Circle

Q. The circumference of a circle with diameter 28 cm is .

1. 80 cm
2. 88 cm
3. 66 cm
4. 44 cm

Q. Question 7
Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Q. The chords of contact of the pair of tangents drawn from each point on the line
$2x+y=4$ to the circle $x^2+y^2=1$ pass through the point ___.

1. $(\frac{1}{2},\frac{1}{4})$
2. (2, 1)
3. (1, 2)
4. $(\frac{1}{4},\frac{1}{2})$

Q.

A circle divides the plane in which it lies into

1. 4 parts

2. 3 parts

3. 5 parts

4. 2 parts

Q. Circle(s) touching X-axis at a distance 3 from the origin and having an intercept of length $2\sqrt{7}$ on Y-axis is/are

1. $x^2+y^2-6x+8y+9=0$
2. $x^2+y^2-6x+7y+9=0$
3. $x^2+y^2-6x-8y+9=0$
4. $x^2+y^2-6x-7y+9=0$

Q. A motorcycle wheel has a radius of 14 cm. The distance covered by the wheel after 2 full rotations is .
$(\pi =\frac{22}{7})$

1. 176 cm
2. 166 cm
3. 156 cm
4. 170 cm

Q. The ratio of circumference of a circle to its diameter is always equal to .

1. $\pi$
2. $\frac{\pi }{d}$
3. 3.366
4. d

Q.

The circumference of a circle is $132cm$ then its diameter is$:$

1. $14cm$

2. $42cm$

3. $30cm$

4. $20cm$

Q.

A quadrilateral ABCD is drawn to circumscribe a circle, as shown in the figure. Prove that AB + CD = AD + BC [1 MARK]

Q. A set of all the points in a plane which are at a fixed distance from a fixed point is .

1. triangle
2. circle
3. parallelogram

Q.

If a wheel has six spokes equally spaced, then find the measure of the angle between two adjacent spokes.

Q. Find the circumeference of the circle having radius 1cm.

Q. A line segment that lies within a circle and does not pass through the centre of the circle is called .

1. tangent
2. secant
3. chord
4. diameter

Q. Question 7
The weights (in kg) of 50 wrestlers are recorded in the following table.
$\begin{array}{cccccc}\text{Weight(in~kg)}& 100-110& 110-120& 120-130& 130-140& 140-150\\ \text{Number of wrestlers}& 4& 14& 21& 8& 3\end{array}$
Find the mean weight of the wrestlers.

Q.

If a circle is divided into three equal arcs, each arc is a

1. Circle

2. Major arc

3. Semi-circle

4. Minor arc

Q.

If the tangent to the curve, $\mathrm{y}={\mathrm{e}}^{\mathrm{x}}$ at a point $\left(\mathrm{c},{\mathrm{e}}^{\mathrm{c}}\right)$ and the normal to the parabola, ${\mathrm{y}}^2=4\mathrm{x}$ at the point $\left(1,2\right)$ intersect at the same point on the $x$-axis, then the value of $c$ is

Q. If x + y + k = 0 is a tangent to the circle $x^2+y^2$ - 2x - 4y + 3 = 0 then k =

1. 20
2. –1, – 5
3. 2
4. 4

Q. In Fig. 9, O is the centre of the circle. The distance between P and Q is 4 cm. Find the ∠ROQ.

Q. Question 1
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Q.

A wheel has a radius of 70 cm. How many revolutions of the wheel are needed to cover a distance of 44 m?

1. 10

2. 14

3. 4

4. 8

Q. Question 4
The weights of tea in 70 packets are shown in the following table
$\begin{array}{cc}\text{Weight(in~g) \& Number of packets}& \\ 200-201& 13\\ 201-202& 27\\ 202-203& 18\\ 203-204& 10\\ 204-205& 1\\ 205-206& 1\end{array}$
Find the mean weight of packets.

Q. How many tangents can be drawn to a circle from a point on the circle?

Q.

The differential equation of the system of circles touching the y-axis at origin is

1. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{\left({\mathrm{x}}^2+{\mathrm{y}}^2\right)}{2\mathrm{xy}}$

2. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{\left({\mathrm{y}}^2-{\mathrm{x}}^2\right)}{\mathrm{xy}}$

3. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{\left({\mathrm{y}}^2-{\mathrm{x}}^2\right)}{2\mathrm{xy}}$

4. $\frac{d\mathrm{y}}{d\mathrm{x}}=\frac{\left({\mathrm{x}}^2-{\mathrm{y}}^2\right)}{2\mathrm{xy}}$

Q.

If the equation of the tangent to the circle$x^2+y^2-2x+6y-6=0$ parallel to $3x-4y+7=0$ is $3x-4y+k=0$, then the values of $k$ are

1. $5,-35$

2. $-5,35$

3. $7,-32$

4. $-7,32$

Q. In the given figure, the major segment and the minor sector are
and respectively.

1. PRQP
2. OPRQ
3. PSQP
4. OPSQ

Q.

The figure shown below is a circle centered at O. AB and CD are ___ of the circle.

1. sectors

2. segments

3. chords

4. diameters

Q. Question 1 (vi)
Fill in the blanks:

(vi) A circle divides the plane, on which it lies, in to __________ parts.

Q.

A circle with center O is shown. AB in the figure is a :

1. Diameter

2. Radius

3. Chord

4. Tangent

Q.

The major segment and the minor segment of the longest chord of a circle are congruent.

1. True

2. False

Q.

The area of a circular field is 88704 sq. m. How long will it take to go round 10 times at the speed of 4.5 km per hour?

1. 2.34 hrs

2. 2.34 hrs

3. 3.24 hrs

4. 4.28 hrs