CBSE Set Qa2 Maths Class X 2000 Sample Test Papers For Class 10th for students online
Q9) In the given
figure chord PQ and RS of a circle intersect at T. If RS = 18 cm, ST = 6 cm and
PT = 18 cm, find the length of TQ. (Marks 2)
Ans9) QT x TP = ST x TR (chords of a circle intersect
proportionally)
= QT x 18 = 6 x 12 (... TP = 18 cm, ST = 6
cm, TR = 12 cm)
= QT = 72/18
= 4
... QT = 4 cm
Q10) In the
given figure DE || BC and AD : DB = 5 : 4
Find ar(
DFE)/ar(CFB).
(Marks 2)
Ans10) DE || BC (given)
= 
ADE = ABC
(corresponding angles)
In ADE and ABC
A = A
(common)
ADE = ABC
(proved)
= ADE ~ ABC
(A.A.)
= AD/AB = DE/BC = 5/9 (corresponding sides proportional and AD/DB =
5/4)
In DFE and CFB
1 = 2
(vertically opp. angles)
3 = 4
(interior alternate angles)
=DFE ~ CFB
(A.A.)
= ar (DFE)/ar (CFB)
= DE2/BC2 (Ratio of areas of two similar
triangles is equal to ratio of
= 25/81
squares of corresponding sides DE/BC = 5/9)
Q11) ) In the
figure BAC = 30o.
Show that BC is equal to the radius of the circum-circle of ABC
whose centre is O. (Marks 2)
Ans11) BOC = 2BAC
(angle subtended at the centre is twice the angle made at any point in
= 60o
the alternate segment)
... BOC is
equlateral
... OBC
= OCB = 60o
(OB = OC = r)
... BOC
equilateral
= OB = CO = BC = r (definition of equilateral triangles)
= BC is equal to the radius of the circumcircle of ABC
Q12) Rita
purchased a car, with a marked price of Rs. 2,10,000 at a discount of 5%. If the
sales tax charged at 10%, find the amount Rita had to pay for purchasing the
car. (Marks 2)
Ans12) Marked price of the car = Rs. 2,10,000
Discount = 5/100 x 2,10,000
= Rs. 10,500
Price of the car after the discount = 1,99,500
Sales tax = 10/100 x 1,99,500
= Rs. 19,950
Rita had to pay fpr the car = Rs. (1,99,500 + 19,950)
= Rs. 2,19,450
Q13) The mean
weight of 21 students of a class is 52 kg. If the mean weight of first 11
students of the class is 50 kg and that of last 11 students is 54 kg, find the
weight of the 11th student. (Marks 2)
Ans13) Total weight of 21 student = 52 x 21
= 1092kg
Total weight of first 11 students = 50 x 11
= 550 kg
Total weight of last 11 students = 11 x 54
= 594 kg
Total weight of 22 students = 550 + 594
= 1144 kg
... Weight of the 11th student = 1144 - 1092
= 52 kg
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