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

 Mathematics Sample Paper 

Part-A

Section-I

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

1. Find the pair of zeroes of the polynomial 2x²+14x+20.

2. Choose the correct statement to correct the following (if required), if 2x²+bx+8=0 has non real roots, then find the value of b.

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3. In the given figure, DE\\AC and DC\\AP, such that BC=4 cm and BP= 6cm, then find BE/EC.

4. Find the value of 

cot² 30° + 8 sin² 45° + 3/2 sec 30° + 2 cos² 90°/

2 sec60° + 3 cosec 30° - 7/3 tan² 60°

Or

If 3 cot∅=2, then find the value of 4 sin∅- 3cos∅/ 2 sin∅+6cos∅.

5. If xi are the mid points of the class intervals of grouped data, fi's are the corresponding frequencies and x bar is the mean, then find sigma (fixi-xbar).

6. Find the distance between the points P(-6,7) and Q(-1,-5).

7. In the given figure, if AD is perpendicular at BC and BD=2, AC=4, then find the value of AB²+CD².

8. If the perimeter of a semi circle protractor is 36 cm, then find it's diameter.

9. The probability of an event that cannot happen is zero. Is this statement true?

Or

State whether the following statement is true/false.

If the occurrence of one event can't be expected  in preference of the other event, then there events are called equally likely events.

10. Find the area of circle, if circumference of circle is 22 cm.

11. To divide a line segment AB in the ratio 3:7, first a ray AX is drawn, so that angle BAX is an acute angle and then at equal distances. Find the number of points are located on the ray AX.

12. In figure, PQ and PR are tangents drawn from P to a circle with centre O. If angle OPQ=35°, then find the values of a and b.

Or

Two circle of radii 5cm and 3cm are concetric. Calculate the length of a chord of the circle which touches the inner circle.

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13. If the HCF of 85 and 153 is expressible in the form of 85m-153, then find the value of m.

14. Find the roots of the quadratic equations 2x²+x+4.

Or

Find the discriminant of quadratic equation x²-4x+1=0.

15. For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an AP?

16. Find the maximum volume of a cone that can be curved out of a solid hemisphere of radius r.

Section-II

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

17. Case Study I 

Gokuldham Society

The resident welfare association of a Gokuldham society  decided to build two straight paths in their neighborhood park such that they don't cross each other, and also plant trees along the boundary lines of each path.

One of the memebers of association popat Lal suggested that the path should be constructed represented by the two linear equations x-3y=2 and -2x +6y=5.

a) If the pair of equations a1x +b1y +c1=0 and a2x +b2y +c2=0 has infinitely solutions, then condition is

i. a1/a2 ≠ b1/b2=c1/c2

ii. a1/a2 =b1/b2=c1/c2

iii. a1/a2=b1/b2≠c1/c2

iv. None of these

b) If pair of lines are parallel, then pair of linear equations is

i. Inconsistent 

ii. Consistent

iii. Consistent or inconsistent

iv. None of the above.

c) Check whether the two paths will cross each other or not.

i. Yes

ii. No

iii. Do not say

iv. None of the above

d) How many points lie on the line x-3y=2?

i. One

ii. Two

iii. Three

iv. Infinitely

e) If the line 2x+6y=5 intersect the X-axis, then find it's coordinate.

i. (-2.5,0)

ii. (2.5,0)

iii. (0,2.5)

iv. (0,-2.5)

18. Case Study III

Angle of Depression

A straight highway leads near to the foot of a tower.

A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the car is found to be 60°, whose distance is 5m.

a) Find the height of the tower.

i. 5√3 m

ii. 6√3 m

iii. 5 m

iv. 6 m

b) Find the distance between the two positions of the car.

i. 8 m

ii. 9 m

iii. 10 m

iv. 11 m

c) Find the further time taken by the car to reach the foot of the tower.

i. 2 s

ii. 3 s

iii. 5 s

iv. 4 s

d) If we interchange the position of the angles, then it will be logically correct.

i. Yes

ii. No

iii. Don't say anything

iv. None of the above

e) Find the distance from observer to the car,in which it makes an angle 60°.

i. 10cm

ii. 9cm

iii. 8cm

iv. 11cm

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Posted by:- Anuranjan Gadekar

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