CLASS 10 MATHS SAMPLE PAPER 3

SAMPLE PAPER PAPER 3

CLASS -X (MATHEMATICS)

Time : 3 Hours M.M.80

GENERAL INSTRUCTIONS :

All questions are compulsory.
There are four section A,B, C and D
Section A contains 10 questions of 1 mark each
Section B contains 5 questions of 2 marks each
Section C contains 10 questions of 3 marks each and
Section D contains 5 questions carrying 6 marks each. There is one internal choice in section B, three in section C and two in section D.
Use of calculator and mobile phone is not permitted

SECTION – A

1. What is the probability for a leap year to have 53 Sundays

4x² ─ 8√x + 3 = 0

4. If one root of quadratic equation 3x² ─ kx + 6 = 0, what is the value of k.

5. Find the sum of all odd integers between 2 and 100 divisible by 3.

6. What is the common difference of an AP in which

a₂₃ ─ a_{18 = 45}

7. The diameter of a sphere is 6 cm. It is melted and drawn into a wire

of diameter 2mm. Find the length of the wire.

SECTION – B

11. Find value of k for which the quadratic equation.

( k + 4 ) x2 + ( k + 1 ) x + 1 = 0 has equal roots.

12.   Three horses are tethered at the corners of a triangular plot having sides
        20m, 30 m and 40 m with ropes of length 7 m each. Find the area of the
        plotwhich can be grazed by the horses.

13. The volume and surface area of a sphere are numerically equal; find the

radius of the sphere.

14. Find the value of p for which the points (-1,3), (2,p) and (5,-1) are collinear

Section– C

16. The some of two natural numbers is 8.Determine the numbers if the sum
of their reciprocals is

17. Find the zero’s of the quadratic polynomial x2 + 11x + 30 and verify
relation between zero’s and coefficient of the polynomial.

19. Two AP’s have the same common difference. The first terms of the AP’s

are 15 and 8 respectively.What is the difference between their 40^th terms

20. A Cylindrical can of internal diameter 21 cm contains water. A solid sphere
    whose diameter is 10.5 cm is lowered into the Cylindrical can.The sphere is
    completely immersed in water.Calculate the rise in the water level,assuming
    that no water overflows.

22. Cards numbered 4, 5, 6, ……...., 50 are place in a box and are mixed

thoroughly. A card is drawn, what is the probability that it is (i) odd (ii)

divisible by 3.

23.

25. A circle is inscribed in the quadrilateral ABCD. Given BC = 38 cm, BQ=27

cm, CD = 25 cm and <ADC = 90°, find the radius of the circle.

SECTION – D

26. Some amount is distributed equally among a certain number of students.If

there are 8 students less, everyone will get Rs 10 more.If there are 16

students more, everyone will get Rs 10 less. What is the number of

students and how much dose each get?

27. If twice the area of the smaller of two squares is subtracted from the area
     of the larger square, the result is 14 cm². However,if twice the area of the
     larger square is added to three times the area of the smaller square, the
     result is 203 cm². Determine the sides of the squares.

28. The height of a cone is 32 cm. A small cone is cut off at the top by a plane

parallel to its base. If its volume be 1/64 of the volume of the given cone,
find at what height above the base is the section made?

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