Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If sin2θ = \(\frac{1 - \cos2θ }{2}\), what is the value of sin4θ in terms of cos2θ?
\( (1 - \cos 2\theta)^2 / 4 \)
\( 1 - \cos 2\theta \)
\( 1 - 2\cos 2\theta + \cos^2 2\theta / 4 \)
\( 1 - \cos^2 2\theta / 2 \)
Correct answer
\( (1 - \cos 2\theta)^2 / 4 \)
Two observers stand 100 meters apart and observe the top of a tower. The angles of elevation are 30° and 45°. Find the height of the tower (assuming both observers are on the same side of the tower).
\( 100\sqrt{3} \) m
\( 100(\sqrt{3} - 1) \) m
\( 50(\sqrt{3} + 1) \) m
\( 100\sqrt{2} \) m
Correct answer
\( 100\sqrt{3} \) m
If, x + y = 7 and xy = 10 then the value of x2 + y2 is:
29
49
59
69
Correct answer
29
A man takes a loan of ₹15,000 from a bank at 8% compound interest per annum, compounded annually. Find the total amount he has to pay after 2 years.
₹17,480
₹17,496
₹16,800
₹17,520
Correct answer
₹17,480
A shopkeeper buys an article for ₹450. He marks up its price by 20%. He then offers a discount of 10% on the marked price to a customer. What is the profit percentage the shopkeeper makes on this transaction?
28
8
37
23
Correct answer
28
If the side length of a regular polygon is doubled, by what factor does the area increase?
2 times
3 times
4 times
Remains the same
Correct answer
2 times
A room has a floor in the shape of a rectangle (18 m × 10 m), with a triangular extension on one end. The triangle has a base of 10 m and height of 6 m. What is the total area of the floor?
200 m2
210 m2
220 m2
216 m2
Correct answer
200 m2
A quadrilateral ABCD is cyclic, ∠A=70° ∠C=110° and diagonals intersect at point E. What is the value of ∠B+∠D?
160°
180°
200°
90°
Correct answer
160°
Which of the following statements is always true for angles subtended by a chord?
Angles subtended at the center and circumference are equal
Angle at the center is half the angle at circumference
Angle at center is twice the angle at circumference
Angles subtended in the same segment are unequal
Correct answer
Angles subtended at the center and circumference are equal
If \( x = \sqrt{3} \) and \( y = 3 - \sqrt{3} \), which of the following is true?
\( x + y \) is irrational
\( x + y \) is rational
\( x - y \) is rational
None
Correct answer
\( x + y \) is irrational
Consider the following two statements, labeled Assertion (A) and Reason (R). Evaluate them and choose the appropriate answer from the given options.
Assertion (A): Any whole number larger than one can be written as the result of multiplying prime numbers together.
Reason (R): The Fundamental Theorem of Arithmetic guarantees unique prime factorizations for all rational numbers.
Both A and R are true, and R is the correct explanation of A.
Both A and R are true, but R is not the correct explanation of A.
A is true, but R is false.
A is false, but R is true
Correct answer
Both A and R are true, and R is the correct explanation of A.
The average monthly salary of 24 workers and 1 manager is ₹5000. The manager earns ₹11000. What is the average salary of the workers?
₹4400
₹4500
₹4600
₹4750
Correct answer
₹4400
A shopkeeper lists a jacket for ₹2000. He offers a discount of 15% on the list price. What additional discount (on the reduced price) must he offer to bring the final price down to ₹1360?
10%
15%
20%
25%
Correct answer
10%
A merchant gains 20% after allowing a discount of 10% on the marked price. Find his profit percentage if no discount were allowed.
56.78%
53.33%
33.33%
54.34%
Correct answer
56.78%
A trader buys 150 mobile phones at ₹8,000 each. He finds 10% of the phones defective and sells them at a 50% discount (on cost price). The rest are sold at a 10% profit. What is his overall profit or loss?
₹48,000
₹87,600
₹88,456
₹81,600
Correct answer
₹48,000
A water tank can be filled by two inlets, labeled A and B, in 12 hours and 15 hours respectively. An outlet pipe C can empty the tank in 10 hours. If all three pipes are opened together, how much time will it take to fill the tank?
10 hours
15 hours
20 hours
25 hours
Correct answer
10 hours
If sin A = 3/5, and A is acute, then cos A + tan A is :
31/20
29/20
7/5
27/20
Correct answer
31/20
If sin(90° - A) = 3/5, then what is the value of tan A?
4/3
12/5
5/12
13/5
Correct answer
4/3
If sec A = cosec B and both A and B are acute angles, then the value of A + B is:
30°
45°
60°
90°
Correct answer
30°
Simplify:
\(\sqrt{12} + \sqrt{27}\)
\(\sqrt{39}\)
\(3\sqrt{3} + 2\sqrt{3}\)
\(5\sqrt{3}\)
\(6\sqrt{2}\)
Correct answer
\(\sqrt{39}\)
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.