Maths Sample Paper 6, Part - A for class 10th

 Maths Sample Paper 6

Part - A 

Section- I

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

1. Find the smallest odd composite number.

2. Find the ration in which the line 3x +y -9=0 divides the line segment joining the points (1,3) and (2,7)

3. If the graph of quadratic equation polynomial intersect the X-axis at two points, then find the shape of parabola.

4. Two cones have their heights in the ratio 1:4 and radii in the ratio 4:1. Find the ratio of their volumes.

5. If 8 tan∅ = 15,  then find sin∅ - cos∅.

6. Find the next term of the AP 5, 2, -1, -4.

Or

Which term of the AP 3, 15, 27, 39, . . . . .will be 132 more than it's 54th term?

7. The length of the minute hand of a clock is 7cm. Find the area swept by the minute hand in one minute.

Or

The radii of the bases of two right circular solid cones of same height are r1 and r2, respectively. If both cones are melted and recast into a solid sphere of radius R. Then, find the height of each cone.

8. If mode of a data is 45,mean is 27, then find the median.

9. If radius of circle is 3cm and tangent is drawn from an external point to the circle is 4cm, then find the distance from centre of circle to the external point.

10. Of ∆ABC ~∆PQR such that AB = 5.5 cm, PQ= 11cm and perimeter of ∆ABC = 70cm, then find the perimeter of ∆PQR.

Or

If two concentric circles, a chord of length 20cm of larger circle becomes a tangent to the smaller circle whose radius is 7cm. Find the radius of the larger circle.

11. Find the probability of getting 101 marks in out of 100 marks.

12. If tan² 45° - cos²30° =x sin45° cos45°, then find the value of x.

Or

If sinA = 2/5, find the value of 5 + 4cot²A.

13. In the given figure, if ∆ACB ~ ∆APQ, BA= 6cm, BC= 8cm and PQ= 4cm, then find the length of AQ.

14. In the given figure, if AP =2cm, BQ= 3cm and RC = 4cm, then calculate the perimeter of ∆ABC.

15. In an isosceles right angled triangle, if the hypotenuse is 6√2 cm, find the length of the sides of the to triangle.

16. Evaluate the value of  sin 45° / sec 30° + cosec 30°.

Or

If sin 2A= 2 sin A, then show that it is true for A = 0°.

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Section- II

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

17. Case Study I

Parabolic Path

A car moves on a highway, the path trace by the car is shown below.

The pattern of the path traced in the shape of parabolic.

In mathematical form, the given path followed the polynomial expression in the form

p(x) = a↓nx^n +a↓n-1 x^n-1 + a↓n-2 x^n-2 +. . . . . . .. . . . . . . 

a) What is the shape of the curve CDE ?

i. Parabolic

ii. Circle

iii. Straight line

iv. Ellipse

b) If the shape of the curve ABC is represented by x² - 7x +12, then find it's zeroes are

i. 2, -3

ii. 3, 4

iii. 4, -5

iv. 3, -5

c) The path trace by the car, whose zeroes are 2 and -4, is

i. x² - 4x -8

ii. x² +2x -8

iii. x² +2x +8

iv. x² -2x +8

d) The given path is show on the coordinates axis, which is shown below.

Find the number of zeroes of the given curve i. 3

ii. 2

iii. 4

iv. 1

e) If the path ABC trace by the car in above question is represented by x² +8x +15, then find the distance between G and F.

i. 2

ii. 3

iii. 1

iv. Can't be determined

18. Case study II

Students studying in class room 

In a mathematical class, a teacher explain the concept for determine the mean by defining the formula 

xbar = sigma fixi/sigma find

Further, a teacher give one example for explaining the above concepts.

The marks obtained by 30 students of class X of a certain school in a mathematics paper consisting of 100 marks are presented in table below

Class                       Number of students

Interval

10-25                                   2

25-40                                   3

40-55                                  7

55-70                                  6

70-85                                  6

85-100                                6

a) Find the average marks obtained by the students.

i. 61

ii. 62

iii. 63

iv. 64

b) Find the cumulative frequency value in the interval (40-55).

i. 5

ii. 12

iii. 2

iv. 18

c) Through cumulative frequency table, which central measurement can be determined.

i. Mean

ii. Mode

iii. Median

iv. None of these

d) Find the lower limit of the median class.

i. 55

ii. 40

iii. 70

iv. 25

e) Find the upper limit of modal class.

i. 40

ii. 55

iii. 70

iv. 25

19. Case Study III

Campaign About Diabetes Awareness.

As a part of a campaign a huge balloon with message of " AWARENESS OF DIABITIES" was displayed from the terrace of a tall building.

It was held by string of length 8m each, which inclined at an angle of 60° at the point, where it was tied as shown in the figure.

a) ∆ABC is a/an

i. Isosceles

ii. Equilateral

iii. Right triangle

iv. Right angled isosceles

b) What is the length of AB?

i. 8m

ii. 6m

iii. 7m

iv. 9m

c) If the perpendicular distance from the centre of the circle to the chord AB is 3cm, then find the radius of the circle

i. 4m

ii. 3m

iii. 5m

iv. 6m

d) Find the distance between the centre of circle and vertex of triangle P.

i. 9.43cm

ii. 9.8cm

iii. 9.9cm

iv. 10.1cm

e) The area of ∆APB is

i. 25√3 

ii. 29√3

iii. 30√3

iv. 16√3

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Posted by :- Anuranjan Gadekar

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