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.
The lengths of a common external tangent and a common internal tangent to two circles are $8\text{ cm}$ and $6\text{ cm}$, respectively. If the distance between their centers is $10\text{ cm}$, what are the radii of the two circles?
If $\cos x = \frac{12}{13}$ and $x \in (0^{\circ}, 90^{\circ})$, then find the value of $\frac{(1 + \sin x)^2 + (1 - \sin x)^2}{\cos^2 x}$.
Find the value of $\frac{\sqrt{1 + \sin 4\theta}}{\sqrt{1 - \sin 4\theta}}$
If $a + b = 3$ and $ab = 1$, find the value of $a^4 - b^4$
Simplify: $\frac{(x + y)^3 + (y + z)^3 + (z + x)^3 - 3(x + y)(y + z)(z + x)}{x^3 + y^3 + z^3 - 3xyz}$
Study the given table and answer the questions.
The table presents the production of vegetable oil (in lakh tonnes) by five factories from the year 1990 to 1994.
| S.No | Factory | 1990 | 1991 | 1992 | 1993 | 1994 |
|---|---|---|---|---|---|---|
| i | Almond | 9.0 | 10.7 | 8.9 | 11.6 | 8.4 |
| ii | Coco-Queen | 14.5 | 16.3 | 16.2 | 16.4 | 16.7 |
| iii | Nut-Megalo | 14.9 | 15.7 | 16.8 | 16.9 | 17.8 |
| iv | Vegeol | 7.6 | 8.4 | 7.4 | 7.9 | 8.7 |
| v | Appella | 21.0 | 22.6 | 23.1 | 22.2 | 23.9 |
During which year was the total annual production of all five factories together the highest?
X, Y, and Z can complete a piece of work alone in 22, 40, and 110 days respectively. If X and Y work together on the first day, and then X and Z work together on the second day, and the same pattern repeats alternately, in how much time would the work be completed?
A circular pipe has an external diameter of $42\text{ cm}$ and an internal diameter of $36\text{ cm}$. Find the area of the cross-section of the pipe.
The base of a right prism is a triangle with sides $14\text{ cm}$, $48\text{ cm}$, and $50\text{ cm}$. If the height of the prism is $5\text{ cm}$, find the volume of the prism.
If $\sin \theta + \cos \theta = \sqrt{2}$ where $0^{\circ} < \theta < 90^{\circ}$, find the value of $\sin^4 \theta + \cos^4 \theta$.
A dealer buys an article at a discount of 25% on its list price and marks it at 35% above the list price. If he allows a discount of 20% on the new marked price, find his profit percent.
Two containers of equal capacity are each filled with a milk-water mixture. In the first container, the ratio of milk to water is 3:2, while in the second container the ratio is 4:1. If the contents of both containers are combined thoroughly in a larger vessel, what will be the resulting ratio of milk to water in the final mixture?
In a partnership, A and B invest in the ratio 4:5. If the total profit is Rs. 1,10,000, how much profit does A get?
X alone can do a work in 15 days. Y alone can do the same work in 20 days. Z alone can do the same work in 30 days. All three together completed the work. Wages received by X out of total wages received by X, Y and Z are Rs. 6000. What are total wages (in Rs.) received by Y and Z?
A sum of money amounts to 12,000 in 5 years and 14,400 in 9 years at simple interest. What is the principal?
Two circles with centres O and O', with radii 6 cm and 8 cm, respectively, intersect at two points A and B. If OA is a tangent to the circle with centre O' and vice versa, what is the length of the common chord AB?
A batsman typically scores 40 runs in 20 innings. To raise his average by two, how many runs does he need to score in the twenty-first inning?
A circular track has a radius of 28 m. If a sector (the pie-shaped region enclosed by two radii and the arc connecting their endpoints) subtending $90^{\circ}$ is to be fenced along its boundary three times at the rate of 15 per meter, the total cost of fencing is: (Use $\pi = 22/7$)
A cylindrical tank with a radius of 7 cm contains water up to a height of 40 cm. After a solid spherical ball with a radius of 7 cm is completely submerged in the tank, what will be the new water height?
A solid hemisphere is joined to a solid cylinder of the same base radius by their flat faces. Find the total surface area of the combined solid (including curved and flat surfaces).
Arvind bought an article for x. He sold it to Biru at a loss of 20%. Biru spent 140 on its transportation and sold it to Minu at a profit of 46%. If Minu bought it for 1,752, then what is the value of x?
If $(125x^3 - 343y^3) \div (5x - 7y) = Ax^2 - By^2 + Cxy$, then find the value of $(2A + B - C)$.
In a circle with center O, two parallel chords AB and CD are on opposite sides of the center. If the length of chord AB is 16 cm and chord CD is 12 cm, and the distance between them is 14 cm, find the radius of the circle.
For which of the following equations is the slope of the line equal to zero?
Kaushal travelled for 16 hours 20 minutes at the speed of $90\text{ km/h}$. At what speed (in km/h) should he travel to cover the same distance in 14 hours?