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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