CGL MAINS SCORE BOOSTER QUANT QUIZ-4

If $x^{3}+6 x^{2}+a x-b$ is exactly divisible by $\left(x^{2}-4\right)$, then the value of $(a+b)$ is:

 The value of $\frac{\sin 37^{\circ} \cos 53^{\circ} \cot 45^{\circ}+\cos 37^{\circ} \sin 53^{\circ} \tan 45^{\circ}}{4 \sin 45^{\circ} \cos 45^{\circ}}$ is:

In a circle centre at $\mathrm{O}$, a tangent $\mathrm{AP}$ is drawn from an external point $\mathrm{A}$. If $\mathrm{OA}=61 \mathrm{~cm}$ and $\mathrm{OP}=11 \mathrm{~cm}$, then the lengthof tangent AP is:

During a month a shopkeeper sells his goods at a discount of 60%. But in the last week, he offers an additional discount of 30%. If the original price of the shirt is Rs. a, then the price during the last week of sale will be?

The single discount equivalent to the discount series of $20 \%, 10 \%$ and $5 \%$ is:

Bella had a certain amount with her. She spent $30 \%$ of that to buy a shirt and $10 \%$ of the remaining on transport then she gifted Rs. 160. If she is left with Rs. 1100 then the amount she spent on transport is -

If a men receives one forth of his capital at $3 \%$ interest , $\frac{2^{\mathrm{rd}}}{3}$ at $5 \%$ and on remaining $11 \%$, the percentage of interest he received on the whole is -

The average age of 11 players of a Cricket team increases by 4 months if two of them aged 21 years 5 months and 22 years 4 months respectively are replaced by two new players. The average age of new players is?

Three pipes A, B and C are connected to a tank. A and B together can fill the tank in 30 minutes B and C together in 20 minutes and C and A together in 15 minutes. In how much time each pipe will fill the tank.

Shivani starts her journey from Delhi to Chennai and simultaneously Radha starts from Chennai to Delhi. After crossing each other they finish their remaining journey $5 \frac{1}{16}$ hours and 9 hours respectively. What is Radha's speed if Shivani's speed is 24 $\mathrm{km} / \mathrm{h}$.