General Instructions:

1. This question paper consists of 40 questions divided into four sections: A, B, C, and D.
2. Section A comprises 20 questions of 1 mark each.
3. Section B comprises 6 questions of 2 marks each.
4. Section C comprises 8 questions of 3 marks each.
5. Section D comprises 6 questions of 4 marks each.
6. All questions are compulsory. Use of calculators is not permitted.

1. 1. What is the smallest number by which 392 must be multiplied so that the product is a perfect cube?
   (a) 2(b) 3 (c) 5(d) 7
2. 2. The value of $\sqrt{0.9}$ is approximately:
   (a) 0.3(b) 0.03 (c) 0.948(d) 0.81
3. 3. Multiplicative inverse of $10^{-100}$ is:
   (a) $10^{-100}$(b) $10^{100}$ (c) $10$(d) $-10^{100}$
4. 4. If 15 workers can build a wall in 48 hours, how many workers will be required to do the same work in 30 hours?
   (a) 15(b) 20 (c) 24(d) 30
5. 5. A table marked at ₹15,000 is available for ₹14,400. The discount percentage is:
   (a) 2%(b) 4% (c) 5%(d) 10%
6. 6. The compound interest on ₹10,000 at 10% per annum for 1 year, compounded half-yearly is:
   (a) ₹1,000(b) ₹1,025 (c) ₹1,050(d) ₹1,100
7. 7. $(a + b)^2 - (a - b)^2$ is equal to:
   (a) $2(a^2 + b^2)$(b) $4ab$ (c) $2ab$(d) $a^2 + b^2$
8. 8. The degree of the polynomial $7x^3 - 5x^2 + 2x - 9$ is:
   (a) 1(b) 2 (c) 3(d) 0
9. 9. Two adjacent angles of a parallelogram are in the ratio 4:5. The angles are:
   (a) $40^\circ, 50^\circ$(b) $80^\circ, 100^\circ$ (c) $100^\circ, 120^\circ$(d) $70^\circ, 110^\circ$
10. 10. The solution of the equation $\frac{3x - 4}{2} - \frac{2x - 1}{3} = {0}{}$ is:
    (a) $x = 2.4$(b) $x = 3$ (c) $x = 2$(d) $x = 1$
11. 11. Which of the following quadrilaterals has diagonals that are equal and bisect each other at $90^\circ$?
    (a) Rectangle(b) Rhombus (c) Square(d) Parallelogram
12. 12. To construct a rectangle, we need to know at least:
    (a) One adjacent side(b) Two adjacent sides (c) All four sides(d) One diagonal only
13. 13. The total surface area of a cube is $96 \text{ cm}^2$. The volume of the cube is:
    (a) $8 \text{ cm}^3$(b) $27 \text{ cm}^3$ (c) $64 \text{ cm}^3$(d) $512 \text{ cm}^3$
14. 14. The point $(0, -5)$ lies on:
    (a) Positive x-axis(b) Negative x-axis (c) Positive y-axis(d) Negative y-axis
15. 15. In a histogram, the width of the bars is determined by:
    (a) Frequency(b) Class Interval (c) Class Mark(d) Upper Limit
16. 16. A bag contains 4 red balls and 6 black balls. A ball is drawn at random. The probability of getting a red ball is:
    (a) $2/5$(b) $3/5$ (c) $4/6$(d) $1/2$
17. 17. Euler’s formula for any polyhedron is:
    (a) $F + V - E = 2$(b) $F + E - V = 2$ (c) $F - V + E = 2$(d) $V + E - F = 2$
18. 18. The order of rotational symmetry of a regular hexagon is:
    (a) 4(b) 6 (c) 3(d) 8
19. 19. Which of the following is a binomial?
    (a) $3x^2$(b) $4x - 5y$ (c) $2x + 3y - 5$(d) $7$
20. 20. If the side of a cube is doubled, its surface area becomes:
    (a) 2 times(b) 3 times (c) 4 times(d) 8 times

21. 21. Find the value of $\sqrt{156.25}$ by the long division method.
22. 22. Evaluate: $\left\{ \left( \frac{1}{3} \right)^{-1} - \left( \frac{1}{4} \right)^{-1} \right\}^{-1}$
23. 23. Factorise completely: $25a^2 - 4b^2 + 28bc - 49c^2$.
24. 24. The area of a trapezium is $34 \text{ cm}^2$ and the length of one of the parallel sides is $10 \text{ cm}$ and its height is $4 \text{ cm}$. Find the length of the other parallel side.
25. 25. Solve for $x$: $5^{x+1} \times 5^3 = 5^9$.
26. 26. A coin is tossed 200 times and it was found that Head appeared 120 times and Tail 80 times. If a coin is tossed at random, what is the probability of getting a Tail?

27. 27. Find the smallest number of 4 digits which is a perfect square. Also, find the square root of the number so obtained.
28. 28. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is added to the original number, we get 143. Find the original number.
29. 29. In the figure below, line $l \parallel m$ and $t$ is a transversal. If $\angle 1 = (2x + 15)^\circ$ and $\angle 2 = (3x - 5)^\circ$, find the measure of all the angles. (Note: $\angle 1$ and $\angle 2$ are consecutive interior angles).
    
30. 30. If $x^2 + \frac{1}{x^2} = 62$, find the value of:
    (i) $x + \frac{1}{x}$
    (ii) $x - \frac{1}{x}$
31. 31. A hostel has enough food provisions for 125 students for 16 days. How long will the food last if 75 more students join the group?
32. 32. A shopkeeper allows a discount of 10% on his goods and still makes a profit of 20%. Find the cost price of an article which is marked at ₹800.
33. 33. Construct a quadrilateral PQRS where $PQ = 4$ cm, $QR = 6$ cm, $RS = 5$ cm, $PS = 5.5$ cm and diagonal $PR = 7$ cm.
34. 34. The following table gives the marks scored by students in an exam. Draw a histogram to represent the data.

    Marks	0-10	10-20	20-30	30-40	40-50
    No. of Students	5	10	15	20	12

35. 35. The difference between the Compound Interest and Simple Interest on a certain sum of money for 3 years at 5% per annum is ₹61. Find the sum.
36. 36. ABCD is a rectangle. Diagonals AC and BD intersect at O.
    (i) Explain why $\Delta AOB \cong \Delta DOC$.
    (ii) If $\angle AOB = 110^\circ$, find $\angle DAO$.
37. 37. Divide the polynomial $6x^4 + 11x^3 - 44x^2 - 12x + 17$ by $(3x^2 + 7x - 5)$ and verify the division algorithm.
38. 38. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of the road roller is 84 cm and length is 1 m. (Take $\pi = 22/7$).
39. 39. The following table shows the interest paid by a bank for different principal amounts deposited for a year:

    Deposit (in ₹)	1000	2000	3000	4000	5000
    S.I. (in ₹)	80	160	240	320	400

    (i) Plot a graph for this data.
    (ii) From the graph, find the interest on ₹2500.
    (iii) From the graph, find the deposit amount to get an interest of ₹280.
40. 40. Two trains are moving in opposite directions. Train A is 150 m long and moving at 60 km/h. Train B is 200 m long and moving at 90 km/h. How much time will they take to cross each other completely?