TISSNET 2016

Let share of Meera = Rs. $$x$$

=> Rajiv's share = Rs. $$2x$$ and Suraj's share = Rs. $$6x$$

Total = $$x+2x+6x=900,000$$

=> $$x=\frac{900,000}{9}=Rs.$$ $$100,000$$

=> Ans - (A)

Let rate of interest be $$r\%$$

Amit borrows Rs. 7000 for 3 years and Rs. 10,000 for 5 years

Simple Interest = $$\frac{P\times R\times T}{100}$$

Total interest paid = $$(\frac{7000\times r\times3}{100})+(\frac{10,000\times r\times5}{100})=4615$$

=> $$210r+500r=4615$$

=> $$r=\frac{4615}{710}=6.5\%$$

=> Ans - (C)

Expression : $$(y^2 - 5y + 5)^{(y - 8)(y + 6)} = 1$$

=> $$log(y^2 - 5y + 5)^{(y - 8)(y + 6)} = log(1)$$

=> $$(y-8)(y+6)log(y^2-5y+y)=0$$

Thus, either $$(y-8)=0$$ or $$(y+6)=0$$ or $$log(y^2-5y+5)=0$$

=> $$y=8,-6$$ ---------------(i)

or $$log(y^2-5y+5)=log(1)$$

=> $$y^2-5y+4=0$$

=> $$(y-4)(y-1)-0$$

=> $$y=4,1$$ -----------(ii)

Also, $$y^2-5y+5$$ can be equal to -1, and the power will be even; thus, it can be equal to 1.

$$y^2-5y+5$$ = -1

$$y^2-5y+6$$ = 0

y = 2 or 3

When y = 2, power will be(y-8)(y+6) = -48 even power, hence = 1

When y = 3, power will be 45 odd power, hence = -1

Thus, y = 2 also satisfies the condition.

From equations (i) and (ii), Possible values of $$y$$ (natural number) = 4

=> Ans - (A)

Expression : $$\log_2 \log_2 \log_3 \log_3 27^3$$

= $$\log_2 \log_2 \log_3 \log_3 (3)^9$$

= $$\log_2 \log_2 \log_3 9$$

= $$\log_2 \log_2 \log_3 (3)^2$$

= $$\log_2 \log_2 2$$

= $$\log_2 1=0$$

=> Ans - (A)

Group 1 Can be selected in $$C^9_3 = \frac{9\times8\times7}{1\times2\times3}=84$$ ways

Group 2 Can be selected in $$C^6_3 = \frac{6\times5\times4}{1\times2\times3}=20$$ ways

Group 3 Can be selected in $$C^3_3 = 1$$ way

=> Total number of ways = $$\frac{84\times20\times1}{3!}$$

= $$14\times20=280$$ ways

=> Ans - (C)

$$AA = \left\{x \mid x \in N, x < 5\right\}$$

=> $$AA=\left\{1,2,3,4\right\}$$

$$BB = \left\{x \mid x \in N, x^2 < 25\right\}$$

=> $$BB=\left\{1,2,3,4\right\}$$

Thus, both sets contain same elements, hence AA = BB

=> Ans - (A)

From the table,

Expenditure for Cement in 2014 = 2628

$$\therefore\ $$Angle sub-divided by Expenditure in the pie-chart = $$\frac{2628}{3018+2628+312+204+16}\times360^{\circ}$$

$$=\frac{2628}{6178}\times360^{\circ}$$

$$=153^{\circ\ }$$

$$=150^{\circ\ }$$  (approximately)

Total interest and net profit in 2014 = 312+67+16+198 = 593

Total interest and net profit in 2015 = 312 -10 +66+220 = 588

Percentage change = 5/593 = 1 % decrease

From the graph,

Exports in 2000 = 6

Exports in 2001 = 30

$$\therefore\ $$The percentage increase in exports from 2000 to 2001= $$\frac{30-6}{6}\times100=\frac{24}{6}\times100=$$ 400%

In year 4, year 6 and year 7 there is rise in the exports of leather. Only in the year 3, there is fall in the exports of leather.

$$\therefore\ $$In year 3, the exports of leather fall the most.

Hence, the correct answer is Option C