CBSE CLASS 10 MATHS SAMPLE PAPER 2018

    CBSE MATHS SAMPLE PAPER / PRACTICE PAPER 2018  

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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 n^th 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 30^o.

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  $\frac{4}{x}-3=\frac{5}{2x+3},x\ne 0,x\ne \frac{-3}{2}$
8. Prove $\frac{\sin \theta }{1-\cos \theta }+\frac{\tan \theta }{1+\cos \theta }=\sec \theta \cos ec\theta +\cot \theta$
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 $2y^2+7y+5$ 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.

Also Read:CBSE Class10 Maths Important Questions of All Chapters

Section – C

13. Solve the quadratic equation $2x^2+x-4=0$, by method of completing square.

14. If ${\tan }^2\alpha =1+2{\tan }^2\beta ,$ Prove that $2{\sin }^2\alpha =1+{\sin }^2\beta$
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 $17,15\frac{4}{5},14\frac{3}{5}\mathrm{............}$ 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 $AE=\frac{1}{4}AC$
18. If α and β are the zeroes of the polynomial $2x^2-5x+7,$ then find a quadratic polynomial whose zeores are $\left(3\alpha +4\beta \right)and\left(4\alpha +3\beta \right)$
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 $ax+by=1,bx+ay=\frac{{\left(a+b\right)}^2}{a^2+b^2}-1$

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 $\tan A+\sin A=mand\tan A-\sin A=n$ then show that $m^2-n^2=4\sqrt{mn}$
26. Solve for x, if possible, $\left(m^2+n^2\right)x^2+\left(m+n\right)x+\frac{1}{2}=0$
27. Prove Basic Proportionality Theorem.
28. If P and Q are two points whose, Co-ordinates are $\left(a{t}^2,2at\right)and\left(\frac{a}{t^2},\frac{-2a}{t}\right)$ respectively. S is a point (a, 0) Show that $\frac{1}{SP}+\frac{1}{SQ}$ 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
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