DELHI POLICE QUANT QUIZ-3

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Question 1:

A can complete a task in 12 days and B can complete the same task in 18 days. They start working together but A works for only 2 days. The remaining work is completed by $B$. If the total wage is ₹ $2,400$, then what is $B$ 's share (in ₹ )?

Question 2:

If $7 \cos ^2 \theta+5 \sin ^2 \theta-6=0,\left(0^{\circ}<\theta<90^{\circ}\right)$, then what is the value of $\sqrt{\frac{\operatorname{cosec} \theta+\cot \theta}{\operatorname{cosec} \theta-\cot \theta}}$ ?

Question 3:

What is the volume of a right circular cylinder whose curved surface area is 12 π cm$^2$ and the circumference of its base is 4 π cm?

Question 4:

If $x^2-4 x-3=0$, then what is the value of $\frac{\left(x^4-\frac{27}{x^2}\right)}{\left(x^2+4 x-3\right)} ?$

Question 5:

The average of first twelve prime numbers is:

Question 6:

When $x$ is added to each of $6,12,18$ and 28, the numbers obtained in this sequence are in a proportion. What will be the value of $(5 x-8):(x+4)$?

Question 7:

The marked price of a shirt is ₹2,150. Let two successive discounts offered by the store be 10% and ‘x%’. If the selling price of the shirt is ₹1,505, then calculate the value of ‘x’. [Give your answer correct to two decimal places.]

Question 8:

$\frac{63.5 \times 63.5 \times 63.5+36.5 \times 36.5 \times 36.5}{6.35 \times 6.35+3.65 \times 3.65-6.35 \times 3.65}$ is equal to


Question 9:

The price of a TV has been reduced by $20 \%$. In order to restore the original price, the new price must be increased by:

Question 10:

If an 11-digit number 765y88436x6 is divisible by 72, and $x$ assumes the largest value, then what is the value of $(x-y) ?$