Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
If sin θ = 5/13 and θ is in the second quadrant, find the value of sin θ + cos θ.
-7/13
7/3
14/13
-14/13
Correct answer
-7/13
If sin A = cos B and both A and B are acute angles, what is the value of A + B?
45°
60°
90°
70°
Correct answer
45°
Arrange the following surds in ascending order: \(\sqrt3, \sqrt[3]{5}, \sqrt[6]{20}\)
\(\sqrt3, \sqrt[3]5, \sqrt[6]{20}\)
\( \sqrt[6]{20}, \sqrt[3]5, \sqrt3\)
\( \sqrt[3]5, \sqrt3, \sqrt[6]{20}\)
\( \sqrt[6]{20}, \sqrt3, \sqrt[3]5\)
Correct answer
\(\sqrt3, \sqrt[3]5, \sqrt[6]{20}\)
Simplify: (√3 + √2)2
5 + 2√6
5 + √6
3 + 2√2
5 + 2√3
Correct answer
5 + 2√6
A sum of Rs. 12,000 is to be paid in 2 equal annual installments at 5% simple interest per annum. Find the amount of each installment.
Rs. 6400
Rs. 5853.66
Rs. 6600
Rs. 6500
Correct answer
Rs. 6400
An airplane is in level flight at an altitude of 1.5 km from the ground is observed at an angle of elevation of 60°. After 10 seconds, its angle of elevation is observed to be 30°. The speed of the airplane in km/hr is:
360√3
180√3
\(\frac{360}{\sqrt3}\)
\(\frac{540}{\sqrt3}\)
Correct answer
360√3
Pipe A can fill a tank in 10 hours, Pipe B in 20 hours. Pipe C can empty the full tank in 25 hours. If all are opened together, how long will it take to fill the tank?
9.09 hrs
9 hrs
10 hrs
11.11 hrs
Correct answer
9.09 hrs
A trader marks his goods 60% above the cost price and allows a discount of 35% Find the profit or loss percent.
5% profit
4% profit
5% loss
4% loss
Correct answer
5% profit
Two cars start simultaneously from the same point, one traveling east at 50 km/h and the other travelling north at 70km / h. How far apart are they after 2 hours?
180.68 km
188.68 km
168.68 km
172.05 km
Correct answer
180.68 km
Each side of a square park is 74 meters. A 2 meter-wide uniform path inside the park along its boundary is formed. Find the difference between the perimeter of the park and the path now.
20 meters
33 meters
16 meters
22 meters
Correct answer
20 meters
The sides of a triangle are in the ratio 17:18:19. If the perimeter of the triangle is 1944 cm, what is the length of the longest side in metres?
7.84 m
9.84 m
4.84 m
6.84 m
Correct answer
7.84 m
Which of the following numbers is a perfect square and a multiple of 4?
625
256
225
169
Correct answer
625
A man sells an article for Rs. 520 and gains 4%. What is the cost price?
Rs. 500
Rs. 400
Rs. 480
Rs. 510
Correct answer
Rs. 500
The average of 8 numbers is 24. If one number is 24, what is the average of the remaining 7 numbers?
24
34
26
28
Correct answer
24
The binary number 11111111 divided by 1111 gives ______ in the decimal system.
an even number as the answer
a composite number as the answer
the highest prime number less than 20
the second highest prime number less than 20
Correct answer
an even number as the answer
A shopkeeper sells mangoes at a loss of 25%. If he had sold them for Rs. 3.5 more per kg, he would have gained 15%. Find the cost price per kg.
Rs. 6.75
Rs. 8.65
Rs. 7.75
Rs. 8.75
Correct answer
Rs. 6.75
A water tanker can hold four-fifth of its capacity when three-fourth of the water is already used. If the tanker's total capacity is 3600 litres, how many litres of water is left in the water tanker?
720 litres
690 litres
660 litres
630 litres
Correct answer
720 litres
A student secured 1080 marks in an exam out of 1800. What is their percentage?
60%
70%
75%
80%
Correct answer
60%
Which of the following numbers is an integer?
6.28318
-10
2/3
\(\sqrt{12}\)
Correct answer
6.28318
Which of the following is the equation of the line that passes through the points (7.5, 3.5) and (2.5, 5.5)?
2x+10y=63
4x+10y=65
2x+5y=65
4x-10y=65
Correct answer
2x+10y=63
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.