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Maths Class X 1997(CBSE)
You are on Set no III Qno. 1 to 30
Time allowed : 3 hours
Maximum Marks :
100
General Instructions :
(i) Question number 1 to 15 carry
2 marks each.
(ii) Question number 16 to 25 carry 4 marks
each.
(iii) Question number 26 to 30 carry 6 marks each.
(iv) Write
the serial number of the question before attempting it.
(v) Use of
logarithmic and trignometric tables is permitted. Use of calculator is not
permitted.
Q4) Reduce the following to the lowest terms :
(x -
3)(x2 - 5x + 4)/(x - 4)(x2 - 2x - 3) (Marks
2)
Q5) Find the value of k such that the sum of the squares of the
roots of the quadratic equation x2 - 8x + k = 0, is 40.
(Marks 2)
Q8)
Show that
sec4  - sec2 = tan4 + tan2
(Marks 2)
Q15)
If  is
the mean of tennatural numbers x1, x2,
x3, ..., x10 , show that
(x1 + ) + (x2 +
) +
(x3 + ) + ... + (x10 + ) = 0 (Marks 2)
Q19)
An iron pillar has some part in the form of a right circular
cylinder and remaining in the form of a right circular cone. The radius of
the base of each of cone and cylinder is 8 cm. The cylindrical part is 240
cm high and the conical part is 36 cm high. Find the weight of the pillar
if the cu.cm of iron weighs 7.8 grams. (Marks 4)
Q21)
Rs. 6,500 were divided equally among a certain number of
persons. Had there been 15 more persons, each would have got Rs. 30 less.
Find the original number of persons. (Marks 4)
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