Master official previous years' questions for Quantitative Aptitude, Reasoning & General Intelligence, English Language & Comprehension, General Awareness, and Computer Knowledge with verified explanations.
Marking pattern: Tier-I (+2.00, -0.50) • Tier-II (+3.00, -1.00) official scheme.
Which of the following points lies on the same straight line as the points (2, 3) and (4, 7)?
A regular right square pyramid has a base side of 8 cm. An insect crawls from a base corner to the midpoint of an opposite slant edge along the surface by the shortest route. If the perpendicular height of the pyramid is 15 cm, find the slant height.
A perfumer blends two perfumes costing ₹900/L and ₹600/L to make 240 L of blend at ₹750/L. Due to poor packaging, 15 L leaks out. How much of the ₹900/L perfume was used?
If $\tan \theta = p$, where $\theta$ is an acute angle, then $\sin \theta$ is equal to:
Two friends, Ghanshyam and Kanhaiya, opened a grocery shop together. Ghanshyam invested ₹40,000 in the business, while Kanhaiya invested ₹50,000. They ran the shop together for one full year, at the end of which they made a total profit of ₹22,500, and they agreed to share this profit in the same ratio as their investments. What is Kanhaiya's share of the profit?
From an external point P, two tangent segments PA and PB are drawn to a circle with center O and a radius of 5 units. The distance from P to O is 13 units. Calculate the area of quadrilateral PAOB.
In a 70 liter mixture of milk and water, the ratio of milk to water is 4:3. How much water must be added to make the ratio of milk to water 2:3?
A loan of Rs. 47,600 is to be paid back in two equal annual instalments. If the interest charged is $12\frac{1}{2}\%$ per annum, compounded annually, then how much is each installment?
Find the median class of the data whose graph is shown below:
Study the following pie chart and table carefully and answer the question based on them.
| Village | % Population Below Poverty Line |
|---|---|
| X | 38% |
| Y | 52% |
| Z | 42% |
| R | 51% |
| S | 49% |
| T | 46% |
| V | 58% |
Find the population of village V if the population of village R living below the poverty line in 2002 is 11,220.
Which of the following statements is not correct?
A wholesale bookseller observes an interesting fact about a particular title of books: the total cost price of 20 copies of that book is exactly equal to the total selling price at which he sells 16 copies of the same book. He wonders what his exact percentage of profit or loss per book is, given that he buys and sells every copy of the book at uniform rates. What is his profit percentage?
A solid metal cone of height 24 cm and base radius 3.5 cm is melted and recast into small spherical balls of radius 1 cm. How many balls are formed?
A trapezium has one parallel side double the other. The height is 10 cm, and the area is $900\text{ cm}^2$. Find the lengths of the parallel sides.
If two circles of radii $r_1$ and $r_2$ have $n$ common tangents, and the distance between their centers is less than $|r_1 - r_2|$, then $n$ is:
A person reaches his destination 30 minutes late, if his speed is $3\text{ km/h}$, and reaches 30 minutes before time if his speed is $4\text{ km/h}$. Find the distance of his destination from his starting point.
Given that ${\left(\sqrt{a} + \frac{1}{\sqrt{a}}\right)}^2 = 10$, find the value of $a^2 + \frac{1}{a^2}$.
If $x = 6\cos A + 8\sin A$ and $y = 6\sin A - 8\cos A$, find the value of $x^2 + y^2$.
A shopkeeper increases the marked price by 25% above cost and then gives a 20% discount. What is his profit percentage?
The population of a place increased at a rate of 5% per annum to reach 66,150 in the year 2023. Find the population in the year 2021.
A fruit vendor sold $\frac{3}{4}$ of his apples at a profit of 20% and the rest at a loss of 10%. If he gained Rs. 90 on the whole, find the cost price of all apples.
10 women can do half part of the total work in 20 days. How many more women will be required to complete the remaining work in 4 days?
The compound interest (compounding half yearly) received on Rs. 6000 for 1.5 years is Rs. 1986. What is the rate of interest per annum?
If $\cos A = \frac{4}{5}$ and $A$ is acute, then find the value of $\frac{1 + \cot^2 A}{1 + \tan^2 A}$.
Select the sentence containing the homonym of the highlighted word:
The professor delivered a lecture on constitutional morality.