Arithmetic, number systems, percentages, ratios, profit and loss, time and work, algebra, geometry, mensuration, and trigonometry.
Study the given graph and answer the question that follows.
The given graph represents the percentage of books on different subjects that a person has in his library.
If the total number of books is 60, then what is the ratio of the number of books on subject C1 to the average number of books per subject?
3 ∶ 7
2 ∶ 3
3 ∶ 5
2 ∶ 5
Correct answer
3 ∶ 7
PQR is a triangle. The bisectors of the internal angle ∠Q and external angle ∠R intersect at S. If ∠QSR = 40°, then ∠P is:
40°
60°
80°
30°
Correct answer
40°
The radius of a circle is 1.75 cm. What is the circumference of the circle? (Take π = \(\frac{22}{7}\))
5.5 cm
11 cm
9.63 cm
22 cm
Correct answer
5.5 cm
The value of \(1\frac{2}{5}-\left[3\frac{3}{4}\div \left{1\frac{1}{4}\div \frac{1}{2}\left(1\frac{1}{2}\times 3\frac{1}{3}\div 1\frac{1}{3}\right)\right}\right]\) is:
3
0
2
1
Correct answer
3
The given table shows the number of students from 4 schools during 2022-2023.
| Schools | Total no. of students | Boys | Girls |
|---|---|---|---|
| A | 2060 | 1339 | 721 |
| B | 1880 | 1034 | 846 |
| C | 2200 | 990 | 1210 |
| D | 1680 | 924 | 756 |
What is the percentage of girls in school B?
65%
45%
60%
55%
Correct answer
65%
The square root of 1/4 × 1/9 × 1/25 × 1/49 ÷ 36/121 is
\(\frac{11}{1260}\)
\(\frac{1260}{11}\)
\(\frac{11}{12.60}\)
\(\frac{1}{1260}\)
Correct answer
\(\frac{11}{1260}\)
The volume of a sphere is given by 130977 cm3. Its surface area (in cm2) is:
16847
12474
17424
14274
Correct answer
16847
If x4 + y4 = x2y2, then the value of x6 + y6 is:
2
0
1
3
Correct answer
2
Let C be a circle with centre O and radius 5 cm. Let PQ be a tangent to the circle and A be the point of tangency. Let B be a point on PQ such that the length of AB is 12 cm. If the line joining O and B intersects the circle at R, find the length of BR (in cm).
2
13
6
8
Correct answer
2
The sales of batteries (in lakhs) manufactured by a company over the years are shown in the given table.
| YEAR | TYPES OF BATTERIES | |||||
|---|---|---|---|---|---|---|
| 4AH | 7AH | 32AH | 35AH | 55AH | Total | |
| 1992 | 75 | 144 | 114 | 102 | 108 | 543 |
| 1993 | 90 | 126 | 102 | 84 | 126 | 528 |
| 1994 | 96 | 114 | 75 | 105 | 135 | 525 |
| 1995 | 105 | 90 | 150 | 90 | 75 | 510 |
| 1996 | 90 | 75 | 135 | 75 | 90 | 465 |
| 1997 | 105 | 60 | 165 | 45 | 120 | 495 |
| 1998 | 115 | 85 | 160 | 100 | 145 | 605 |
Which type of battery had the highest total sales over the last seven years?
32 AH
35 AH
4 AH
55 AH
Correct answer
32 AH
A company is manufacturing boxes of three types – plastic, wood and glass. The ratio of the numbers of plastic, wood and glass boxes is 2 : 3 : 5. The difference between the numbers of wood and glass boxes is 144. If the number of plastic boxes is increased by 25%, then what will be the number of plastic boxes now?
144
360
216
180
Correct answer
144
The table below shows the number of students commuting to school by different modes of transport:
| Modes of transport | School bus | Bicycle | Walking | Other vehicles |
|---|---|---|---|---|
| No. of boys | 80 | 280 | 130 | 200 |
| No. of girls | 140 | 190 | 90 | 250 |
Which mode of transport is used by maximum number of students?
Bicycle
Walking
Other vehicles
School bus
Correct answer
Bicycle
Find the mean proportional between 32 and 162.
99
65
72
97
Correct answer
99
Study the given pie-chart and answer the question that follows.
The pie-chart shows the number of students (boys and girls) studying in standard 10 of various schools (X, Y, Z in the year 2022).
What is the difference between the total number of students (boys and girls) in school Y and Z together and the total number of students (boys and girls) in school X and Y together?
720
840
780
820
Correct answer
720
The product of two numbers is 20000. If their LCM is 800, then what is their HCF?
25
30
35
20
Correct answer
25
Simplify: \(5\frac{1}{3}-\left{4\frac{1}{3}+\left(3\frac{1}{3}\div \overline{2\frac{1}{3}-\frac{1}{3}}\right)\right} \)
\(\frac{2}{3}\)
\(\frac{1}{3}\)
\(-\frac{1}{3}\)
\(-\frac{2}{3}\)
Correct answer
\(\frac{2}{3}\)
Study the given table and answer the question that follows. The table shows the number of students studying in 6 different classes of 6 different schools.
| Schools | V | VI | VII | VIII | IX | X |
|---|---|---|---|---|---|---|
| P | 152 | 160 | 145 | 156 | 147 | 144 |
| Q | 148 | 166 | 150 | 155 | 157 | 143 |
| R | 161 | 152 | 140 | 145 | 143 | 165 |
| S | 159 | 142 | 149 | 140 | 142 | 168 |
| T | 147 | 144 | 158 | 163 | 154 | 150 |
| U | 150 | 160 | 162 | 160 | 160 | 140 |
| Total | 917 | 924 | 904 | 919 | 903 | 910 |
Which class has the maximum number of students from all schools together?
X
VII
VI
V
Correct answer
X
If \(a + \frac{1}{a} = 3\), then the value of \(\rm a^4+\frac{1}{a^4}\) is
48
81
27
47
Correct answer
48
Find the value of \(\rm \frac{\cos 37^\circ}{\sin 53^\circ}-cos47^\circ cosec43^\circ\)
0
-1
2
1
Correct answer
0
The radius of the base of a right circular cone is 5 cm. Its slant height is 13 cm. What is its volume (in cm3, rounded off to 1 decimal place)? (Take π = \(\frac{22}{7}\))
328.6
323.4
314.3
340.5
Correct answer
328.6
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.