Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
The lengths of the diagonals of a rhombus compare as 3 times some value to 4 times that same value. If the area of the rhombus is 216 cm2, what are the actual lengths of the two diagonals?
18 cm and 24 cm
27 cm and 36 cm
30 cm and 40 cm
24 cm and 32 cm
Correct answer
18 cm and 24 cm
Two right prisms have the same height, but their bases are triangles with areas in the ratio 3:5. What is the ratio of their volumes?
3:5
5:3
9:25
9:15
Correct answer
3:5
A right circular cylinder has height 20 cm and curved surface area 880 cm2. What is its volume? (use π=22/7)
1077 cm3
3080 cm3
3140 cm3
3200 cm3
Correct answer
1077 cm3
Find the value of: \((\sqrt{625} - \sqrt{81}) \times (\sqrt{49} + \sqrt{121})\)
288
275
270
280
Correct answer
288
Let a = 24 · 32 · 5 and b = 22 · 3 · 73. which of the following is true?
L.C.M(a, b) = 24 · 32 · 5 · 73
G.C.D(a, b) = 22 · 3 · 5
L.C.M(a, b) × GCD(a, b) = a + b
L.C.M(a, b) = G.C.D(a, b)
Correct answer
L.C.M(a, b) = 24 · 32 · 5 · 73
An online seller purchases a laptop at ₹40,000. He lists it at a 25% markup. Due to a festive sale, he gives a flat 10% discount on the listed price and offers free shipping costing him ₹500. What is the net profit or loss percentage?
15.11%
11.11%
51.17%
91.11%
Correct answer
15.11%
A and B together can complete a piece of work in 10 days. B alone can complete it in 15 days. In how many days can A alone complete the work?
20 days
25 days
30 days
35 days
Correct answer
20 days
If \( \sec \theta + \tan \theta = p \), what is the value of \( \sec \theta \) in terms of p?
(p2 + 1)/2p
(p2 - 1)/2p
(p2 - 1)/2
(p2 + 1)/2
Correct answer
(p2 + 1)/2p
If a + b + c = 0, then a3 + b3 + c3 is equal to:
a2 + b2 + c2
3abc
abc
0
Correct answer
a2 + b2 + c2
The difference between the compound interest and simple interest on ₹10,000 for 2 years at 5% per annum is:
₹20
₹25
₹30
₹50
Correct answer
₹20
If ₹12,000 is deposited in a simple interest account that yields 10% annually, what will be the interest earned after two and a half years?
₹2,800
₹3,000
₹3,200
₹3,500
Correct answer
₹2,800
A trader sells two items. On the first item, he makes a profit of 15%, and on the second item, he incurs a loss of 10%. If the selling price of both items is the same (₹3450 each), what is his overall profit or loss percentage on the entire transaction?
1.25% profit
0.98% profit
0.98% loss
No overall profit or loss
Correct answer
1.25% profit
Consider two points on the ground, at distances a and b from the base of a tower (a > b) from the foot of the tower and in the same straight line with it are 30° and 60° respectively. The height of the tower is:
\(\sqrt{ab}\)
\(\frac{\sqrt{a}}{b}\)
\(\frac{\sqrt{b}}{a}\)
\(\frac{a}{b}\)
Correct answer
\(\sqrt{ab}\)
The square root of \( 7 + 4\sqrt{3} \) is:
\( 2 + \sqrt{3} \)
\( 2 - \sqrt{3} \)
\( \sqrt{7} + 2\sqrt{3} \)
\( \sqrt{7} - 2\sqrt{3} \)
Correct answer
\( 2 + \sqrt{3} \)
A is twice as efficient as B. Together they finish a work in 12 days. How long would B take alone?
38
36
34
32
Correct answer
38
A train moving at a speed of 126 km/h crosses a bridge of length 250 meters in 50 seconds. What is the length of the train?
1200 meters
1550 meters
1400 meters
1500 meters
Correct answer
1200 meters
The radii of two concentric circles with centre 'O' is 12 cm and 18 cm, respectively. AB is a chord on the larger circle that is tangent to the smaller circle making contact at point 'C'. If AD is a diameter of the larger circle, then find the length of CD.
\(\sqrt{844}\) cm
\(\sqrt{756}\) cm
\(\sqrt{972}\) cm
\(\sqrt{1008}\) cm
Correct answer
\(\sqrt{844}\) cm
The distance between the centres of the two circles is 73 cm, and the radii of the circles are 29 cm and 19 cm. Find the length of the transverse common tangent drawn to the two circles.
65 cm
55 cm
45 cm
25 cm
Correct answer
65 cm
If 13A = 12B and 14B = 15C, then find A:C.
80:81
90:91
70:71
91:90
Correct answer
80:81
Find the average of -80, -20, 30, 40, and 50.
4
5
6
7
Correct answer
4
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.