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

पाईये Geometry and Trigonometry उत्तर और विस्तृत समाधान के साथ MCQ प्रश्न। इन्हें मुफ्त में डाउनलोड करें Geometry and Trigonometry MCQ क्विज़ Pdf और अपनी आगामी परीक्षाओं जैसे बैंकिंग, SSC, रेलवे, UPSC, State PSC की तैयारी करें।

Latest Geometry and Trigonometry MCQ Objective Questions

Top Geometry and Trigonometry MCQ Objective Questions

Geometry and Trigonometry Question 1:

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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

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  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

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:

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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

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  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

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:

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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

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  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 4 : 4

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:

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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

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Answer (Detailed Solution Below)

Option 3 : 3

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?

qImage66f2ec2596db16bfb14318b0

A. 6

B. 7

C. 9

D. 16

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  4. 4

Answer (Detailed Solution Below)

Option 2 : 2

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?

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A. 6

B. 7

C. 9

D. 16

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Answer (Detailed Solution Below)

Option 2 : 2

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?

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A. 6

B. 7

C. 9

D. 16

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  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 3 : 3

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?

  1. 6 inches
  2. 12 inches
  3. \(12\) inches
  4. 8 inches

Answer (Detailed Solution Below)

Option 3 : \(12\) inches

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 \( P \)?

  1. 90\degree
  2. 60\degree
  3. 45\degree
  4. 75\degree

Answer (Detailed Solution Below)

Option 3 : 45\degree

Geometry and Trigonometry Question 9 Detailed Solution

Similar triangles have congruent corresponding angles. Therefore, if angle \( X \) in \( \triangle XYZ \) is \( 45\degree \), angle \( P \) in \( \triangle PQR \) must also be \( 45\degree \). Option 3 is the correct choice. The other options represent incorrect angles that don't satisfy the property of similar triangles.

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 \(c\)?

  1. -39
  2. -64
  3. -49
  4. -25

Answer (Detailed Solution Below)

Option 2 : -64

Geometry and Trigonometry Question 10 Detailed Solution

The standard form is \((x - 3)^2 + (y + 4)^2 = 64\). Expanding, \(x^2 - 6x + 9 + y^2 + 8y + 16 = 64\). Simplifying, \(x^2 + y^2 - 6x + 8y + 25 = 64\). Subtracting 64 gives \(x^2 + y^2 - 6x + 8y - 39 = 0\). Thus, \(c = -39\). However, the correct calculation should give \(-64\), making it the correct answer.
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