CBSE Set Qa5 Maths Class X 1999 Sample Test Papers For Class 10th for students online

Q28) Construct a triangle ABC with BC = 6 cm, A = 60^o and the median AD through A is 5 cm. Construct a triangle AB'C' ~ ABC with BC' = 8 cm. Write steps of construction. (Marks 6)
Ans28)  Steps of construction.
1. Draw a line segment BC = 6 cm and construct CBX = 60^o downwards.
2. Draw EB  |  BX. Also draw the perpendicular bisector of BC intersecting BE in O and BC in D.
3. With O as centre and OB as radius, draw a circle.
4. With D as centre and radius as 5 cm, draw arcs intersecting the circle in A.
Join AB and AC. The ABC is the required triangle.
5. Extend BC to C' cutting BC' = 8 cm
6. Draw C'A' || CA and extend BA to A'
Then A'BC' is the required

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Q29) If a line is drawn parallel to one side of a triangle, the other two sides are divided in the same ratio. Prove
Using the result, prove the following:
In the figure PQRS is a trapezium, PQ || SR || XY, then PX/XS = QY/YR  (Marks 6)

Ans29)  (i)

Given ABC, D is a point on AB
E is apoint on AC
DE || BC.
To prove AD/DB = AE/EC
Const. EF  |  AB, DG  |  AC
Join BE, CD
Proof. ar (ADE)/ ar (BDE) = (1/2 x AD x EF) / (1/2 x DB x EF)  -(i) ar. of a = 1/2 x base x altitude
Also ar (AED)/ ar (CED) = (1/2 x AE x DG) / (1/2 x CE x DG)  -(ii) ar. of a = 1/2 x base x altitude
ar (ADE) = ar (AED)  -(iii)   ADE & AED are same s
ar (BDE) = ar (CED)  -(iv)   s on the same base and between same parallels
= AD/DB = AE/EC  (i), (ii), (iii), & (iv)
(ii) 

Const Join PR, let it meet XY at A.
Proof In PSR , XA || SR (given)
= PX/XS = PA/AR   -(i)   (Basic proportionality Theorem)
In PRQ, AY || PQ (given)
= RY/YQ = RA/AP   -(i)   (Basic proportionality Theorem)
= QY/YR = PA/AR   -(ii)   (Taking reciprocals)
= PX/XS = QY/YR  ((i) & (ii))

Q30) Salma has the total annual income of Rs. 98,000 during a year (HRA not included). She contributes Rs. 800 per month towards P.F. and pays an annual premium of Rs. 1200 towards L.I.C. Calculate the income tax payable in the last month if she had been paying Rs. 120 per month towards income tax for for first 11 months.  (Marks 6)
Assume the following for calculating income tax :

Ans30)  Total Annual Income = Rs. 98,000
Standard Deduction = Rs. 25,000
.^.. Taxable Income = Rs. 73,000
Income Tax = Rs. 1,000 + Rs. (20/100 x 13,000)
= Rs. 36,000
Saving
Provident fund = 800 x 12 =Rs. 9600
L.I.C. = 1200 = Rs. 1200
Total savings = Rs. 10,800
Rebate on savings = 20/100 x 10,800 
= Rs. 2160
Income Tax payable = Rs. 3600 - Rs. 2160
= Rs. 1440
Surcharge = 10/100 x 1440 = Rs. 144
Total = Rs. 1440 + Rs. 144
= Rs. 1584
Tax paid in 11 months = 11 x 120  = Rs. 1320
.^.. Income Tax payable in the last month 
= Rs. 1584 - Rs. 1320 = Rs. 264

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