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 pie chart given below shows the number of nurses in the 5 hospitals. The data is presented in the terms of degrees.
Total number of nurses in H5 and H1 = 3240.
Number of nurses in H1 are what percent less than the number of nurses in H4?
A solid metal sphere of radius 15 cm is melted and recast into 27 identical smaller spheres. What is the ratio of the surface area of the original sphere to the total surface area of all 27 smaller spheres?
If $\sin\theta - \cos\theta = p$, then $\sin\theta + \cos\theta$ is equal to (where $0^\circ < \theta < 45^\circ$):
The number of candidates (in lakh) appearing in an entrance examination from six different cities are shown below:
| City | A | B | C | D | E | F |
|---|---|---|---|---|---|---|
| No. of candidates | 1.25 | 3.14 | 1.08 | 2.27 | 1.85 | 2.73 |
| City | Ratio of Passing and Failing Candidates |
|---|---|
| A | 7:3 |
| B | 5:3 |
| C | 4:5 |
| D | 1:3 |
| E | 3:2 |
| F | 7:5 |
A graduate student's semester performance is evaluated based on course credits and percentage scores. The university uses the following grading scale to convert percentage scores to grade points:
| Percentage Range | Grade Point |
|---|---|
| 90-100 | 4.0 |
| 85-89 | 3.7 |
| 80-84 | 3.3 |
| 75-79 | 3.0 |
| 70-74 | 2.7 |
| 65-69 | 2.3 |
| 60-64 | 2.0 |
| Below 60 | 0.0 |
Solve for x:
$$\left[\left\{\left(\frac{3}{4}\right)^2\right\}^{(x+3)}\right] = \left[\left\{\left(\frac{9}{16}\right)^{\frac{1}{2}}\right\}^{(x-2)}\right]^2$$
Two equal circles, each having a radius of 24 cm, intersect each other, such that each passes through the centre of the other. The length of the common chord is ________ cm.
Let C1, C2 be two circles which do not externally touch and intersect each other and O1, and O2 be the centers of the circles, respectively. Let AB be the common transverse tangent to the circles such that P, Q are the points of tangency respectively to C1, C2. Let R be the point of intersection of O1O2 and AB. If ∠PO1R = 60°, find ∠QO2R and ∠QRO2, respectively.
The sides of a triangular field are 180m, 240 m and 300m. Its area is equal to the area of a square field. What is the side of the square field?
Study the information given in the graph below and answer the following question based on it.
If the net availability of food grains is only 80% of the total food production of the country, then what was the population of the country in the year 2011? [Correct your answer to the nearest 10 million]
The angles of elevation of the top of a tower from two points X and Y (on opposite sides of the tower) at distances b2 m and a2 m, respectively, from the base and in the same straight line with it are complementary. The height (in m) of the tower is
The pie chart shows the percentage of employees in 5 branches. Total employees in B1 = 5000.
In which of the following sets of branches is the average number of employees 4000?
The ratio of the height of a tower and the distance between the top of the tower and the end of the shadow of the tower is √3: 2. What is the angle of elevation of the sun and what is the ratio of the length of the shadow of the tower to the height of the tower?
The centers of two circles of radii 25 cm and 35 cm are 80 cm apart. What is the ratio of the lengths of the transverse common tangent to the direct common tangent to these circles?
At the election for the President of Students' Union in a university, the number of votes not cast for the person A increased by 25% over those not cast for her in the previous election, and A lost by a majority twice as large as that by which she had won the previous election. If a total of 26000 students voted each time, how many voted for A in the previous election?
The cost of 7 kg of sugar of quality A is 245, and the cost of 5 kg of sugar of quality B is 300. In what ratio should quality A sugar and quality B sugar be mixed so that the cost of 1 kg of the mixture is 50?
The value of $$\frac{[(6.4)^2 - (5.6)^2] \times 9.12}{6.4 \times 40.96 + 5.6 \times 31.36}$$ is:
If the selling price of an item is increased by 25% and the profit also increases from 20% to 30%, what is the percentage increase in the cost price?
The ratio of two number A and B is 7: 5. If both numbers are increased by 3, then the ratio of A and B becomes 4: 3. What is the sum of initial values of A and B?
A alone can do a work in 15 days. B alone can do the same work in 20 days. C alone can do the same work in 30 days. They started the work together. B left after 2 days. A and C together completed the remaining work. In how many days remaining work was completed?
For a cone, the curved surface area is two-thirds of its total surface area. What is the ratio of its slant height to its radius?
A, B and C start a business. A invests 1,21,500 for 12 months, B invests 1,02,060 for 9 months and C invests 97,200, but withdrew 24,500 after 6 months. If the total profit earned at the end of the year is 1,69,797, find the difference between the profit share of A and the profit share of B.
$$\frac{(3.57)^2 + (4.54)^2 + 32.4156}{(4.54)^2 - (3.57)^2} = ?$$
A chord CD of a circle has a length of 12 cm. The angle subtended by the chord at a point E on the major arc is 45°. Find the radius of the circle.
A circular garden is surrounded by a path of uniform width 3 m. The total area of the garden including the path is 1256.64 m2. If the area of the garden excluding the path is 907.92 m2, find the radius of the garden and the radius including the path. (Use π = 3.1416)