Geometry and Trigonometry MCQ Quiz in हिन्दी - Objective Question with Answer for Geometry and Trigonometry - मुफ्त [PDF] डाउनलोड करें
Last updated on Mar 11, 2025
Latest Geometry and Trigonometry MCQ Objective Questions
Top Geometry and Trigonometry MCQ Objective Questions
Geometry and Trigonometry Question 1:
The glass pictured above can hold a maximum volume of 400 cubic centimeters. What is the value of k, in centimeters?
A. 9.56
B. 7.67
C. 7.79
D. 10.11
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 1 Detailed Solution
Choice 1 is correct.
Using the volume formula \(V=\frac{7 \pi k^3}{48}\) and the given information that the volume of the glass is 400 cubic centimeters, the value of k can be found as follows:
\(400=\frac{7 \pi k^3}{48}\)
\(k^3=\frac{400(48)}{7 \pi}\)
\(k=\sqrt[3]{\frac{400(48)}{7 \pi}} \approx 9.556\)
Therefore, the value of k is approximately 9.56 centimeters.
Geometry and Trigonometry Question 2:
The figure shows the lengths, in centimeters cm, of the edges of a right rectangular prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?
A. 160
B. 240
C. 120
D. 110
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 2 Detailed Solution
Choice 1 is correct.
It's given that the volume of a right rectangular prism is ℓwh. The prism shown has a length of 5 cm, a width of 8 cm, and a height of 4 cm .
Thus, ℓwh = (5)(8)(4), or 160 cubic centimeters.
Geometry and Trigonometry Question 3:
The figure shows the lengths, in centimeters cm, of the edges of a prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?
A. 360
B. 240
C. 120
D. 250
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 3 Detailed Solution
Choice 4 is Correct.
It's given that the volume of a prism is ℓwh. The prism shown has a length of 5 cm, a width of 5 cm, and a height of 10 cm.
Thus, ℓwh = (5)(5)(10), or 250 cubic centimeters.
Geometry and Trigonometry Question 4:
The figure shows the lengths, in centimeters cm, of the edges of a right rectangular prism. The volume V of a right rectangular prism is ℓwh, where ℓ is the length of the prism, w is the width of the prism, and h is the height of the prism. What is the volume, in cubic centimeters, of the prism?
A. 36
B. 24
C. 66
D. 11
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 4 Detailed Solution
Choice 3 is correct.
It's given that the volume of a right rectangular prism is ℓwh. The prism shown has a length of 11 cm, a width of 2 cm, and a height of 3 cm .
Thus, ℓwh = (11)(2)(3), or 66 cubic centimeters.
Geometry and Trigonometry Question 5:
The triangle shown has a perimeter of 25 units. If x = 10 units and y = 8 units, what is the value of z, in units?
A. 6
B. 7
C. 9
D. 16
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 5 Detailed Solution
Choice 2 is correct.
The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 25 units. Therefore, x + y + z = 25. If x = 10 units and y = 8 units, the value of z, in units, can be found by substituting 10 for x and 8 for y in the equation x + y + z = 25, which yields 10 + 8 + z = 25, or 18 + z = 25. Subtracting 18 from both sides of this equation yields z = 7.
Therefore, if x = 10 units and y = 8 units, the value of z, in units, is 7.
Geometry and Trigonometry Question 6:
The triangle shown has a perimeter of 20 units. If x = 8 units and y = 5 units, what is the value of z, in units?
A. 6
B. 7
C. 9
D. 16
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 6 Detailed Solution
Choice 2 is correct.
The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 20 units. Therefore, x + y + z = 20. If x = 8 units and y = 5 units, the value of z, in units, can be found by substituting 8 for x and 5 for y in the equation x + y + z = 20, which yields 8 + 5 + z = 20, or 13 + z = 20. Subtracting 16 from both sides of this equation yields z = 7.
Therefore, if x = 8 units and y = 5 units, the value of z, in units, is 7 .
Geometry and Trigonometry Question 7:
The triangle shown has a perimeter of 32 units. If x = 13 units and y = 10 units, what is the value of z, in units?
A. 6
B. 7
C. 9
D. 16
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 7 Detailed Solution
Explanation:
The perimeter of a triangle is the sum of the lengths of its three sides. The triangle shown has side lengths x, y, and z. It's given that the triangle has a perimeter of 32 units.
Therefore, x + y + z = 32. If x = 13 units and y = 10 units, the value of z, in units, can be found by substituting 13 for x and 10 for y in the equation x + y + z = 32, which yields 13 + 10 + z = 32, or 23 + z = 32. Subtracting 23 from both sides of this equation yields z = 9.
Therefore, if x = 13 units and y = 10 units, the value of z, in units, is 9.
Hence Option(3) is correct.
Geometry and Trigonometry Question 8:
A rectangle is inscribed in a circle with a radius of \(10\) inches. If the length of the rectangle is \(16\) inches, what is the width of the rectangle?
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 8 Detailed Solution
The diagonal of the rectangle is equal to the diameter of the circle. The diameter is \(2 \times 10 = 20\) inches.
Using the Pythagorean theorem for the rectangle, where \(d^2 = l^2 + w^2\), we have \(20^2 = 16^2 + w^2\).
Solving for \(w\), \(400 = 256 + w^2\), \(w^2 = 144\), \(w = 12\) inches.
Option 3 is correct. Option 1 is incorrect because it represents an incorrect calculation. Option 2 and Option 4 do not satisfy the Pythagorean theorem with the given length.
Geometry and Trigonometry Question 9:
In triangle \( XYZ \), angle \( X \) is \( 45\degree \), and triangle \( XYZ \) is similar to triangle \( PQR \). What is the measure of angle \( P \)?
Answer (Detailed Solution Below)
Geometry and Trigonometry Question 9 Detailed Solution
Geometry and Trigonometry Question 10:
A circle with a center \((3, -4)\) and radius 8 is in the form \(x^2 + y^2 + ax + by + c = 0\). What is the value of \(c\)?