Q. In triangle ABC, if the lengths of sides a, b, and c are 7, 24, and 25 respectively, what is the area of the triangle?
-
A.
84
-
B.
96
-
C.
120
-
D.
168
Solution
Using Heron's formula, s = (7 + 24 + 25)/2 = 28. Area = √[s(s-a)(s-b)(s-c)] = √[28(28-7)(28-24)(28-25)] = √[28*21*4*3] = 84.
Correct Answer: B — 96
Learn More →
Q. In triangle ABC, if the lengths of sides a, b, and c are 8, 15, and 17 respectively, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the lengths of sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Isosceles
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the lengths of the sides are 10 cm, 24 cm, and 26 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 10² + 24² = 100 + 576 = 676 = 26², triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the lengths of the sides are 5, 12, and 13, what is the perimeter?
Solution
Perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
Learn More →
Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the perimeter?
-
A.
30 cm
-
B.
40 cm
-
C.
50 cm
-
D.
60 cm
Solution
Perimeter = 8 + 15 + 17 = 40 cm.
Correct Answer: A — 30 cm
Learn More →
Q. In triangle ABC, if the lengths of the sides are 8 cm, 15 cm, and 17 cm, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the area of the triangle?
-
A.
60
-
B.
80
-
C.
120
-
D.
150
Solution
Using Heron's formula, the semi-perimeter s = (8 + 15 + 17)/2 = 20. Area = √[s(s-a)(s-b)(s-c)] = √[20(20-8)(20-15)(20-17)] = √[20*12*5*3] = 60.
Correct Answer: A — 60
Learn More →
Q. In triangle ABC, if the lengths of the sides are 8, 15, and 17, what is the type of triangle?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since 8² + 15² = 64 + 225 = 289 = 17², triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the lengths of the sides are a = 5, b = 12, and c = 13, what is the perimeter of the triangle?
Solution
The perimeter of a triangle is the sum of its sides. Therefore, perimeter = a + b + c = 5 + 12 + 13 = 30.
Correct Answer: B — 25
Learn More →
Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the value of cos A?
-
A.
0.5
-
B.
0.6
-
C.
0.8
-
D.
0.9
Solution
Using the cosine rule, cos A = (b² + c² - a²) / (2bc) = (15² + 17² - 8²) / (2 * 15 * 17) = 0.8.
Correct Answer: C — 0.8
Learn More →
Q. In triangle ABC, if the lengths of the sides are a = 8, b = 15, and c = 17, what is the perimeter?
Solution
The perimeter of a triangle is the sum of its sides: a + b + c = 8 + 15 + 17 = 40.
Correct Answer: A — 30
Learn More →
Q. In triangle ABC, if the lengths of the sides are in the ratio 3:4:5, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
Since the sides are in the ratio of a Pythagorean triplet (3, 4, 5), triangle ABC is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the sides are in the ratio 3:4:5, what is the nature of the triangle?
-
A.
Equilateral
-
B.
Isosceles
-
C.
Right
-
D.
Scalene
Solution
The sides satisfy the Pythagorean theorem, hence it is a right triangle.
Correct Answer: C — Right
Learn More →
Q. In triangle ABC, if the sides are in the ratio 3:4:5, what type of triangle is it?
-
A.
Acute
-
B.
Obtuse
-
C.
Right
-
D.
Equilateral
Solution
A triangle with sides in the ratio 3:4:5 is a right triangle, as it satisfies the Pythagorean theorem.
Correct Answer: C — Right
Learn More →
Q. In triangle DEF, if angle D = 45 degrees and angle E = 45 degrees, what is the type of triangle? (2020)
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right
Solution
Since two angles are equal (45 degrees), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
Learn More →
Q. In triangle DEF, if angle D is 45 degrees and angle E is 45 degrees, what type of triangle is DEF?
-
A.
Scalene
-
B.
Isosceles
-
C.
Equilateral
-
D.
Right-angled
Solution
Since two angles are equal (45 degrees each), triangle DEF is an isosceles triangle.
Correct Answer: B — Isosceles
Learn More →
Q. In triangle GHI, if GH = 10 cm, HI = 24 cm, and GI = 26 cm, what is the length of the longest side? (2022)
-
A.
10 cm
-
B.
24 cm
-
C.
26 cm
-
D.
Cannot be determined
Solution
The longest side of triangle GHI is GI, which measures 26 cm.
