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

**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/AC^{2} + 1/BC^{2} = 1/CD^{2} **(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 = y^{o} and
AOD= x^{o}, 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 :

(x^{2} - 16) - (x
- 4) = (x^{2} - 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 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) **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
Slab (i) Upto Rs. 50,000 |
Income Tax No tax |

(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.