Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If \(\cos \theta =\frac{m^{2}-n^{2}}{m^{2}+n^{2}}\), then what is \(\tan \theta \) ?
\(\frac{2mn}{m^{2}-n^{2}} \)
\(\frac{m^{2}-n^{2}}{2mn} \)
\(\frac{m^{2}+n^{2}}{2mn}\)
\(\frac{2mn}{m^{2}+n^{2}}\)
Correct answer
\(\frac{2mn}{m^{2}-n^{2}} \)
If sin x = cos(2x + 15°) what is the value of x?
20°
30°
25°
15°
Correct answer
20°
For a triangle with vertices A(0, 0), B(5, 0), and c(0, 10), where is its Orthocenter located?
(0,0)
(0,5)
(5,0)
(5, 10)
Correct answer
(0,0)
In \(\triangle ABC\), the angle bisector AD of ∠A divides side BC. If AB = 10 cm, AC = 12 cm, and BC = 11 cm, what is the length of the segment BD?
5 cm
8 cm
11 cm
6 cm
Correct answer
5 cm
Simplify \(\sqrt{50}+\sqrt{18}-\sqrt{8}\)
\(7\sqrt{7}\)
\(6\sqrt{2}\)
\(5\sqrt{2}\)
\(4\sqrt{2}\)
Correct answer
\(7\sqrt{7}\)
In a circle, the angle subtended by chord AB at a point on the circumference is 35°. What is the angle subtended by the same chord at the center of the circle?
35°
70°
90°
105°
Correct answer
35°
A point P lies outside a circle with center O and radius r = 6 cm. Two tangents PA and PB are drawn from P to the circle, and the angle between the tangents ∠APB = 60°. What is the distance from point P to the center O?
6 cm
6√3 cm
6√2 cm
12 cm
Correct answer
6 cm
1.75 ÷ 0.25 = ?
7
8
4
5
Correct answer
7
A lends $5000 at 5% for 4 years. B lends $4000 at 6% for 3 years. Who earns more SI?
A earns more
B earns more
Both same
Can't say
Correct answer
A earns more
A can complete a task in 12 days and B in 18 days. If they work together, how long will they take to complete the task?
6 days
7.2 days
7.5 days
8 days
Correct answer
6 days
A sum of money at simple interest doubles in 8 years. It will become four times in:
24 years
22 years
28 years
18 years
Correct answer
24 years
The principal is 1600, the interest rate is 8%, and the time is 5 years. What will be the simple interest?
640
620
600
590
Correct answer
640
What will be the ratio of simple interest earned by a certain amount at the same rate of interest for 14 years and 18 years ?
1 ∶ 3
5 ∶ 9
9 ∶ 11
7 ∶ 9
Correct answer
1 ∶ 3
The union of rational and irrational numbers is equal to:
Real Numbers
Natural Numbers
Complex Numbers
Whole Numbers
Correct answer
Real Numbers
The speeds of A and B are in the ratio 4 ∶ 7. A takes 30 minutes more than B to reaches a destination. Time in which A reach the destination?
72 m
55 m
65 m
70 m
Correct answer
72 m
A rectangular water tank is 1.5 m long, 1.2m wide, and 0.8m deep. How many liters of water can it hold? (Given : 1m3 = 1000 liters)
1440 liters
144 liters
14.4 liters
14400 liters
Correct answer
1440 liters
A storage container in the shape of a cuboid has a square base with sides of 7 cm and height of 10 cm. What is the difference between its total surface area and its lateral surface area?
49 cm2
98 cm2
140 cm2
196 cm2
Correct answer
49 cm2
The total surface area of a cone is 616 cm2 and its base radius is 7 cm. Find the slant height.
22 cm
21 cm
20 cm
18 cm
Correct answer
22 cm
A cone has base radius 6 cm and slant height 10 cm. If a conical frustum is cut from it, the top radius is 3 cm and height is proportionally scaled. Find the height of the frustum.
4 cm
6 cm
8 cm
10 cm
Correct answer
4 cm
If (a + b + c) = 20 and (a2 + b2 + c2) = 200, find the value of (a - b)2 + (b - c)2 + (c - a)2.
300
-200
200
123
Correct answer
300
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.