# BHARDWAJ CLASSES

## Class 10 Maths Practice Paper – 2

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. What are the points where the graph of $P\left(x\right)={x}^{2}+x-12$.
2. For any integers ‘a’ and 3 , there exists unique integers ‘q’ and ‘r’ such that $a=3q+r$ , find the possible value of ‘r’.
3. Write the next term of the A.P. $\sqrt{8},\sqrt{18},\sqrt{32,}.........$
4. Evaluate $\mathrm{sin}{60}^{o}\mathrm{cos}{30}^{o}+\mathrm{sin}{30}^{0}\mathrm{cos}{60}^{0}$
5. A solid sphere of radius 20cm is converted into eight equal solid spherical balls. Find the diameter of the spherical balls obtained.
6. Find the value of ‘k’ so that the following system of equations has no solution $3x−y−5=0, 6x−2y+k=0$
Section – B
7. Find the roots of the quadratic equation by factorization method $\frac{6}{x}-\frac{2}{x-1}=\frac{1}{x-2};x\ne 0,1,2$
8.The following figure represents the area swept by a wiper of car.
If OA = 21cm & AB = 14cm, find the area and the perimeter of the area swept.
9. Find the value of p, if the mean of the following distribution is 20.

10. Show that the points (2,3), (3,4), (5,6) and (4,5) are the vertices of a parallelogram.
11. Find the sum of all 2-digits positive numbers divisible by 3.
12. Prove that $a{\mathrm{sec}}^{2}\theta -5{\mathrm{tan}}^{2}\theta =5+4{\mathrm{sec}}^{2}\theta$ .

Section – C
13. Prove that $\frac{\mathrm{sin}\theta }{1-\frac{1}{\mathrm{sin}\theta }}\text{\hspace{0.17em}}+\text{\hspace{0.17em}}\frac{\frac{1}{\mathrm{sin}\theta }}{1-\mathrm{sin}\theta }\text{\hspace{0.17em}}\text{\hspace{0.17em}}=\text{\hspace{0.17em}}\text{\hspace{0.17em}}1+\text{\hspace{0.17em}}\mathrm{sin}\theta \text{\hspace{0.17em}}+\text{\hspace{0.17em}}\frac{1}{\mathrm{sin}\theta }$ .
14.A bag contains 10 red balls, 15 white balls and 5 black balls. A ball is drawn from this bag. What is the probability that the ball drawn is neither white nor black.
15. Construct a triangle of sides 5cm, 6cm and 7cm and then a triangle similar to it whose sides are 4/5 of the corresponding sides of the first triangle.
16. The angle of elevation of the top ‘P’ of the vertical tower PQ from a point ‘X’ is 60o at a point Y, 40m vertically above the point X, the angle of elevation of the top P is 45o
i) Find the height of the tower
ii) Find the distance XQ.
17. In the given figure , if LM || CB and LN || CD Prove that $\frac{AM}{AB}=\frac{AN}{AD}$
18. If M, N and T are in A.P. , Prove that ( M + 2N – T )(2N + T – M )( T + M – N ) = 4MNT
19. There is a square field whose side is 44 meter. A square flower bed is prepared in it centre leaving a gravel path all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 2.75 and Rs. 1.50 per square meter respectively is Rs.4909. Find the width of the gravel path.
20. The iron pillar has some part in the form of a right circular cylinder and the remaining in the form of a right circular cone. The radius of the base of each cone and cylinder is 8cm. The cylindrical part is 240cm high and the conical part is 36cm high. Find the weight of the pillar if one cubic cm of iron weight 10gm.
21. The area of an equilateral triangle is 49√3 square cm. Taking each vertex as centre, circles are described with radius equal to half the length of the sides of the triangle. Find the area of the part of triangle not included in the circles. (√3 = 1.73, π=22/7)
22. If the zeores of the polynomials $3{x}^{2}-px+2\text{\hspace{0.17em}}and\text{\hspace{0.17em}}4{x}^{2}-qx-10$ is 2 , find the value of 2p -3q.
Section – D
23. A metallic right circular cone 20cm high and whose vertical angle is 60o is cut into two parts at the middle of its height by a plane parallel to its base. It the frustum so obtained be drawn into a wire of diameter 1/16 cm, find the length of the wire.
24. ABC is an isosceles triangle with AB = AC and D is a point on AC such that $B{C}^{2}=AC×CD,\text{\hspace{0.17em}}prove\text{\hspace{0.17em}}that\text{\hspace{0.17em}}BD=BC$
25.Sides of a triangular field are 15m, 16m and 17m. with the three cornerns of the field, a cow, a buffalo and a horse and tied separately with ropes of length 7m each to graze in the field. Find the area of the field which cannot be grazed by the three animals.
26. Drawn both ‘Less than ogive’ and ‘more than ogive’ of the following distribution and hence find the median.

27. In Triangle ABC right angled at C if $\mathrm{tan}A=\frac{1}{\sqrt{3}}\text{\hspace{0.17em}}and\text{\hspace{0.17em}}\mathrm{tan}B=\sqrt{3}$ Show that $\mathrm{sin}A\mathrm{cos}B+\mathrm{cos}A\mathrm{sin}B=1$
28. A marble statue of height h meters is mounted on a pedestal, The angles of elevation of the top and bottom of the statue from a point h2 meters above the ground level are $\alpha \text{\hspace{0.17em}}and\text{\hspace{0.17em}}\beta$ respectively. Show that the height of the pedestal is $\frac{\left({h}_{1}-{h}_{2}\right)\mathrm{tan}\beta +{h}_{2}\mathrm{tan}\alpha }{\mathrm{tan}\alpha -\mathrm{tan}\beta }$
29. In the given figure ABC is a triangle co-ordinates of whose one vertex is A(0, -1), D and E are the mid points of the sides AB and AC and their co-ordinates are (1, 0) and (0,1) respectively if f is the mid points of BC, find the areas of triangle ABC and triangle DEF.

30. On van mahotsav day some students planted trees in horizontal and vertical rows. They planted 480 trees in all such that there were four trees more in each horizontal row then in vertical row.
i) Find the no. of trees in each horizontal row.
ii) What values was exhibited by the students who planted trees?

2.  0, 1, 2
3. √50 or 5√2
4. 1
5. 20cm
6. K ≠ 10
7. x = 3 or x = 4/3
8. 28 + 56π/3
9. p = 1
11. 1665
14. 1/3
16. i) 20√3 (√3 +1)
ii) 20 (√3 +1)
19. 2m
20. 506.881 Kg
21. 7.77cm2
25. (24√21 -77)m2
30.  i) 24 trees

ii) Environmental Awarencess

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