Chhatrapati Shahu Ji Maharaj University 2000 CBSE X MATHS - Question Paper

CBSE MATHS CLASS :X 2000 SECTION A
Q1. For what value of k will the subsequent system of linear equations have an infinite number of solutions:
2x + 3y = 2; (k + 2)x + (2k + 1)y = 2(k - 1)?
for the system to have infinite number of solutions.
Q2. obtain whether the numbers 6, 10, 14 and 22 are in proportion or not. If not, what number be added to every of the numbers so that they become proportional ?
Q3. decrease the subsequent rational expression into its least form:

Q4. Solve for x and y: ax + by = a - b, bx - ay = a + b
Q5. obtain the value of k such that sum of the roots of the quadratic formula
3x2 + (2k + 1)x - (k + 5) = 0 is equal to the product of its roots.
Q6. obtain 2 consecutive numbers, whose squares have the sum 85.
Q7. Without using trigonometric tables, show that: tan7°.tan23°.tan60°.tan67°.tan83°= .
Q9. In the provided figure, chords PQ and RS of a circle intersect at T. If RS = 18 cm, ST = six cm and PT = 18 cm, obtain the length of TQ.

Q10. In the provided figure, DE ½½ BC and AD:DB = 5:4.
obtain
Q11. In the provide figure, Ð BAC = 30°. Show that BC is equal to the radius of the circumcircle of DABC whose centre is at O.

Q12. Rita purchased a car, with a marked price of Rs 210,000 at a discount of 5%. If sale tax is charged at 10%, obtain the amount Rita had to pay for purchasing the car.
Q13. The mean weight of 21 students of a class is 52 kg. If the mean weight of the 1st 11 learner of the class is 50 kg and that of the last 11 learner is 54 kg, obtain the weight of the eleventh learner.
Q14. The subsequent data have been organizes in ascending order:
12, 14, 17, 20, 22, x, 26, 28, 32, 36.
If the median of the data is 23, obtain x.
In the above data, if 32 is changed to 23, obtain the new median.
Q15. For what value of x, is the mode of the subsequent data 5?
2, 4, 3, 5, 4, 5, 6, 4, x, 7, 5.
Q16. Determine graphically the co-ordinates of the vertices of the triangle, the equations of whose sides are
y = x, 3x = x and x + y = 8.
Q17. A part of monthly hostel charges in a college are fixed and the remaining depend on the number of days 1 has taken food in the mess. When a learner A takes food for 20 days, he has to pay Rs 1000 as hostel charges whereas a learner B, who takes food for 26 days, pays Rs 1180 as hostel charges. obtain the fixed charge and the cost of food per day.
Ans17. Let the fixed charges be Rs x and the charge for food per day is Rs y.
Then, x + 20y = 1000 and x + 26y = 1180
Solving we get, 6y = 180 Þ y = 30 and x = 1000 - 20 × 30 = 400.
Q18. obtain the values of a and b so that the polynomials P(x) and Q(x) have (x + 1)(x - 2) as their HCF:
P(x) = (x2 + 3x + 2)(x2 + x + a), Q(x) = (x2 - 3x + 2)(x2 - 3x + b).
Q19. A page from the pass book of Ved is provided below:

Date Particulars Amount withdrawn Amount deposited Balance
Rs P Rs P Rs P
8 March, 98 B/F __ __ __ __ 4,500 00
12 March, 98 To cheque 600 00 __ __ 3,900 00
18 April, 98 By cheque __ __ 1,600 00 5,500 00
26 April, 98 By cash __ __ 3,500 00 9,000 00
12 August, 98 By cash __ __ 500 00 9,500 00
16 October, 98 To cheque 4,500 00 __ __ 5,000 00
12 November, 98 By cheque __ __ 1,650 00 6,650 00
3 December By cash __ __ 1,350 00 8,000 00
obtain the interest Ved gets for the period March, 98 to the end of December, 98 at 5% per annum simple interest.
Q20. The annual income of Seema (excluding HRA ) is Rs 1,60,000. She contributes Rs 5,000 per month to her provident fund account and pays a half-yearly insurance premium of Rs 5,000. compute the income tax along with surcharge that Seema has to pay in the last month of the year if her earlier deductions as income tax for the 1st 11 months were at the rate of Rs 400 per month.
Q21. Show that: 2sec2q - sec4q - 2cosec2q + cosec4q = cot4q - tan4q
Q22. In the figure, AB is the diameter of the circle with centre O and OA = seven cm. obtain the area of the shaded region .
Q23. In the figure, AB and CD are 2 parallel tangents to a circle with centre O. ST is the tangent segment ranging from the 2 parallel tangents touching the circle at Q. Show that
ÐSOT = 90°.
Q24. Construct a quadrilateral ABCD in which AB = 2.5 cm, BC = 3.5 cm, AC = 4.2 cm, CD = 3.5 cm and AD = 2.5 cm. Construct a different quadrilateral AB'C'D' with diagonal AC' = 6.3 cm such that it is similar to quadrilateral ABCD.
Q25. obtain the cost of residing index number for the year 1995 taking 1990 as base year, from the subsequent data:

Commodity Quantity (in kg) Rate per k. (in Rs)
in 1990 in 1995
A 10 7.00 10.00
B 15 12.00 20.00
C 8 25.00 25.00
D 25 12.00 20.00
E 5 50.00 60.00

Q26. Solve for x: 9x+2 - six ´ 3x+1 + one = 0
Q27. If the radii of the circular ends of a conical bucket, which is 45 cm high , are 28 cm and seven cm, obtain the capacity of the bucket.
Q28. Prove that the ratio of the areas of 2 similar triangles is equal to the squares of their corresponding sides.
Using the above, do the following:
In the figure, DABC and DPQR are isoceles triangles in which ÐA = Ð P.



Q29. Prove that the sum of either pair of opposite angles of a cyclic quadrilateral is 180°. Using the above, solve the subsequent :
In the figure, POQ is the diameter and PQRS is the cyclic quadrilateral. If ÐPSR = 150°, obtain ÐRPQ.

Q30. A man on the roof of a house, which is 10 m high, observes the angle of elevation of the top of a building as 42° and the angle of depression of the base of the building as 40°. obtain the height of the building and its distance form the house.

Earning:   Approval pending.