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.
A right square pyramid has a base of side $10\text{ cm}$. Its slant height along the diagonal (face diagonal) is $13\text{ cm}$. Find the vertical height of the pyramid.
Consider two triangles, $\Delta KLM$ and $\Delta XYZ$. It is stated that these two triangles are congruent to each other, which is denoted as $\Delta KLM \cong \Delta XYZ$ and $\angle K = 65^{\circ}$, what is the measure of $\angle X$?
If $a = \sqrt{5}$ and $b = 5 - \sqrt{5}$, which of the following is true?
If $\left(a + \frac{1}{a}\right) = 4$, then what is the value of $a^5 + \frac{1}{a^5}$?
Bharati started a business with ₹18,000 and Manju joined it afterwards with ₹36,000. Find out after how many months did Manju joined the business, if profit were distributed equally after the end of a year.
A boat goes $20,000\text{ m}$ upstream and $44,000\text{ m}$ downstream in 8 hours while it goes $15,000\text{ m}$ upstream and $22,000\text{ m}$ downstream in 5 hours. The speed of boat in still water is:
Yashika buys 6 apples and 6 mangoes for ₹216. When the cost of an apple is decreased by 30% and that of a mango remains the same, then the cost of 5 apples and 8 mangoes is ₹162. What is the original cost of 7 apples and 2 mangoes?
A certain sum of money is invested at simple interest for 3 years at 3% per annum. The simple interest earned is equal to half of the compound interest earned on ₹6,000 invested for 2 years at 6% per annum, compounded annually. Find the sum invested at simple interest.
A right circular cone is surmounted on a hemisphere. Base radius of the cone is equal to radius of the hemisphere. The diameter of the hemisphere is $12\text{ cm}$ while the height of the cone is $8\text{ cm}$. Find the cost of painting the compound object if it costs ₹25 to paint $\pi\text{ cm}^2$.
The price of 4 pens and 5 notebooks is ₹130. If the price of a pen increases by 25% and the price of a notebook decreases by 20%, then the price of 2 pens and 4 notebooks becomes ₹82. What is the original price of 1 pen and 2 notebooks?
If $\sin A = 3/5$, find the value of $\sin^4 A + \cos^4 A$.
An EdTech company allocates its monthly budget across five different departments: Content Creation (A), Marketing (B), Tech Support (C), HR (D), and Miscellaneous (E). The funds for the first four departments A, B, C, and D are distributed in the ratio of 4:7:9:12 respectively. The budget allocated to the Miscellaneous department (E) is designed to be exactly the arithmetic mean of the budgets of Content Creation (A) and HR (D). During a financial audit, it was noted that Tech Support (C) received Rs. 12,000 more than Marketing (B). What is the total monthly budget of the company across all five departments combined?
While designing a shortcut trick reel for a quantitative aptitude social media channel, a content developer creates the following complex-looking arithmetic fraction:
$$E = \frac{0.1250 \times 0.7500 \times 0.4000}{0.200 \times 0.500 \times 0.1500}$$To quickly verify the options for their audience, the developer uses standard fractional equivalents to find the approximate value. What should be the correct approximate result of this calculation?
If the radii of two circles be $8\text{ cm}$ and $6\text{ cm}$ and the length of the transverse common tangent be $14\text{ cm}$, then the distance between the two centres is:
A merchant has $2650\text{ kg}$ of rice, one part of which he sells at 36% profit and the rest at 16% profit. He gains 28% on the whole. Find the quantity sold at 16%.
Two tangents, PQ and QR, are drawn from an external point Q to a circle of centre O. If $OQ = 41\text{ cm}$, $\angle PQR = 60^{\circ}$ and the radius of the circle is $9\text{ cm}$, find the perimeter of $\Delta PRQ$.
A person P can complete a project in 24 days, and the person Q can complete it in 36 days. They work together for 4 days, after which Q leaves. In how many days will P complete the remaining work? (Give your answer rounded off to two decimal places.)
Three identical solid spheres of radius r are melted and recast into a single larger sphere. The radius of the new sphere is:
The difference between the selling prices with a discount of 32% and two successive discounts of 20% and 12% is ₹36. What is the marked price (in ₹) of the article?
A car moves at a steady pace from point P to point Q. It would have taken an hour less if it had accelerated by $10\text{ km/h}$. It would have saved an additional forty-five minutes if its speed had been increased by an additional $10\text{ km/h}$. How far are P and Q?
A sum of 2,400 doubles in 8 years under simple interest. Another sum Q is invested at the same rate. The interest earned on Q for 5 years exceeds the interest earned on 2,400 for 3 years by ₹300. What is Q?
Total cost price of 1600 articles is Rs. 300. Total selling price of 10 articles is Rs. 3. What is the profit percentage? (Cost price of all the articles is same. Selling price of all the articles is same.)
An item is sold at 20% profit. If CP and SP increase by Rs. 50 and Rs. 30 respectively, profit becomes 10%. Find original CP.
$\sin^2 60^{\circ} + \cos^2 30^{\circ} + \cot^2 45^{\circ} + \sec^2 60^{\circ} = \ ?$
The difference between the ages of Sakshi and Priya is 37 years. Five years ago from now, the sum of their ages was 95 years. If Sakshi is older than Priya, find Priya's present age (in years).