Q. If the angles of triangle JKL are in the ratio 2:3:4, what is the measure of the largest angle? (2023)
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A.
40 degrees
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B.
60 degrees
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C.
80 degrees
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D.
90 degrees
Solution
Let the angles be 2x, 3x, and 4x. Then, 2x + 3x + 4x = 180 degrees. Therefore, 9x = 180, x = 20. The largest angle is 4x = 80 degrees.
Correct Answer: C — 80 degrees
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Q. If the area of a triangle is 48 cm² and the base is 12 cm, what is the height? (2022)
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A.
6 cm
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B.
8 cm
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C.
4 cm
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D.
10 cm
Solution
Area = 1/2 * base * height, so 48 = 1/2 * 12 * height, height = 48/(6) = 8 cm.
Correct Answer: B — 8 cm
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Q. If the area of triangle ABC is 60 square units and the base is 10 units, what is the height of the triangle? (2019)
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A.
6 units
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B.
12 units
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C.
10 units
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D.
8 units
Solution
Area = 1/2 * base * height. Therefore, 60 = 1/2 * 10 * height, which gives height = 12 units.
Correct Answer: A — 6 units
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Q. If the atmospheric pressure is 1013 hPa, what is it in mmHg?
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A.
760 mmHg
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B.
800 mmHg
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C.
850 mmHg
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D.
900 mmHg
Solution
The atmospheric pressure of 1013 hPa is equivalent to 760 mmHg.
Correct Answer: A — 760 mmHg
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Q. If the average incubation period of a disease is 14 days, how many days will it take for 3 incubation periods to pass? (2020)
Solution
Total days = 3 × 14 = 42 days.
Correct Answer: B — 42
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Q. If the coordinates of a point are (x, y) and it lies on the line 2x + 3y = 12, what is the value of y when x = 2?
Solution
Substituting x = 2: 2(2) + 3y = 12 => 4 + 3y = 12 => 3y = 8 => y = 8/3 ≈ 2.67, closest is 3.
Correct Answer: B — 3
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Q. If the coordinates of a point are (x, y) and it lies on the line 3x + 4y = 12, what is y when x = 0?
Solution
Substituting x = 0: 3(0) + 4y = 12 => 4y = 12 => y = 3.
Correct Answer: B — 4
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Q. If the data set is: 5, 5, 5, 5, what is the variance? (2019)
Solution
All values are the same, so variance = 0.
Correct Answer: A — 0
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Q. If the diagonals of a rhombus are 8 cm and 6 cm, what is the area of the rhombus? (2023)
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A.
24 cm²
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B.
48 cm²
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C.
36 cm²
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D.
18 cm²
Solution
Area = (d1 * d2) / 2 = (8 * 6) / 2 = 48 cm²
Correct Answer: A — 24 cm²
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Q. If the diameter of a circle is 12 cm, what is the circumference? (2019)
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A.
12π cm
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B.
24π cm
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C.
6π cm
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D.
36π cm
Solution
Circumference = πd = π(12) = 12π cm.
Correct Answer: B — 24π cm
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Q. If the focus of a parabola is at (0, 2) and the directrix is y = -2, what is the equation of the parabola?
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A.
x^2 = 8y
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B.
x^2 = 4y
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C.
y^2 = 8x
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D.
y^2 = 4x
Solution
The distance from the focus to the directrix is 4, so the equation is x^2 = 8y.
Correct Answer: A — x^2 = 8y
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Q. If the length of a side of a square is doubled, what happens to the area? (2023)
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A.
It remains the same
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B.
It doubles
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C.
It triples
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D.
It quadruples
Solution
Area of square = side². If side is doubled, new area = (2 * side)² = 4 * side², so area quadruples.
Correct Answer: D — It quadruples
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Q. If the lengths of the sides of a rectangle are 4 cm and 6 cm, what is its perimeter? (2022)
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A.
20 cm
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B.
24 cm
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C.
10 cm
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D.
12 cm
Solution
Perimeter = 2 * (length + width) = 2 * (4 + 6) = 20 cm
Correct Answer: A — 20 cm
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Q. If the lengths of the sides of a triangle are 3 cm, 4 cm, and 5 cm, what type of triangle is it? (2023)
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A.
Acute
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B.
Obtuse
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C.
Right
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D.
Equilateral
Solution
A triangle with sides 3 cm, 4 cm, and 5 cm satisfies the Pythagorean theorem (3² + 4² = 5²), thus it is a right triangle.
Correct Answer: C — Right
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Q. If the lengths of the sides of a triangle are 7 cm, 24 cm, and 25 cm, is it a right triangle? (2023)
-
A.
