NICL Assistant Online Exam 2015 Question paper

Let time taken by the car to reach city B by travelling at 60 km/hr = $$t$$ hrs

=> Time taken to reach city B by travelling at 50 km/hr = $$(t + \frac{16}{60})$$ hrs

$$\because spped \propto \frac{1}{time}$$

=> $$\frac{s_1}{s_2} = \frac{t_2}{t_1}$$

=> $$\frac{60}{50} = \frac{t + \frac{16}{60}}{t}$$

=> $$6t = 5t + \frac{16}{12}$$

=> $$6t - 5t = t = \frac{4}{3}$$ hrs

$$\therefore$$ Distance between city A & B = speed $$\times$$ time

= $$60 \times \frac{4}{3} = 80$$ km

Let side of square = $$a$$ m

=> Area of square = $$a^2 = 784$$

=> $$a = \sqrt{784} = 28$$ m

=> Diagonal of square = $$\sqrt{28^2 + 28^2} = 28 \sqrt{2}$$ m = Diameter of circle

=> Radius of circle = $$\frac{28 \sqrt{2}}{2} = 14 \sqrt{2}$$ m

$$\therefore$$ Area of circle = $$\pi r^2$$

= $$\frac{22}{7} (14 \sqrt{2})^2 = 22 \times 28 \times 2$$

= $$1232 m^2$$

Let price of 1 register = $$Rs. x$$

=> Price of book = $$Rs. (x + 124)$$

Acc. to ques, => $$8 (x + 124) + 24x = 1760$$

=> $$8x + 992 + 24x = 1760$$

=> $$32x = 1760 - 992 = 768$$

=> $$x = \frac{768}{32} = 24$$

Thus, price of book = $$24 + 124 = 148$$

$$\therefore$$ Total price of 4 books and 2 registers

= $$(4 \times 148) + (2 \times 24)$$

= $$592 + 48 = Rs. 640$$

Expression : $$\frac{1.12 \times 2.24 - 0.78 \times 1.56}{4 \times (1.12 - 0.78)} = ?$$

= $$\frac{2 (1.12)^2 - 2 (0.78)^2}{4 (1.12 - 0.78)}$$

= $$\frac{2 (1.12 - 0.78) (1.12 + 0.78)}{4 (1.12 - 0.78)}$$     [Using, $$a^2 - b^2 = (a - b) (a + b)$$]

= $$\frac{1.12 + 0.78}{2}$$

= $$\frac{1.9}{2} = 0.95$$

Expression : $$29^{2} - 435 + ?= 1652 \times 0.5$$

=> $$841 - 435 + x = 826$$

=> $$x = 826 - 406$$

=> $$x = 420$$

Expression : $$10 (1024.8 + 24.6 - 4.2) = ?^{2} + 48$$

=> $$10 \times 1045.2 = (x)^2 + 48$$

=> $$(x)^2 = 10452 - 48 = 10404$$

=> $$x = \sqrt{10404} = 102$$

Expression : $$(\frac{1\frac{7}{60}}{1\frac{27}{40}})\times(1\frac{29}{34})\times? = 231$$

=> $$\frac{\frac{67}{60}}{\frac{67}{40}} \times (\frac{63}{34}) \times x = 231$$

=> $$\frac{40}{60} \times (\frac{63}{34}) \times x = 231$$

=> $$\frac{2}{3} \times (\frac{63}{34}) \times x = 231$$

=> $$\frac{21}{17} \times x = 231$$

=> $$x = 231 \times \frac{17}{21}$$

=> $$x = 11 \times 17 = 187$$

Expression : (0.6 + 0.4 + 10) (0.8 - 0.4 + 10) = ?

= $$11 \times 10.4$$

= $$114.4$$

Expression : $$(\frac{42.25}{0.5}+\frac{16.2}{0.2})\times?=1986$$

=> $$(84.5 + 81) \times x = 1986$$

=> $$165.5 \times x = 1986$$

=> $$x = \frac{1986}{165.5} = 12$$