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CBSE Class 10 Mathematics Worksheet

1.

A pair of tangents can be constructed to a circle inclined at an angle of ______.

A)

B)

C)

D)

2.

By geometrical construction, it is possible to divide a line segment in the ratio

A)

TRUE

B)

FALSE

3.

A pair of tangents can be constructed to a circle inclined at an angle of

A)

TRUE

B)

FALSE

4.

To construct a triangle similar to a given with its sides 3/7 of the corresponding sides of , first draw a ray BX such that is an acute angle and X lies on the opposite side of A with respect to BC. Then locate points B1 , B2 , B3 , ... on BX at equal distances and next step is to join______.

A)

B10 to C

B)

B7 to C

C)

B3 to C

D)

5.

Which theorem criterion we are using in giving the just the justification of the division of a line segment by usual method ?

A)

SSS criteria

B)

Basic proportionality theorem

C)

Pythagor

6.

Construct an isosceles triangle whose base 7 cm and altitude is 3.5 cm?

7.

To divide a line segment PQ in the ratio a : b (a, b are positive integers), draw a ray PX so that is an acute angle and then mark points on ray PX at equal distances such that the minimum number of these points is_____.

A)

a

B)

a - b

C)

8.

To draw a tangent at point B to the circumcircle of an isosceles right ΔABCright angled at B, we need to draw through B ______

A)

a line perpendicular to BC

B)

a line perpendicular to AB

C)

9.

To divide a line segment PQ in the ratio 3:2, a ray PX is drawn first such that is an acute angle and then points P1 , P2 , P3 , .... are located at equal distances on the ray PX and the point Q is joined to_____.

A)

P5

B)

P2

C)

P3

D)

10.

To divide a line segment AB in the ratio 4 : 5, draw a ray AX such that is an acute angle, then draw a ray BY parallel to AX and the points A1 , A2 , A3 , ... and B1 , B2, B3, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are_______.

A)

A6 and B5

B)

A4 and B5

C)

A5 and B4

11.

Divide a line segment AB of length 5 cm into 3:2 ratio

12.

To draw a pair of tangents to a circle which are at right angles to each other, it is required to draw tangents at end points of the two radii of the circle, which are inclined at an angle of_______.

A)

B)

C)

D)

13.

To divide a line segment AB in the ratio 4:5, first a ray AX is drawn so that is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is______.

A)

8

B)

9

C)

4

D)

14.

In division of a line segment AB, any ray AX making angle with AB is_____.

A)

right angle

B)

obtuse angle

C)

ac

15.

Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameter each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q?

16.

To draw tangents to a circle of radius ‘p’ from a point on the concentric circle of radius ‘q’, the first step is to find_____.

A)

mid point of q

B)

mid point of p

C)

mid point of q-p

D)

17.

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 3/4 of the corresponding sides of the first triangle?

18.

Two distinct tangents can be constructed from a point P to a circle of radius r situated at a distance.

A)

r from centre

B)

r/2 from centre

C)

More than r from centre

19.

Construct a triangle similar to a given triangle PQR with PQ = 4cm, QR = 5 cm and PR = 6 cm with its sides equal to 4/5 of the corresponding sides of the triangle PQR?

20.

Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths?

CBSE Class 10 Mathematics Worksheet

Answers

1.
Option B
2.
Option A
3.
Option A
4.
Option B
5.
Option B

6.

  1. Draw a line AB = 7 cm

  2. From mid point D of AB draw a line CD = 3.5 cm perpendicular to AB.

  3. Join AC and BC and ABC is the required triangle.

7.
Option C
8.
Option C
9.
Option A
10.
Option C

11.

  1. Draw a line segment AB = 5 cm

  2. Locate 5 points A1 , A2 , A3 , A4 and A5 on AX so that AA1 = A1 A2 = A2 A3 = A3 A4 = A4 A5

  3. Join BA5

  4. Through the point A3 , draw a line parallel to A5B (by making an angle equal to ) at A3 intersecting AB at the point C. Then, AC : CB = 3 : 2  

12.
Option D
13.
Option B
14.
Option C

15.

  1. With O as a centre and radius equal to 3 cm, a circle is drawn.

  2. The diameter of the circle is extended both sides and an arc is made to cut it at 7 cm.

  3. Perpendicular bisector of OP and OQ is drawn and X and Y be its mid-point.

  4. With O as a centre and OX be its radius, a circle is drawn which intersected the previous circle at M and N.

  5. Step 4 is repeated with O as centre and Oy as radius and it intersected the circle at R and T.

  6. PM and PN are joined also QR and QT are joined.

16.
Option A

17.

  1. Construct triangle PQR using SSS criteria

  2. Locate 5  points Q1 , Q2 , Q3 , Q4  on QX so that QQ1 = Q1Q2 = Q2Q3 = Q3Q4

  3. Join Q3R and draw a line through Q3  parallel to Q5C to intersect QR at R′  

  4. Draw a line through R′ parallel to the line PR to intersect PQ at P′. Then, P′QR′ is the required triangle.

18.
Option C

19.

  1. Construct triangle PQR using SSS criteria

  2. Locate 5  points Q1 , Q2 , Q3 , Q4 , Q5 on QX so that QQ1 = Q1Q2 = Q2Q3 = Q3Q4 = Q4Q5

  3. Join Q5R and draw a line through Q4  parallel to Q5C to intersect QR at R′  

  4. Draw a line through R′ parallel to the line PR to intersect PQ at P′. Then, P′QR′ is the required triangle   

20.

  1. Draw a circle of radius 6 cm with centre O.

  2. Draw PO = 10 cm and bisect it. Let M be the midpoint of PO where is P is outside the circle.

  3. Taking M as centre and MO as radius, draw a circle. Let it intersect the given circle at the points Q and R.

  4. Join PQ and PR. Then PQ and PR are the required two tangents.