Yes
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B.
No
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C.
Cannot be determined
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D.
Only if angles are known
Solution
Using Pythagoras theorem, 7² + 24² = 49 + 576 = 625 = 25², so it is a right triangle.
Correct Answer: A — Yes
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Q. If the lengths of two sides of a triangle are 8 cm and 15 cm, what is the maximum possible length of the third side? (2021)
-
A.
22 cm
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B.
23 cm
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C.
24 cm
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D.
25 cm
Solution
The maximum length of the third side is less than the sum of the other two sides, so it can be 22 cm.
Correct Answer: A — 22 cm
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Q. If the mean of a dataset is 50 and there are 10 numbers, what is the total sum of the numbers? (2021)
-
A.
500
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B.
600
-
C.
550
-
D.
450
Solution
Total sum = Mean * Number of elements = 50 * 10 = 500.
Correct Answer: A — 500
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Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)
-
A.
180
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B.
150
-
C.
120
-
D.
200
Solution
Total sum = Mean * Number of elements = 30 * 6 = 180.
Correct Answer: A — 180
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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)
Solution
Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.
Correct Answer: A — 30
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Q. If the median of the data set 3, 7, 9, x, 15 is 9, what is the value of x? (2022)
Solution
For the median to be 9, x must be 9. The ordered set is 3, 7, 9, 9, 15.
Correct Answer: A — 8
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Q. If the mode of the following numbers: 3, 3, 4, 5, 5, 5, 6, 7 is removed, what will be the new mode? (2019)
Solution
Removing 5, which is the mode, leaves 3 as the new mode since it appears twice.
Correct Answer: A — 3
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Q. If the mode of the following set of numbers: 1, 2, 2, 3, 4, 4, 4, 5 is increased by 1, what will be the new mode? (2022)
Solution
The original mode is 4. Increasing it by 1 gives a new mode of 5.
Correct Answer: C — 4
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Q. If the mortality rate of a disease is 5% and 2000 people are diagnosed, how many deaths are expected? (2023)
-
A.
50
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B.
75
-
C.
100
-
D.
125
Solution
Expected deaths = 5% of 2000 = 0.05 * 2000 = 100 deaths.
Correct Answer: C — 100
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Q. If the Parliament has 790 members and 20% are women, how many women are there in the Parliament?
-
A.
158
-
B.
160
-
C.
150
-
D.
170
Solution
Number of women = 20% of 790 = 0.2 * 790 = 158.
Correct Answer: A — 158
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Q. If the Parliament has 790 members and 40% are from the opposition, how many members are from the opposition?
-
A.
316
-
B.
320
-
C.
300
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D.
310
Solution
Opposition members = 40% of 790 = 0.4 * 790 = 316.
Correct Answer: A — 316
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Q. If the Parliament is in session for 120 days in a year and the Lok Sabha meets for 75% of those days, how many days does the Lok Sabha meet?
Solution
Days Lok Sabha meets = 75% of 120 = 0.75 * 120 = 90.
Correct Answer: A — 90
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Q. If the perimeter of a rectangle is 30 cm and the length is 10 cm, what is the width?
-
A.
5 cm
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B.
10 cm
-
C.
7.5 cm
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D.
15 cm
Solution
Perimeter P = 2(length + width). So, 30 = 2(10 + width). Dividing by 2 gives 15 = 10 + width. Thus, width = 15 - 10 = 5 cm.
Correct Answer: A — 5 cm
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Q. If the perimeter of a rectangle is 50 cm and the length is 15 cm, what is the width? (2020)
-
A.
10 cm
-
B.
12.5 cm
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C.
15 cm
-
D.
20 cm
Solution
Perimeter = 2(length + width). So, 50 = 2(15 + width). Solving gives width = 10 cm.
Correct Answer: B — 12.5 cm
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Q. If the perimeter of a triangle is 30 cm and the lengths of two sides are 10 cm and 12 cm, what is the length of the third side? (2020)
-
A.
8 cm
-
B.
10 cm
-
C.
12 cm
-
D.
14 cm
Solution
Let the third side be x. Then, 10 + 12 + x = 30, so x = 30 - 22 = 8 cm.
Correct Answer: A — 8 cm
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Q. If the pH of a river is measured to be 7.5, what type of water is it considered? (2020)
-
A.
Acidic
-
B.
Neutral
-
C.
Alkaline
-
D.
Distilled
Solution
A pH greater than 7 is considered alkaline.
Correct Answer: C — Alkaline
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