CBSE 11 Math Practice Paper 03

CBSE 11 Mathematics 

Practice Paper 03

1. Find the degree measures corresponding to the following radian measures (Use \(\pi = \frac{22}7\) ).

 (i)  \(\frac{11}{15}\)    (ii)  \(– 5 \)   (iii)  \(\frac{-7π}3\)   (iv)  \(\frac{7π}2\)

2. Find the radian measures corresponding to the following degree measures: 

   (i)  \(15°\)         (ii)  \(-27°30'\)     (iii)  \(210°\)        (iv)  \(720°\)

3. Find the radius of the circle in which a central angle of 60° intercepts an arc of  length 37.4 cm (use \(π = \frac{22}7\)).

4. The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes? (Use \(π = 3.14\)).

5. If the arcs of the same lengths in two circles subtend angles 162° and 54° at the centre, find the ratio of their radii.

6. A wheel of a bicycle completes 210 revolutions in one minute. Through how many radians does it turn in one second? 

7. A circle of diameter 40 cm and the length of a chord is 20 cm. Find the length of minor arc of the chord.

8. Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm (Use \(π =\frac{22}7\)). 

9. If in two circles, arcs of the same length subtend angles 70° and 65°  at the centre, find the ratio of their radii.

10. Find the value of: 

      (i)  \(sin15°\)

      (ii)  \(tan 75°\)

      (iii) \(tan\frac{19π}3\) 

      (iv)  \(sin\frac{– 13π}3\)  

      (v)  \(cot\frac{– 17π}5\)

     (vi)  \(cos(–540°)\)

     (vii)  \(cos (–270°)\)

11. Prove that:

    (i)  \(sin^2\frac{π}3 + cos^2\frac{π}4  –  tan^2 \frac{\pi}3 =-2\)

   (ii)  \(tan4x = \frac{4tanx(1-tan^2x) }{1-6tan^2x+tan^4x}\)

   (iii)  \(cos4x = 1-8sin^2xcos^2x\)

   (iv)  \(cos6x = 32cos^6 x – 48cos^4 x + 18cos^2 x – 1\)

  (v)  \(\frac{sinx - siny}{cosx + cosy} = tan\frac{ (x-y)}2\)

  (vi)  \(sin (n + 1)x.sin (n + 2)x+\) \(cos(n + 1)x.cos (n + 2)x=\)\(cos x\)

 (vii)  \(cos\frac{3\pi}{4+x }- cos\frac{3\pi}{4 -  x }=\)\(-\sqrt2 sinx\)

12. Solve  \(sin 2x- sin 4x + sin 6x = 0\)

13. Solve  \(2cos^2 x + 3 sin x = 0\)

14. Prove that

 \(sin (40 + θ).cos(10 + θ)–\) \(cos(40 + θ).sin(10 + θ)\)\(= \frac{1}2\)

15. Find the principal solution of the eq.   \(sinx=\frac{\sqrt3}2\)

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