 - 1/3) + (1/3 - 1/4) + (1/4 - 1/5) + ................. + [1/n - 1/(n+1)]
= 1/2 + 1/2 - 1/(n+1)
= 1 - 1/(n+1)
= n/(n+1)
Q20. 3/4 + 5/36 + 7/144 + ...................... + 17/5184 + 19/8100 = ?
= (1 - 1/4) + (1/4 - 1/9) + (1/9 - 1/16) + ...................... + (1/64 -1/81) + (1/81 - 1/100)
= (1 - 1/100)
= 99/100
= 0.99
