Header Ads Widget



CBSE Class 10 Maths Sample Paper
Image Credit : www.cbse.nic.in

Click here for CBSE Class 10 Science Sample Paper 2018

Practice Paper – 1

Time Allowed : 3 Hours                                                                                                Maximum Marks : 100
General Instructions :
(i) All questions are compulsory.
(ii) This model test paper contains 30 questions.
(iii) Questions 1 to 6 in section – A are very short answers type questions carrying mark each.
(iv)Questions 7 to 12 in section – B are short answer type questions carrying 2 marks each.
(v) Questions 13 to 22 in section – C are long answer – I type questions carrying 3 marks each.
(vi) Questions 23 to 30 in section – D are long answer – II type questions carrying 4 marks each.
Section A

1. If P( x, y) is equidistant from Q( -2, 5) and R(6, -1) then determine a relationship between x and y.
2. If the nth term of an A.P. is (2n + 1). What is the sum of its first three terms.
3. If P(E) = 0.06, then what is the probability of “not E”.
4. Find the value of x: If cos( 40 + x) = sin 30o.
5. Find the curved surface area of a right circular cone whose radius is 5cm and vertical height is 15cm.
6. What will be the angle of elevation of the sun when the length of a shadow of a vertical Pole is equal to its height.

Section – B

7. Solve   4 x 3= 5 2x+3 ,x0,x 3 2
8. Prove sinθ 1cosθ + tanθ 1+cosθ =secθcosecθ+cotθ
9. Find the radius of a circle, if the length of tangent from a point at distance of 25cm from the centre of the circle is 24cm.
10. If α and β are the zeros of the polynomial 2 y 2 +7y+5 write the values of α + β + αβ.
11. Construct a line segment AB of length 7cm, Using ruler and compass. Find a point P on AB such that P divides AB in to 3 : 2.
12. Prove that the points (a, b + c), (b, c + a), and (c, a + b) are collinear.

Section – C

13. Solve the quadratic equation 2 x 2 +x4=0 , by method of completing square.
14. If tan 2 α=1+2 tan 2 β, Prove that 2 sin 2 α=1+ sin 2 β
15. From a top of a 50m high tower, the angles of depression of the bottom of a pole are observed to be 30o and 45o, respectively. Find the height of the pole. ( √3 =1.73).
16. What least number of the terms of the sequence 17,15 4 5 ,14 3 5 ............ should be taken, so that the sum is negative.
17. ABC is an isosceles triangle such that AB = AC. D is the mid point of AC, A circle is drawn taking BD as diameter which intersects AB at the point E. Prove that AE= 1 4 AC
18. If α and β are the zeroes of the polynomial 2 x 2 5x+7, then find a quadratic polynomial whose zeores are ( 3α+4β )and( 4α+3β )
19. Mallica and Deepica are friends what is the probability that both have
i) different birthdays.
Ii) Same birthday ( ignoring a leap year)
20. Determine the co-ordinates of the centre of a circle passing through the points A(8, 6), B(2, -2) and C(8,-2), Also find the radius of the circle.
21. A survey regarding the heights( in cm) of 50 girls of class X of a school was conducted and the following data was obtained.
Heights(in cm) 120-130 130-140 140-150 150-160 160-170
No. of girls 2 8 12 20 8
Find the mean,meadian and mode of the above data.
22. Solve ax+by=1,bx+ay= ( a+b ) 2 a 2 + b 2 1

Section – D

23. The perimeters of the ends of the frustum of a cone are 207.24cm and 169.56cm. If the height of the frustum be 8cm, find the whole surface of the frustum. [ Use π = 3.14].

24. The sum of five consecutive odd integers is 686. What are the numbers.
25. If tanA+sinA=mandtanAsinA=n then show that m 2 n 2 =4 mn
26. Solve for x, if possible, ( m 2 + n 2 ) x 2 +( m+n )x+ 1 2 =0
27. Prove Basic Proportionality Theorem.
28. If P and Q are two points whose, Co-ordinates are ( a t 2 ,2at )and( a t 2 , 2a t ) respectively. S is a point (a, 0) Show that 1 SP + 1 SQ is independent of “t”.
29. In given fig. triangle ABC is an obtuse triangle, obtuse angled at B. If AD is perpendicular to CB (produced)Prove that A C 2 =A B 2 +B C 2 +2BC.BD
30. It can take 12 hours to fill a swimming pool using two pipes. If the pipe of larger diameter is used for 4 hours and the pipe of smaller diameter for 9 hours, Only half the pool can be filled . How long would it take each pipe to fill the pool separately.

Also Read : CBSE Class10 Sample Papers with Solutions
                                  Pair Of Linear Equations in Two Variables Practice Paper
If You have any Query or suggestion,Please let us know in comment section and you can also contact us via whatsapp on +91 8439619735.

Post a Comment


  1. Also give their answers along with the,,, solution

    1. Contact on Whatsapp number above,we will provide you solution.

  2. Is it possible to download the practice paper? Thanks for your support and help

  3. Excellent contribution by bharadwaj classes for the students.Especially for those who can not afford coaching classes.