Quantitative Aptitude PYQs

The data given below shows the rainfall (in cm) recorded in a city on 5 different days.

Rainfall: 5, 6, 8, 10, 11

Find the sample variance of the given data.

Find the value of:

\(\sqrt{5 + 2\sqrt{6}} + \sqrt{5 - 2\sqrt{6}}\)

The angle between two tangents from an external point to a circle is equal to the angle subtended by the chord of contact at the center. What is the relationship between this angle and the angle subtended by the chord at the circumference?

If sin A - cos A = 1/3 and \( A \in (0, \pi/2) \), then what is sin 2A?

A tangent to a circle has length 8 cm, and the shortest distance from the external point to the circle is 4 cm. What is the radius of the circle?

The unit digit of 7¹⁰³ is:

Evaluate: \( \left(\frac{1}{28}\right) + \left(\frac{1}{35}\right) + \left(\frac{1}{49}\right) + \left(\frac{1}{56}\right)\)

M and N invest ₹80,000 and ₹1,20,000. After a year, the total profit, including 10% interest, is ₹33,000. What is N's share?

The average age of a group of 8 people increases by 2 years when a person aged 14 is replaced by a new person. Find the age of the new person.

The price of cooking oil increased by 8%. A family uses 12 litres of cooking oil per month. If the original price was ₹150 per litre, what is the additional annual expenditure (to the nearest Rs.) for the family due to the price hike?

A certain amount of money triples in 8 years under compound interest. How many years will it take for that amount to increase to nine times its original value?

A milkman bought 50 liters of milk for ₹2000. 5 liters of milk spoiled. At what rate per liter should he sell the remaining milk to make a profit of 20% on his total outlay?

A merchant mixes 60 kg of coffee at ₹90 /kg with a dearer variety at ₹120 /kg. He sells the blend at ₹110 /kg and gains 10 % profit.

How many kg of the dearer variety did he add?

A can complete a job in 36 days.

Every third day, he is assisted by B who can complete the job alone in 48 days. In how many days will the job be completed?

A large ship consumes 0.2 liters of fuel per km, and a smaller ship consumes 0.15 liters per km. If the large ship travels 500 km and the small ship travels 400 km, what is the total fuel cost at a rate of ₹110 per liter?

If \( x + \frac{1}{x+2} = 6\), determine the value of \( (x + 2)^3 + \frac{1}{(x+2)^3} \)

You are faced with 5 doors. Behind one door is a car, and behind the other four are goats. You pick one door. The host, who knows where the car is, then opens 3 of the remaining doors, all revealing goats. You are then offered the chance to switch your choice to the one remaining unopened door. What is the probability of winning the car if you decide to switch?

A hot-air balloon directly above point A is rising vertically at 2 m/s. An observer at point B, 500 m due east of A, watches the balloon. At the moment when the angle of elevation is 30°, how long until it reaches an angle of elevation of 60°? (Assume no horizontal drift.)

From the summit of a 100 m high cliff, the angles of depression to two boats situated on the same side of the cliff are measured at 30° and 45° respectively. The boats are moving towards the cliff in a straight line. After 5 minutes, the angle of depression to the first boat becomes 60°, while the angle to the second boat becomes 75°. If both boats move at constant but different speeds, determine the initial distance between the two boats.

A solid hemisphere is drilled with a cylindrical with radius \( \frac{R}{2} \) hole through its center. If the height of the removed cylinder equals the hemisphere's radius R, find the ratio of the volume removed to the volume remaining.