Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
A and B can complete a work in 36 days and 45 days respectively. They worked together for 2 days and then A left the work. In how many days will B complete the remaining work?
41.5
40
41
40.5
Correct answer
41.5
If the radius of a sphere increases by 10%, what would be the change in the surface area of the sphere?
20%
21%
31%
25%
Correct answer
20%
The cost price of an article is Rs. 1,200. On buying four such articles, the customer gets one for free. If the selling price of each article is Rs. 1,800, then determine the net percentage profit earned by the shop keeper on selling four articles.
12%
20 %
18%
15%
Correct answer
12%
If x2 + 6x + 1 = 0, then the value of (x + 6)3 + \(\frac{1}{{{{\left( {x + 6} \right)}^3}}}\) = ?
245
216
186
198
Correct answer
245
A can complete a work in 8 days and B can complete the same work in 11 days. How long will they take, if both work together?
4\({12 \over 17}\) days
5\({12 \over 19}\) days
4\({11 \over 19}\) days
4\({12 \over 19}\) days
Correct answer
4\({12 \over 17}\) days
Find cos\(\left( { - \frac{{7\pi }}{2}} \right)\).
\({1 \over 2}\)
1
-1
0
Correct answer
\({1 \over 2}\)
The height and curved surface area of a right circular cylinder are 7 cm and 70 π cm2. Its total surface area is:
140 π cm2
150 π cm2
180 π cm2
120 π cm2
Correct answer
140 π cm2
Find the HCF of \(\frac{{11}}{{25}}\), \(\frac{{9}}{{20}}\), \(\frac{{16}}{{15}}\) and \(\frac{{10}}{{33}}\).
\(\frac{{1}}{{3300}}\)
\(\frac{{1}}{{330}}\)
\(\frac{{1}}{{33}}\)
\(\frac{{1}}{3{00}}\)
Correct answer
\(\frac{{1}}{{3300}}\)
If 86y5 is exactly divisible by 3, then the least value of y is:
3
0
1
2
Correct answer
3
Study the given bar-graph and answer the question that follows.
The bar-graph shows the exports and imports (in Rs. lakh) of a company from 2000-2004.
What is the average export (in Rs. lakh) from the year 2000 to 2004?
100
125
112
130
Correct answer
100
Refer to the following table. Read the table and answer the question. Food grain Production in a country in 1999. (in lakh tons)
| State | Rice | Wheat | Jowar | Pulses | Other |
|---|---|---|---|---|---|
| P | 55 | 113 | --- | 37 | 39 |
| Q | 58 | 96 | 83 | 29 | 25 |
| R | 69 | 42 | 77 | 24 | 41 |
| S | 51 | 47 | 69 | 31 | 25 |
| T | 47 | 32 | 51 | 23 | 21 |
| U | 78 | 25 | 22 | --- | 28 |
| V | 67 | 18 | 17 | 22 | 20 |
| W | 48 | 38 | 41 | 32 | 55 |
What was the proportion of rice production to wheat production in the country?
411 ∶ 422
473 ∶ 411
418 ∶ 422
322 ∶ 311
Correct answer
411 ∶ 422
Find the least value of p so that 246p48 is divisible by 8.
2
1
4
0
Correct answer
2
Ravi buys salt at ₹16 per kg and sells it at ₹18 per kg. He also uses the weight of 900 gm instead of 1000 gm. What is Ravi's actual profit percentage?
23%
20%
\(23 \frac{11}{18} \)
25%
Correct answer
23%
A cylindrical tank of capacity 64π litres has equal height and radius. What would be the radius of the cylinder?
(1 litre = 1000 cm3)
5 cm
40 cm
50 cm
4 cm
Correct answer
5 cm
If 4 Cos θ + 3 Sin θ = x and 4 Sin θ - 3 Cos θ = y, find the value of x2 + y2.
16
9
25
1
Correct answer
16
The value of \(\left[1 \frac{2}{7} \times\left{3 \frac{1}{2} \div\left(\frac{1}{2}-\frac{1}{7}\right)\right}\right] \div\left(4 \frac{1}{5} \times 1 \frac{1}{2}\right)\) is:
\(\frac{1}{3}\)
\(\frac{3}{4}\)
2
1
Correct answer
\(\frac{1}{3}\)
Study the given table and answer the question that follows.
The distance travelled by two online-delivery employees during a week.
| Day | Distance travelled (in km) | |
|---|---|---|
| First | Second | |
| Monday | 200 | 250 |
| Tuesday | 300 | 400 |
| Wednesday | 200 | 350 |
| Thursday | 150 | 250 |
| Saturday | 250 | 350 |
| Sunday | 350 | 100 |
Find the ratio of the total distance covered by the first employee during first three days and the last three days by the second employee.
2 ∶ 1
1 ∶ 1
1 ∶ 2
3 ∶ 1
Correct answer
2 ∶ 1
If in ΔABC, AB = AC and ∠ACD = 125°, then ∠BAC is:
75°
55°
60°
70°
Correct answer
75°
Two circles touch each other externally. The radius of the first circle with centre A is 18 cm. The radius of the second circle with centre B is 8 cm. Find the length of their common tangent CD.
23 cm
26 cm
24 cm
25 cm
Correct answer
23 cm
The following table shows the data of different colleges whose students participated in the Olympiad.
| Subjects | College A | College B | College C | College D | College E |
|---|---|---|---|---|---|
| Hindi | 110 | 100 | 125 | 103 | 112 |
| English | 98 | 120 | 80 | 122 | 105 |
| Maths | 130 | 110 | 250 | 160 | 180 |
| Science | 100 | 100 | 150 | 200 | 80 |
| GK | 182 | 200 | 120 | 130 | 183 |
What is the percentage increase in the number of students who participated in the GK Olympiad to those who participated in the Science Olympiad from all colleges? (Correct to two decimals places.)
29.37%
29.89%
29.74%
29.01%
Correct answer
29.37%
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.