Geometry and Trigonometry MCQ Quiz in हिन्दी - Objective Question with Answer for Geometry and Trigonometry - मुफ्त [PDF] डाउनलोड करें

Choice B is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and ∠AOC is a central angle of the circle. From the figure, the two diameters that meet to form ∠AOC are perpendicular, so the measure of ∠AOC is 90°.

Therefore, the length of minor arc $\stackrel{⏜}{\mathrm{A}\mathrm{C}}$ is $\frac{90}{360}$ of the circumference of the circle.

Since the circumference of the circle is 40, the length of minor arc $\stackrel{⏜}{\mathrm{A}\mathrm{C}}$ is $\frac{90}{360}\times 40=10$  

Choice A is correct. A circle has 360 degrees of arc. In the circle shown, O is the center of the circle and ∠AOC is a central angle of the circle. From the figure, the two diameters that meet to form ∠AOC are perpendicular, so the measure of ∠AOC is 90°.

Therefore, the length of minor arc $\stackrel{⏜}{\mathrm{A}\mathrm{C}}$ is $\frac{90}{360}$ of the circumference of the circle. Since the circumference of the circle is 64, the length of minor arc $\stackrel{⏜}{\mathrm{A}\mathrm{C}}$ is $\frac{90}{360}\times 64=16$

Choices B, C, and D are incorrect. The perpendicular diameters divide the circumference of the circle into four equal arcs; therefore, minor arc $\stackrel{⏜}{\mathrm{A}\mathrm{C}}$ is $\frac{1}{4}$ of the circumference. However, the lengths in choices B and C are, respectively, $\frac{1}{3}$ and $\frac{1}{2}$ the circumference of the circle, and the length in choice D is the length of the entire circumference. None of these lengths is $\frac{1}{4}$ the circumference. 

Choice 4 is correct. Using the volume formula $V=\frac{7\pi k^3}{48}$ and the given information that the volume of the glass is 473 cubic centimeters, the value of k can be found as follows:

$664=\frac{7\pi k^3}{48}$

$k^3=\frac{664(48)}{7\pi }$

$k=\sqrt[3]{\frac{664(48)}{7\pi }}\approx 11.3151$

Therefore, the value of k is approximately 11.32 centimeters.

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.

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.

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.

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.

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.

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 .

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.