Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A 25% decrease in the cost of flour enables a consumer to purchase an additional 3 kg for ₹360. What was the initial price per kg of the flour?
₹30
₹36
₹40
₹45
Correct answer
₹30
The compound interest on a certain principal at 12½% per annum for 2 years is ₹265.625. What is the simple interest on the same principal for the same time and rate?
₹250
₹200
₹300
₹350
Correct answer
₹250
A shopkeeper claims to sell goods at a profit of 10% on the cost price but uses a false weight of 900 g for every 1 kg. What is his actual profit percentage?
20.62%
22.22%
19.62%
21.32%
Correct answer
20.62%
A solution of 120 liters contains 40% acid. How much pure acid (in liters) must be added to make the solution 60% acid?
60 liters
36 liters
40 liters
48 liters
Correct answer
60 liters
A, B, and C can complete a work in 24, 36, and 72 days respectively. A works daily, and B and C assist him every 4th day. In how many days will the work be completed?
18 days
19.5 days
25 days
16.5 days
Correct answer
18 days
Two ships take different routes to reach the "spice capital of the world". The Distances travelled by the two ships are in the ratio of 3:2. Ship 1 moves at 40kmph, and ship 2 travels at 60kmph. If the two ships arrived at their destination with a Time gap of 1 hour, what is the distance travelled by both ships together?
120 km
150 km
180 km
140 km
Correct answer
120 km
If a = 0.25, b = -0.05, c = 0.5 find \( \frac{a^2 - b^2 - c^2 - 2bc}{a^2 - b^2 - 2ab - c^2} \) is?
\( \frac{28}{33} \)
\( \frac{14}{35} \)
\( \frac{25}{34} \)
\( \frac{16}{33} \)
Correct answer
\( \frac{28}{33} \)
A group of 20 students consists of 12 boys and 8 girls. A committee of 5 students is to be selected randomly from this group. What is the probability that the committee has more boys than girls?
Approximately 0.65
Approximately 0.70
Approximately 0.90
Approximately 0.80
Correct answer
Approximately 0.65
A tower stands vertically on the ground. From point P, which is located 40 meters from the ground at the base of the tower, the angle of elevation to the tower's top is α, where tan(α) equals 1.5. From another point Q, situated 60 meters away from the foot of the tower (in line with point P and the tower's base), the angle of elevation to the top of the tower is β. What is the value of tan(β)?
0.5
0.75
1
1.25
Correct answer
0.5
A hemisphere and a right circular cone have the same volume and radius. Find the ratio of their curved surface areas (Hemisphere : Cone).
2 : √5
3 : √5
4 : √5
7 : √5
Correct answer
2 : √5
A metallic wire is melted and recast into a circular ring of radius 28 cm. If the volume of the wire was 1,232 cm3 and its thickness is 2 cm, what is the width of the ring?
2.5 cm
3 cm
3.5 cm
4 cm
Correct answer
2.5 cm
If 3n = 243, what will be the value of (1)(n-1)?
0
1
2
3
Correct answer
0
If sinθ = 5/13, and θ is acute, find the value of (1 + cot2θ).
13/12
169/25
0
3
Correct answer
13/12
If the difference between an angle and its complement is 18°, what is the larger angle?
36°
54°
60°
72°
Correct answer
36°
If the mean of 5 observations (x+1), (x+3), (x+5), (x+7) and (x+9) is given as 20, then find the value of Median.
16
18
20
22
Correct answer
16
In triangle ABC, if the orthocenter is (3,-2) and the circumcenter is (0,4), find the centroid.
(1,1)
(2,1)
(1,2)
(2,2)
Correct answer
(1,1)
Which of the following equations represents a line that does not cross the x-axis?
x = 5
y = -4
y = 2x + 1
x = -1
Correct answer
x = 5
Calculate Karl – Pearson’s coefficient of skewness for the following data. 25, 15, 23, 40, 27, 25, 23, 25, 20
−0.036
−0.0036
−3.6
Correct answer
−0.036
In a given figure, ∠TQR = 49° and QT is the diameter of the circle. The value of ∠QTR + ∠QSR + ∠QPR = ?
220°
123°
222°
223°
Correct answer
220°
Two circles with radii 10 cm and 6 cm have their centers 20 cm apart. What is the approximate length of their common external tangent?
10 cm
15 cm
20 cm
24 cm
Correct answer
10 cm
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.