Quantitative Aptitude PYQs

Find the value of (1 + cotA - cosecA)(1 + tanA + secA) - 3(sin²A + cos²A).

Simplify 8.2 + 2.6 + 3.2 - 4.5 ÷ 0.9 × 1.2. 

Find the value of cosec θ (1 − cos θ) (cosec θ + cot θ). 

The volumes of two spheres are in the ratio of 512 ∶ 3375. The ratio of their surface areas is: 

A mixture of 750 kg of alloy of copper and tin contains 25% tin. How much tin must be added so that it becomes 70% of the mixture?  

The length of the largest possible rod that can be placed in a cubical room is 42√3m. The surface area (in m²) of the largest possible sphere that fit within the cubical room is:

[Use л = \(\frac{22}{7}\)]

Simplify

5 × [14 ÷ 13 × {13 × 14 ÷ (14 × 14)}]

Two cars run to a place at the speeds of 45 km/h and 55 km/h, respectively. If the second car takes 40 minutes less than the first for the journey, then what is the length of the journey (in km)? 

A doll is marked for Rs. 2,500. A customer pays Rs. 1,800 for it. If the customer got a series of two discounts and the rate of the first discount is 10%, then the rate of the second discount is:  

The value of 30 + 180 ÷ 30 × 6 − 15 − 16 − 60 ÷ 3 − 15 is: 

Find the value of the given expression.

\(\frac{1}{4} × \frac{4}{3} ÷ \frac{5}{3} + \frac{1}{2}\)

A and B can do a work in 13 days and 26 days, respectively. If they work for a day alternately, starting with A, then in how many days will the work be completed? 

Find the fourth proportion to 10, 12, and 15.  

Two circles with centers B and D have radii DA = 8 cm and BC = x cm, respectively. AC is tangent to both circles. If DB and AC intersect the point E, AE = 12 cm and EC = 18 cm, then find the value of x (in cm). 

Find the total surface area of a hemisphere with a radius of 11 cm?  

On account of corona virus, 5% of the population of a village died. Out of the remaining population, 20% fled due to panic. If the present population is 4655, then what was the population of the village before the corona attack? 

Simplify 

9¹⁸ ÷ 3¹⁴ of 27³ × \(\sqrt{6561}\)

If x = 3y + 4, then what is the value of (x³ - 27y³ – 36 xy) ?

If (sin x + sin y) = a and (cos x + cos y) = b, then find the value of (sin x sin y + cos x cos y). 

A 255-m long train is running at a speed of 72 km/h. It crosses a platform of length 745 m in: