CGL MAINS SCORE BOOSTER QUANT QUIZ-9

If $\alpha$ and $\beta$ are the roots of equation $a^{2}-2 a+$ $4=0$, then what is the equation whose roots are $\frac{\alpha^{3}}{\beta^{2}}$ and $\frac{\beta^{3}}{\alpha^{2}} ?$

Shivani deposited a certain sum of money in a company at $12 \%$ per annum simple interest for 4 years and desisted equal amounts in fixed deposit in a bank for 5 years at $15 \%$ per annum SI. If the difference in the interest from two sources is Rs. 1080 then the sum deposited in each case is:

The number to be added to each of the number $7,16,43,79$ to make the number in proportion is:

The one-meter-wide path is built inside a square park of side $30 \mathrm{~m}$ along its sides. The remaining part of the park is covered by grass. If the total cost of covering by grass is Rs 1176, find the rate per square meter at which the park is covered by the grass.

A vertically straight tree, $15 \mathrm{~m}$ high, is broken by the wind in such a way that it tops just touches the ground and makes an angle of $60^{\circ}$ with the ground. At what height from the ground did the tree break?

$\mathrm{A}$ and $\mathrm{B}$ are gamblers. Last year the ratio between money lost by A and B was $4: 5$. The ratio of their individual losses of the last year and present year are $3: 5$ and $2: 5$ respectively. If total loss incurred to both of them this year is Rs. 187000 the present loss of $A$

The percentage of loss when an article is sold at Rs. 60 is the same as that of the profit when it sold at Rs. 80 . The above mentioned percentage of profit or loss on the article is:

A trader bought $10 \mathrm{~kg}$ of apples for Rs, 405 out of which $1 \mathrm{~kg}$ of apples were found to be rotten. If he wishes to make a profit of $10 \%$ at what rate should he sell the remaining apple per kg -