Question: The value of cos 0° cos 1° cos 2° cos 3° … cos 89° cos 90° is.
(a) 1
(b) -1
(c) 0
(d) None
(c) 0
Explanation:
The product includes the term cos90∘, which
equals 0. Therefore, the entire product is 0.
Question: Three circles touch each other externally. The distance between their centers is 5 cm, 6 cm and 7 cm. Find the radii of the circles.
(a) 2 cm, 3 cm, 4 cm
(b) 1 cm, 2 cm, 4 cm
(c) 1 cm, 2.5 cm, 3.5 cm
(d) 3 cm, 4 cm, 1 cm
(a) 2 cm, 3 cm, 4 cm
Explanation:
Let radii be r1,r2,r3. We get r1+r2=5,r2+r3=6,r3+r1=7. Solving these simultaneous equations gives the radii as 2, 3, and 4 cm.
Question: A point P is 13 cm from the Centre of a circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.
(a) 5 cm
(b) 7 cm
(c) 10 cm
(d) 12 cm
(a) 5 cm
Explanation:
Using the Pythagorean theorem, radius2+tangent2=distance2⟹r2+122=132⟹r2=169−144=25,
so r=5 cm.
Question: Consider point A on the circle of radius 7/π cm. A ball on point A moves along the circumference until it reaches point B. The tangent at B is parallel to the tangent at A. What is the distance travelled by the ball? (Consider the ball to be a point object).
(a) 3.5 cm
(b) 7 cm
(c) 14cm/
(d) 28 cm
(b) 7 cm
Explanation:
Parallel tangents mean the ball travels along a semi-circle. Circumference C=2πr=2π(7/π)=14 cm. Distance = C/2=7 cm.
Question: A pendulum swings through an angle of 30° and describes an arc 8.8 cm in length. Find the length of the pendulum in cm.
(a) 16.8 cm
(b) 17.3 cm
(c) 15.1 cm
(d) 14.5 cm
(a) 16.8 cm
Explanation:
Using the arc length formula l=(θ/360)×2πr, we get 8.8=(30/360)×2×(22/7)×r. Solving for r (the pendulum length) gives 16.8 cm.