Mathematics Sample Paper 7, Part- A for class 10th

 Maths Sample paper

Part- A 

Section- I

Directions (Q.nos 1-16 are of 1 marks each)

1. A five digit number is a multiple of 11 and 91. If the second digit from the left is 8, then find the fourth digit from the left of the number.

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2. Find the number of solutions of the pair of equations x=0 and x=3.

3. If the 5th term of an AP is zero, then find the relation between 12th and 26th term.

Or

If the sum of n terms of an AP is 3n² + 5n, then which of it's term is 164?

4. Rubal standing in his  backyard decides to estimate the height of a tree. He stands such that the tip of his shadow coincides with the tip of the tree's shadow, as shown. Rubal is 66inch tall. The distance between the tip of the shadow and Rubal is 7ft. Find the height of the tree to the nearest foot.

5. In the given figure, O is the centre of the circle with PA and PB as tangents.

If measure of angle ADB= 60°, then show that ∆PAB is an equilateral triangle.

Or

If a ∆ABC, D and E are points on the sides AB and AC respectively such that DE\\BC. If AD/DB= 2/3 and AC=18cm, then find the value of AE.

6. If cosecA =2, then find the value of 1/tanA+ sinA/1+cosA.

7. The minute hand of a clock is 10cm long. Find the area swept by the minute hand between 8:00 to 8:25.

8. The diameter of a copper sphere is 6cm. The sphere is melted and recast into a wire. If the length of wire is 36cm, then find it's radius.

9. In the given figure, angle ABC=90° and BD perpendicular AC. If BD =8cm and AD=4cm, then find the value of CD.

10. Find the distance between two parallel tangents of a circle having radius 3cm.

11. If a cylinder is filled with water and spherical ball of r is dropped into the cylinder, find the quantity of water is spread out.

Or

When we rotate a right triangle about the perpendicular line, then write the shape of the three dimensional formed figure.

12. Find the discriminant of the quadratic equation 6x² -7x +2=0.

13. If the length of a tangent to a circle from a point is 0.5 cm, then find it's radius.

14. A standard deck of 52 cards is shuffled. Ritu draws a single card from the deck at random. What is the probability that the card is Jack?

Or

Two dice are thrown together. Find the probability that sum of the two numbers will be multiple of 4.

15. Find the value of 1-tan²45°/ 1+tan²45°.

Or

Find the simplified value of (1-cos²A) cosec²A.

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16. The mean of n observations is xbar. If the first term is increased by 1, second by 2 and so on, then find the new mean.

Section- II

Directions (Q.nos 17-20 are of 4 marks each)

Rampur Village 

People of village want to construct a road nearer to a circular village Rampur. The road can't pass through the village. But the people want the road should be at the shortest distance from the centre of the village.

Suppose the road start from point O which is outside the circular village and touch the boundary of the circular village at point A such that OA=20cm.

And also, the straight distance of the point O from the centre C of the village is 25cm.

a) Find the shortest distance of the road from the centre of the village.

i. 15cm

ii. 14cm

iii. 13 cm

iv. 12cm

b) Which method should be apply to find the shortest distance?

i. Concept of tangent to a circle

ii. Pythagoras theorem

iii. Both i and ii

iv. None of the above

c) If a point in inside the circle, how many tangents can be drawn from that point

i. 0

ii. 1

iii. 2

iv. 3

d) If two circles are externally and they don't touch, then find the number of common tangents.

i. 2

ii. 3

iii. 4

iv. 1

e) If we draw two tangents at the end of the diameter, then these tangents are always

i. parallel

ii. Perpendicular

iii. Coincident

iv. None of the above

18. Case study II

Sports Day

In a sports day celebration, the school decided to make activity between students in such a way that Vicky, Garvit and Shalini are standing at positions A, B and C whose coordinates are (3,3), (5,9) and (9,3) respectively. The teacher asked Deepanshi to fix the country flag at the mid point of the line joining point A and B.

a) Find the coordinates of the mid point of A and B.

i. (4,3)

ii. (3,4)

iii. (4,4)

iv. (3,3)

b) Find the distance between Garvit and Vicky.

i. 3√10

ii. 2√10

iii. √10

iv. 4√10

c) What is the space covered by these persons?

i. 18

ii. 17

iii. 16

iv. 15

d) Find the point on X axis, which is equidistant from points A and C.

i. (0,-6)

ii. (-6,0)

iii. (0,6)

iv. (6,0)

e) If vertices of a ∆PQR are (x1 and y1), (x2, x2) and (x3, y3), then centroid of a ∆PQR is

i. (x1+x2+x3/2, y1+y2+y3/2)

ii. (x1+x2+x3/3, y1+y2+y3/3)

iii. (x1+x2+x3/4, y1+y2+y3/4)

iv. None of the above.

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Posted by :- Anuranjan Gadekar

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