Math's Class X (CBSE)
Sample Paper Set - II

Time allowed : 3 hours
Maximum Marks : 100

General Instructions :

(i) Question number 1 to 15 carry 2 marks each.
(ii) Question number 16 to 25 carry 4 marks each.
(iii) Question number 26 to 30 carry 6 marks each.
(iv) Write the serial number of the question before attempting it.
(v) Use of logarithmic and trignometric tables is permitted. Use of calculator is not permitted.

Section - A

Q1) If -4 is a root of the quadratic equation x² + px - 4 = 0 and the quadratic equation x² + px + k = 0 has equal roots, find the value of k.  (Marks 2)

Q2) Reduce the following to the lowest terms :
((x - 1)(x - 2)(x² - x - 72))/((x - 9)(x² + x - 2))  (Marks 2)

Q3) If the mean of the following distribution is 6, find the value of p :  (Marks 2)

Q4) A shopkeeper buys a number of books for Rs. 80. If he had bought 4 more books for the same amount, each book would have cost him Rs. 1 less. How many books did he buy? (Marks 4)

Q5) A vessel, in the form of a hemispherical bowl, is ful of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are 3.5 cm and 7 cm respectively. Find the height to which water will rise in the cylinder.  (Marks 4)

Q6) Reduce the following to the lowest terms :
(x - 3)(x² - 5x + 4)/(x - 4)(x² - 2x - 3)  (Marks 2)

Q7) Find the value of k such that the sum of the squares of the roots of the quadratic equation x² - 8x + k = 0, is 40.  (Marks 2)

Q8) An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight of the pillar if the cu.cm of iron weighs 7.8 grams.  (Marks 4)

Q10) Rs. 6,500 were divided equally among a certain number of persons. Had there been 15 more persons, each would have got Rs. 30 less. Find the original number of persons.  (Marks 4)

Q11) Determine the value of c for which the following system of linear equation has no solution:
cx + 3y = 3; 12x + cy = 6  (Marks 2)

Q12) The GCD and LCM of two polynomials P(x) and Q(x) are x(x + a) and 12x²(x + a)(x² + a²) respectively. If P(x) = 4(x + a)², find Q(x)  (Marks 2)

Q13) If q is the mean proportional between p and r, show that pqr(p + q + r)³ = (pq + qr + pr)³  (Marks 2)

Q14) The sales price of a television, inclusive of sales tax, is Rs. 13,500. If sales tax is charged at the rate of 8% of the list price, find the list price of the television.  (Marks 2)

Q15) Without using trigonometric tables evaluate : 2(cos 67^o/sin 23^o) - (tan 40^o/cot 50^o) - sin90^o  (Marks 2)

Q16) Flow Chart - Omitted being out of Syllabus.  (Marks 2)

Q17) The median of the following observations arranged in ascending order is 24. Find x.
11, 12, 14, 18, x + 2, x + 4, 30, 32, 35, 41  (Marks 2)

Section - B

Q18) Solve graphically the following system of linear equations : 2x - y = 2; 4x - y = 8.
Also, find the co-ordinates of the points where the lines meet the axis of x.  (Marks 4)

Q19) Factorise. Omitted, being out of Syllabus.  (Marks 4)

Q20) Students of a class are made to stand in rows. If 4 students are extra in a row, there would be 2 rows less. If 4 students are less in a row, there would be 4 more rows. Find the number of students in the class.  (Marks 4)

Q21) In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed for the trip was reduced by 100 km/hour and time increased by 30 minutes. Find the original duration of flight.  (Marks 4)

Q22) A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 19 cm and the diameter of the cylinder is 7cm. Find the volume and surface area of the solid.  (Marks 4)

Q21) In a right triangle ABC, right angled at C, at point D is taken on AB such that CD is perpendicular to AB, Prove that
1/AC² + 1/BC² = 1/CD²  (Marks 4)

Q23) Algorithm - Omitted being out Syllabus.  (Marks 4)

Q24) Flow Chart - Omitted, being out of Syllabus.  (Marks 4)

Q25) The population of two towns A and B are 8,76,000 and 6,90,000 respectively and the respective crude death rates are 14.3 and 16.2 respectively. Find to the nearest whole number, the crude death rate for the two towns taken together.  (Marks 4)

Q27) A man on the deck of a ship is 16 m above water level. He observes that the angle of elevation of the top of a cliff is 45^o and the angle of depression of the base is 30^o, Calculate the distance of the cliff from the ship and the height of the cliff.  (Marks 6)

Q28) If a line is drawn parallel to one side of a triangle, the two sides are divided in the same ratio - Prove
Use the result to prove the following :
In Fig 5, if ABCD is a trapezium in which AB || DC || EF, then
AE/ED = BF/FC  (Marks 6)

Q29) The annual income of Shyam Lal (excluding HRA) is Rs. 1,65,000. He contributes Rs. 4,000 per month in his provident fund and pays an annual premium or Rs. 16,000, towards his Life Insurance Policy. Calculate the income tax paid by Syam Lal in the last month of the year if his earlier deduction for first 11 months for income tax were at rate of Rs. 400 per month. (changed)  (Marks 6)
Assume the following for calculating income tax :

Note: Question done according to the latest syllabus. Annual salary taken as Rs.1,65,000 in place of  Rs.1,60,000.