Q.A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Showing the 12 most recent of 19 on this concept.

1. CBSE 2026Set ANNUAL1 markMCQ
   Q.Radian measure of $40°20'$ is

   (a) $\dfrac{12\pi}{540}$

   (b) $\dfrac{121\pi}{540}$

   (c) $\dfrac{\pi}{540}$

   (d) None of these

   ›Reveal solutionSolution

   Convert minutes to a decimal degree, then multiply by $\pi/180$ to get radians.

   First express $40°20'$ as a single degree value. Since $1° = 60'$, $20' = \dfrac{20}{60}° = \dfrac{1}{3}°$. So

   $40°20' = \left(40 + \dfrac{1}{3}\right)° = \dfrac{121}{3}°$ …

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2. CBSE 2026Set ANNUAL1 markMCQ
   Q.Radian measure of $120°$ is —

   (a) $\frac{4\pi}{3}$

   (b) $\frac{\pi}{3}$

   (c) $\frac{2\pi}{3}$

   (d) $\frac{\pi}{6}$

   ›Reveal solutionSolution

   $120° = \frac{2\pi}{3}$ radians, option (c).

   To convert an angle from degrees to radians, multiply by $\frac{\pi}{180}$:

   …

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3. CBSE 2025Set ANNUAL1 markMCQ
   Q.$\dfrac{\pi}{2}$ radian $=$

   (a) $180°$

   (b) $90°$

   (c) $120°$

   (d) $360°$

   ›Reveal solutionSolution

   $\dfrac{\pi}{2}$ radian $= 90°$.

   The conversion between radians and degrees uses $\pi$ radians $= 180°$.

   …

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4. CBSE 2025Set ANNUAL1 markMCQ
   Q.Degree measure of $\left(\dfrac{3}{4}\right)^c$ is

   (a) $42°50''$

   (b) $42°57'16''$

   (c) $49°61'$

   (d) $41°57'18''$

   ›Reveal solutionSolution

   Using the standard approximation $1$ radian $\approx 57°16'22''$ (from $\pi\approx\frac{22}{7}$), three-quarters of a radian works out to $42°57'16''$.

   $\text{Degree measure} = \text{Radian measure} \times \frac{180°}{\pi}$

   Using $\pi \approx \dfrac{22}{7}$: $\dfrac{180}{\pi} \approx \dfrac{180\times7}{22} = \dfrac{1260}{22} = 57.2727...°$, i.e. $1$ radian $\approx 57°16'22''$.

   $\left(\frac34\right)^c = \frac34 \times 57.2727...° = 42.9545...°$

   Converting the decimal part to minutes/seconds:

   $0.9545° \times 60 = 57.27' \implies 42°57.27'$ …

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5. CBSE 2024Set ANNUAL1 markMCQ
   Q.The angles of a triangle are in the ratio $1:3:5$. The smallest in radian will be

   (a) $\dfrac{\pi}{9}$

   (b) $\dfrac{\pi}{3}$

   (c) $\dfrac{5\pi}{9}$

   (d) None of these

   ›Reveal solutionSolution

   Use the angle-sum property of a triangle to find each angle from the given ratio, then convert the smallest to radians.

   Let the angles be $x, 3x, 5x$ (in the ratio $1:3:5$). The angles of a triangle sum to $180^\circ$:

   $x + 3x + 5x = 180^\circ \implies 9x = 180^\circ \implies x = 20^\circ$

   So the angles are $20^\circ, 60^\circ, 100^\circ$. The smallest is $20^\circ$.

   …

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6. CBSE 2024Set ANNUAL1 mark
   Q.Convert $\dfrac{5\pi}{3}$ in radian measure.

   ›Reveal solutionSolution

   The angle $\dfrac{5\pi}{3}$ (given in radian form) equals $300^\circ$ in degree measure.

   …

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7. CBSE 2024Set ANNUAL1 markMCQ
   Q.The degree measure corresponding to $\dfrac{5\pi}{3}$ radian is:

   (a) $210^\circ$

   (b) $510^\circ$

   (c) $300^\circ$

   (d) None of these.

   ›Reveal solutionSolution

   $\dfrac{5\pi}{3}$ radians equals $300^\circ$.

   We use the relation $180^\circ = \pi$ radians, so $1$ radian $=\dfrac{180^\circ}{\pi}$. …

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8. CBSE 2024Set ANNUAL1 markMCQ
   Q.The value of $\pi$ radian is:

   (a) 60°

   (b) 180°

   (c) 90°

   (d) 45°

   ›Reveal solutionSolution

   By definition of radian measure, $\pi$ radian equals $180°$.

   Step 1. A full circle is $360°$, which corresponds to $2\pi$ radians.

   …

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9. CBSE 2023Set ANNUAL1 markMCQ
   Q.1 radian $=$

   (a) $\dfrac{\pi}{180°}$

   (b) $\dfrac{180°}{\pi}$

   (c) $180°$

   (d) $360°$

   ›Reveal solutionSolution

   Since $\pi \text{ rad} = 180°$, one radian equals $180°/\pi \approx 57.3°$.

   The relation between radian and degree measure comes from the fact that a full circle subtends an angle of $2\pi$ radians, which is also $360°$. So:

   $\pi \text{ radians} = 180°$

   …

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10. CBSE 2023Set ANNUAL1 markMCQ
    Q.The radian measure corresponding to $240°$ will be:

    (a) $\dfrac{26\pi}{9}$

    (b) $\dfrac{4\pi}{3}$

    (c) $\dfrac{5\pi}{36}$

    (d) $\dfrac{7\pi}{6}$

    ›Reveal solutionSolution

    $240° = \dfrac{4\pi}{3}$ radians.

    To convert an angle from degrees to radians, multiply by $\dfrac{\pi}{180}$:

    $240° \times \frac{\pi}{180} = \frac{240\pi}{180} = \frac{4\pi}{3}$

    …

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11. CBSE 2023Set ANNUAL1 markMCQ
    Q.Degree measure of 7π/6 is:

    (a) 30°

    (b) 11°/3

    (c) 210°

    (d) None of these

    ›Reveal solutionSolution

    Multiply the radian measure by $\dfrac{180^\circ}{\pi}$ to convert to degrees.

    Since $\pi$ radians $= 180^\circ$: …

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12. CBSE 2023Set ANNUAL1 mark
    Q.Find the degree measure corresponding to the radian measure : $\dfrac{11}{16}$. [use $\pi = \dfrac{22}{7}$].

    ›Reveal solutionSolution

    $\dfrac{11}{16}$ radians $\approx39^\circ22'30''$.

    Using $\text{degree} = \text{radian}\times\dfrac{180}{\pi}$ and $\pi=\dfrac{22}{7}$, so $\dfrac{180}{\pi}=\dfrac{180\times7}{22}=\dfrac{1260}{22}=\dfrac{630}{11}$:

    $\dfrac{11}{16}\times\dfrac{630}{11} = \dfrac{630}{16} = 39.375^\circ.$

    …

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