CBSE Set Q1 Maths Class X 1998 Sample Test Papers For Class 10th for students online

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Maths Class X (CBSE)
You are on Set no 1 Qno. 21 to 30

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)

Q22) In Fig. 4, AB is the chord of a circle with centre O. AB is produced to C such that BC = OB. CO is joined and produced to meet the circle in D. If ACD = yo and AOD= xo, prove that x = 3y (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)

Section - C

Q26) Solve for x :
(x2 - 16) - (x - 4) = (x2 - 5x + 4)  (Marks 6)

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 45o and the angle of depression of the base is 30o, 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) Construct a ABC in which AB = 5cm, B = 60o and altitude CD = 3 cm. Construct AQR similar to ABC such that each side of AQR is 1.5 times that of the corresponding side of ABC.  (Marks 6)

Q30) 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 :

(a) Standard Deduction 1/3 of the total income subject to a maximum of Rs. 20,000
(Rs. 25,000 if income is less than Rs. 1 lac)
(b) Rates of Income tax


(i) Upto Rs. 50,000
(ii) From Rs. 50,001 to 60,000
(iii) From Rs. 60,001 to Rs. 1,50,000
(iv) From Rs. 1,50,001 onwards


Income Tax

No tax
10% of the amount exceeds Rs. 50,000
Rs. 1,000 + 20% of the amount exceeding Rs. 60,000

Rs. 19,000 + 30% of the amount exceeding Rs. 1,50,000

(c) Rebate in Tax 20% of the total savings subject to a maximum of Rs. 12,000
(d) Surcharge 10% of the tax payable

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