Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Simplify the given expression.
\(\left(7.2 \times 4.1 \div 12.3+22.5 \text { of } \frac{1}{25}-\frac{1}{10}\right)\)
4.9
9.6
7.4
3.2
Correct answer
4.9
The difference between the two perpendicular sides of a right-angled triangle is 2 cm and its area is 24 cm2. What is the perimeter (in cm) of the triangle?
18
16
14
24
Correct answer
18
If a + b + c = 15 and ab + bc + ca = 35, then find the value of a3 + b3 + c3 - 3abc.
1200
2100
1800
1500
Correct answer
1200
A school has two rectangular playgrounds, which are similar in shape. If the length and the breadth of the first playground are given as 224 m and 160 m, respectively, then which of the following options CANNOT be the dimensions of the second playground?
Length = 168 m; Breadth = 120 m
Length = 343 m; Breadth = 255 m
Length = 273 m; Breadth = 195 m
Length = 210 m; Breadth = 150 m
Correct answer
Length = 168 m; Breadth = 120 m
If sin4 θ + cos4 θ = 2 sin2 θ cos2 θ, 0º < θ < 90º, then find the value of cot θ.
1/√(2
1/3
1
1/2
Correct answer
1/√(2
Simplify the given expression.
\(\frac{\left(2 \frac{1}{7}+6 \frac{1}{7}\right) \div \frac{9}{7}}{1 \frac{1}{9} \div\left{\frac{7}{9}+\left(\frac{4}{9} \div \frac{4}{3}\right)\right}} \)
\(\frac{56}{9} \)
\(\frac{55}{9}\)
\( \frac{58}{9}\)
\( \frac{53}{9}\)
Correct answer
\(\frac{56}{9} \)
tan4A + tan2A is equal to:
sec4A - sec2A
sec2A - sec4A
sec2A + sec4A
-(sec2A + sec4A)
Correct answer
sec4A - sec2A
The height and radius of a cone-shaped storage tank are 9 ft. and 7 ft., respectively. Find the volume of water the tank can hold? (Use $\pi=(22)/(7))$
1423 cubic ft.
462 cubic ft.
1386 cubic ft.
527 cubic ft.
Correct answer
1423 cubic ft.
If two kinds of rice which cost Rs. 25 a kg and Rs. 40 a kg are mixed in the ratio of 3 ∶ 2, then find the cost of the mixture per kg.
Rs. 31
Rs. 30
Rs. 32
Rs. 33
Correct answer
Rs. 31
The following table shows the marks obtained out of 100, by four students in four different subjects.
| Students | Hindi | Maths | Science | Social |
|---|---|---|---|---|
| Arnav | 83 | 87 | 90 | 92 |
| Ronak | 75 | 89 | 79 | 82 |
| Shivam | 88 | 95 | 90 | 87 |
| Sonu | 92 | 85 | 90 | 88 |
The total marks scored by Ronak in all the subjects is what percentage of the total marks scored by Shivam, Sonu, Arnav together in all the subjects?
44.46%
34.63%
40.63%
30.46%
Correct answer
44.46%
In a school, the total number of boys is 20% more than the total number of girls. What is the ratio of the number of boys to that of girls in the school?
6 ∶ 5
4 ∶ 5
5 ∶ 3
5 ∶ 6
Correct answer
6 ∶ 5
Two successive price increases of 25% and 25% of an article are equivalent to a single price increase of:
52.25%
50.25%
48.50%
56.25%
Correct answer
52.25%
42% of Ranita's weekly income is equal to 56% of Bhaskar's weekly income. If Bhaskar's weekly income was raised by Rs. 200, while Ranita's weekly income did not change, the ratio of the weekly incomes of Ranita and Bhaskar, respectively, would have been 5 ∶ 4. What is Ranita's weekly income (in Rs.)?
3000
4000
3600
4200
Correct answer
3000
Simplify
\(\left(\frac{3}{4}+\frac{5}{4}\right) \times\left(\frac{9}{5}-\frac{4}{5}\right) \div\left(\frac{3}{2}+\frac{1}{2}\right)\).
1
-1
2
-2
Correct answer
1
Amita can build a room in the same amount of time that Bina and Sita working together can build. If Amita and Bina together could do it in 25 days and Sita alone in 35 days, then how many days are required for Bina alone to do the same work?
180 Days
165 Days
152 Days
175 Days
Correct answer
180 Days
A part of Rs. 48,500 is invested at a simple interest of 15% per annum. The rest of the money is invested at the rate of 10% simple interest per annum after 2 years of the first investment. The ratio of interest after 5 years from the time when the first amount was invested is 5 : 3. How much is the second part that was invested( in Rs.) at the rate of 10% simple interest?
29,100
20,940
19,400
24,900
Correct answer
29,100
Find the curved surface area (in cm2) of a cone of radius 3 cm and height 4 cm.
12π
14π
15π
7π
Correct answer
12π
Solve the following: (tan θ + sec θ + 1)(cot θ - cosec θ + 1) = ?
0
2
-1
1
Correct answer
0
In a 100-km journey, the average speed of S is 40 km/h. He covers the first 60 km in 40 minutes and the next 20 km in 50 minutes. What is his speed in the last 20 km (in km/h)?
30
40
25
20
Correct answer
30
Simplify the given expression. 4 × 5 ÷ 4 of 5 × 4 ÷ (6 + 6 × 6 ÷ 6 of 6 - 6 ÷ 6 × 6)
12
4
2
20
Correct answer
12
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.