Mathematics - Class X Question Paper - Central Board Of Secondary Education Page 5

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Q4.
A suit is available for Rs. 1500 cash or for Rs. 500 cash down payment followed by 3
monthly instalments of Rs. 345 each. Find the rate of interest charged under the
instalment scheme.
Q5.
A loan has to be returned in two equal annual instalments. If the rate of interest is 16%
per annum compounded annually and each instalment is of Rs. 1682, find the sum
borrowed and the total interest paid.
2
Q6.
If (x — 2) is a factor of x
+ ax + b and a + b = 1, find the values of a and b.
Q7.
Using quadratic formula, solve the following equation for x :
2
2
abx
+ (b
—ac) x — bc = 0
OR
The sum of the squares of two positive integers is 208. If the square of the larger number
is 18 times the smaller, find the numbers.
Q8.
Which term of the A.P. 3, 15, 27, 39.... is 132 more than its 54th term ?
OR
Derive the formula for the sum of first n terms of an A.P. whose first term is 'a' and the
common difference is 'd'
Q9.
Find the sum of the following arithmetic progression
1+3+5+7+................+199
Q10. Show that a line drawn parallel to the parallel sides of a trapezium divides the non non-
parallel sides proportionally.
SECTION B
1
2
4
Q11. Solve for x,
+
=
, (x = -1, -2, -4)
x+1
x+2
x+4
Q12. Find graphically, the vertices of the triangle formed by the x-axes and the lines
2x — y + 8 = 0
8x + 3y — 24 = 0
Q13. Construct a triangle ABC in which BC = 13cm, CA = 5cm and AB = 12cm. Draw its
incircle and measure its radius.
Q14. The total surface area of a closed right circular cylinder is 6512 cm², and the
22
circumference of its base is 88 cm. Find the volume of the cylinder (use π =
)
7
Q15. Prove the identity :
(1 + Cotθ - Cosecθ) (1 + tanθ + secθ) = 2.
140

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