CBSE Set Q1 Maths Class X 1997 Sample Test Papers For Class 10th for students online
Maths Class X (CBSE)
You are on Set no 1 Qno. 21 to 30
Q21) P is
a point in the interior of rectangle ABCD. If P is joined to each of the
vertices of the rectangle and the lengths of PA, PB and PC are 3 cm, 4 cm and 5
cm respectively, find the length of PD. (Marks 4)
Q22) In
ABC, if AD is the median,
show that AB2 + AC2 = 2[AD2 + BD2] (Marks
4)
Q23) Flow Chart. Omitted, being out of Syllabus. (Marks 4)
Q24) The
data on number of patients attending a hospital in a month are given below. Find
the average number of patients attending the hospital in a day. (Marks
4)
| Number of Patients | Number of
days attending hospital |
| 0 - 10 | 2 |
| 10 - 20 | 6 |
| 20 - 30 | 9 |
| 30 - 40 | 7 |
| 40 - 50 | 4 |
| 50 - 60 | 2 |
Q25) Algorithm. Omitted, being out of Syllabus. (Marks 4)
Section - C
Q26) Solve
for x :
(x2 - 5x)2 - 7(x2 - 5x) + 6 = 0: x
R (Marks 6)
Q27) The
angle of elevation of a Jet plane from a point A on the ground is 60o.
After a flight of 15 seconds, the angle of elevation changes to 30o.
If the Jet plane is flying at a constant height 0f 1500
3
m, find the speed of the Jet plane. (Marks 6)
Q28) Construct
a ABC with AB = 4.4 cm, 
ACB
= 65o and the median through C is of length 3.2 cm. Also, find the
length of the altitude drawn from the vertex C on AB. (Marks 6)
Q29) If
PAB is a secant to a circle, intersecting the circle at A and B, and PT is a
tangent to the circle at T, then PA x PB = PT2 - Prove.
Use the above result to prove the following:
" In Fig 3, ABC is an isosceles triangle in which AB = AC. A circle through
B touches the side AC at D and intersect the side AB at P. If D is the mid point
of side AC, then AB = 4AP." (Marks 6)
Q30) The
annual income of Ramesh (excluding HRA) is Rs. 1,65,000. He contributes Rs. 2000
per month in his Provident Fund and pays annual premium of Rs. 8,000 towards his
Life Insurance Policy. Calculate the income tax paid by Ramesh in the last month
of the year if his earlier deductions for 11 months for income tax were at the
rate of Rs. 800 per month. (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 income taken as
Rs.165000 instead of Rs.125000.
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