Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If \( x + \frac{1}{x+2} = 6 \), determine the value of \( (x+2)^3 + \frac{1}{(x+2)^3} \)
488
386
250
405
Correct answer
488
There are 6 doors. Behind one is a car, and behind the other five are goats. You pick one door. The host, knowing the car's location, then opens 4 of the remaining doors, all revealing goats. You are then offered the opportunity to switch your choice to the one remaining unopened door. What is the probability of winning the car if you decide to switch?
\( \frac{1}{2} \)
\( \frac{2}{3} \)
\( \frac{3}{4} \)
\( \frac{5}{6} \)
Correct answer
\( \frac{1}{2} \)
A 150-meter-tall tower stands on level ground. From the top of the tower, two cyclists are seen on the same side, moving directly towards the tower in straight lines. Initially, the angles of depression to the two cyclists are 35° and 20°, respectively. After 6 minutes, the angles change to 60° and 40°, respectively. Assuming both cyclists maintain a constant speed, find the approximate initial distance between them.
198 m
188 m
185 m
190 m
Correct answer
198 m
A researcher collected data on the growth of a specific bacteria strain in a new nutrient medium. The following table shows the colony diameter (in mm) for a sample of n=10 colonies after 24 hours. The average colony diameter is 5.65 mm, rounded to two places. Find the sample standard deviation, rounded to two decimal places.
| 4.5 | 6 | 6.5 | 5 | 7 | 4 | 6.5 | 7 | 5.5 | 4.5 |
|---|
2.90 mm
0.92 mm
1.11 mm
3.85 mm
Correct answer
2.90 mm
A solid hemisphere is drilled with a cylindrical with radius \(\frac{R}{2}\) hole through its center. If the height of the removed cylinder equals the hemisphere's radius R, find the ratio of the volume removed to the volume remaining.
4 : 1
7 : 4
6 : 5
3 : 5
Correct answer
4 : 1
The base of a right prism is a regular hexagon with a side length of 8 cm. The height of the prism is 15 cm. Find the volume of the prism.
1536 cm3
2494 cm3
2048 cm3
2304 cm3
Correct answer
1536 cm3
If Yx = 121, what will (Y - 1)(x - 2) = ?
2
11
10
1
Correct answer
2
A composite shape has a rectangle (10 cm × 4 cm) with a semicircle on one short side. What is the total area of the shape?
54.22 cm2
58.34 cm2
46.28 cm2
56.42 cm2
Correct answer
54.22 cm2
Find the angle if 3 times its complement equals the angle itself.
22.5°
30°
45°
67.5°
Correct answer
22.5°
If secA + tanA = 10 and A is acute, find the value of secA - tanA.
0.1
0.2
1
0.5
Correct answer
0.1
In triangle ABC, the coordinates of vertices A and B are (0,0) and (6,0), respectively. Vertex C lies somewhere on the line y=x, and the centroid of triangle ABC is (5,3).
What are the coordinates of point C?
(3,3)
(4,4)
(5,5)
(9,9)
Correct answer
(3,3)
What is the slope of the line perpendicular to 7x+4y=6?
2/4
4/3
7/4
4/7
Correct answer
2/4
Complement of an angle is 12° more than twice the angle. Find the angle.
24°
36°
48°
26°
Correct answer
24°
The data given below shows the marks scored by 5 different students in two different subjects.
Marks scored in Science: 64, 72, 55, 90, 47
Marks scored in Mathematics: 35, 66, 94, 80, 48
Find the difference between the median marks scored in Science and the mean marks scored in Mathematics.
0.6
0.4
0.2
0.7
Correct answer
0.6
There are two circles with radii of 5 cm and 3 cm are positioned so that they touch each other internally. What is the distance between their centers?
2 cm
3 cm
5 cm
8 cm
Correct answer
2 cm
The base of a right prism is a square of side 10 cm. If the height of the prism is 7 cm, find its volume in cubic centimetres.
710
700
720
690
Correct answer
710
The difference between the two numbers is 1365. On dividing the larger by the smaller, the quotient is 6, and the remainder is 15.
Find the smaller number.
240
270
285
295
Correct answer
240
Simplify: \( (4 \frac{1}{2} + 2.75) \times (\frac{5}{8} - 0.25) \div (1 \frac{1}{5} + \frac{3}{10}) \)
\( \frac{29}{16} \)
\( \frac{39}{16} \)
\( \frac{49}{16} \)
\( \frac{59}{16} \)
Correct answer
\( \frac{29}{16} \)
P and Q invest ₹1,20,000 and ₹90,000 respectively in a business. After 4 months, P increases his capital by 50%. If the total profit after 1 year is ₹99,000, what is Q's share?
₹35,640
₹42,000
₹50,000
₹60,000
Correct answer
₹35,640
The average of 5 numbers is 72. The average of the first three is 70, and the last three is 75. What is the third number?
65
75
85
95
Correct answer
65
Solving previous year questions by topic helps identify recurring concepts, question patterns, and frequently asked sub-topics. Attempt each question, review the step-by-step explanation, and note down key formulas or facts for quick revision before the exam.