Correct Answer: C — 26 cm
Learn More →
Q. In triangle MNO, if angle M = 45 degrees and angle N = 45 degrees, what is angle O?
-
A.
90 degrees
-
B.
45 degrees
-
C.
60 degrees
-
D.
30 degrees
Solution
Angle O = 180 - (angle M + angle N) = 180 - (45 + 45) = 90 degrees.
Correct Answer: A — 90 degrees
Learn More →
Q. In triangle PQR, if PQ = 10 cm, QR = 24 cm, and PR = 26 cm, what is the area of the triangle?
-
A.
120 cm²
-
B.
120√3 cm²
-
C.
240 cm²
-
D.
48 cm²
Solution
Using Heron's formula, s = (10 + 24 + 26)/2 = 30. Area = √(30(30-10)(30-24)(30-26)) = √(30*20*6*4) = 120 cm².
Correct Answer: A — 120 cm²
Learn More →
Q. In triangle PQR, if PQ = 8 cm, QR = 6 cm, and PR = 10 cm, what is the perimeter of the triangle? (2022)
-
A.
24 cm
-
B.
26 cm
-
C.
22 cm
-
D.
20 cm
Solution
Perimeter = PQ + QR + PR = 8 + 6 + 10 = 24 cm.
Correct Answer: A — 24 cm
Learn More →
Q. In triangle XYZ, if side XY is 8 cm, side YZ is 6 cm, and side XZ is 10 cm, which of the following is true?
-
A.
It is a right triangle.
-
B.
It is an isosceles triangle.
-
C.
It is an equilateral triangle.
-
D.
It is a scalene triangle.
Solution
Since all sides are of different lengths, triangle XYZ is a scalene triangle.
Correct Answer: D — It is a scalene triangle.
Learn More →
Q. In triangle XYZ, if XY = 8 cm, YZ = 15 cm, and XZ = 17 cm, is it a right triangle?
-
A.
Yes
-
B.
No
-
C.
Cannot be determined
-
D.
Only if XY is the hypotenuse
Solution
Since 8^2 + 15^2 = 17^2, triangle XYZ is a right triangle.
Correct Answer: A — Yes
Learn More →
Q. In triangle XYZ, if XY = 8 cm, YZ = 6 cm, and XZ = 10 cm, which of the following is true?
-
A.
It is an equilateral triangle.
-
B.
It is an isosceles triangle.
-
C.
It is a scalene triangle.
-
D.
It is a right triangle.
Solution
Since all sides are of different lengths, triangle XYZ is a scalene triangle.
Correct Answer: C — It is a scalene triangle.
Learn More →
Q. In uniform circular motion, which of the following quantities remains constant?
-
A.
Speed
-
B.
Velocity
-
C.
Acceleration
-
D.
Centripetal force
Solution
In uniform circular motion, the speed remains constant, but velocity and acceleration change direction.
Correct Answer: A — Speed
Learn More →
Q. In uniform circular motion, which of the following statements is true?
-
A.
Velocity is constant
-
B.
Acceleration is zero
-
C.
Speed is constant
-
D.
Net force is zero
Solution
In uniform circular motion, speed is constant but velocity changes due to direction change.
Correct Answer: C — Speed is constant
Learn More →
Q. In what year did India gain independence and subsequently join the United Nations? (1947)
-
A.
1947
-
B.
1948
-
C.
1950
-
D.
1952
Solution
India gained independence in 1947 and joined the United Nations on October 30, 1948.
Correct Answer: B — 1948
Learn More →
Q. In what year did India gain independence from British rule? (1947)
-
A.
1942
-
B.
1945
-
C.
1947
-
D.
1950
Solution
India gained independence from British rule on August 15, 1947.
Correct Answer: C — 1947
Learn More →
Q. In what year did the Rwandan Genocide occur? (1994)
-
A.
1992
-
B.
1994
-
C.
1996
-
D.
1998
Solution
The Rwandan Genocide occurred in 1994, resulting in the deaths of an estimated 800,000 people.
Correct Answer: B — 1994
Learn More →
Q. In which case does total internal reflection occur? (2022)
-
A.
When light travels from a denser to a rarer medium
-
B.
When light travels from a rarer to a denser medium
-
C.
At the critical angle
-
D.
None of the above
Solution
Total internal reflection occurs when light travels from a denser medium to a rarer medium at an angle greater than the critical angle.
Correct Answer: A — When light travels from a denser to a rarer medium
Learn More →
Showing 8791 to 8820 of 19973 (666 Pages)
