CBSE Set Qa5 Maths Class X 1998 Sample Test Papers For Class 10th for students online
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)
Ans28) Part I Read Q21, Se1 I, 1996
Part II
Join AC which intersects EF at G
In 
CAB, GF || AB
... FC/BF = CG/AG = BF/FC = AG/CG ...(i)
In ADC, EG || DC
... AE/ED = AG/GC ...(ii)
From (i) and (ii), we get AE/ED = BF/FC
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)
Ans29)
Steps of construction.
1. Draw AB = 5 cm.
2. At B, make an angle ABP
= 60o of any length.
3. Draw lm || AB at a distance of 3 cm which intersect BP at C.
4. From C draw CE | AB intersecting AB at D such that CD = 3
cm. Join AC.
5. Extend AB to Q making AQ = 7.5 cm
6. Draw QX || BC. Extend AC intersecting QX at R.
Then AQR is the required triangle.
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 |
Ans30)
| Total Annual
Income S.D. (Permissible)* Income tax on Rs. 50,000 Income tax on next Rs. 10,000 (given) Income tax on next Rs. 85,000 @20% = 20/100 x 85,000 Total Income Tax Saving for tax rebate P.F. = 4000 x 12 = Rs. 48,000 L.I.C. Premium = Rs. 16,000 = Rs. 64,000 Rebate in tax @ 20% = 20/100 x 64,000 = Rs. 12,800 But Rs. 12,800 is more than Rs. 12,000 ... Rebate in Tax Income tax payable Surcharge @ 10% Total Tax paid in 11 months @ Rs. 400pm ... Tax to be paid in last month |
= Rs. 1,65,000 = Rs. 20,000 = Rs. 1,45,000 = Nil = Rs. 1,000 = Rs. 17,000 = Rs. 18,000 = Rs. 12,000 = Rs. 6,000 = Rs. 600 = Rs. 6,600 = Rs. 4,400 = Rs. 2,200 |
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