# CBSE Set Q Maths Class X 1997 Sample Test Papers For Class 10th for students online

**Maths Class X
(CBSE)
You are on Set no 1 Qno. 1 to 20
**

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.

**Section - A**

**Q1) **Determine the value of
for which the following system of linear equations has an infinite number of
solutions :

x + 3y =
- 3; 12x + y =
**(Marks 2)**

**Q2) **Find the g.c.d. of the
following polynomials :

p(x) = 8(x^{4} - 16); q(x) = 12(x^{3} - 8) **(Marks 2)**

**Q3) **If b is the mean
proportional between a and c, prove that

(a^{2} - b^{2} + c^{2})/(a^{-2} - b^{-2}
+ c^{-2}) = b^{4} **(Marks 2)**

**Q4) **Find the values of k so
that the quadratic equation

x^{2} - 2x(1 - 3k) + 7(3 + 2k) = 0

has equal roots. **(Marks 2)
**

**Q5) **OABC is a rhombus whose
three vertices A, B, and C lie on a circle with centre O. If the radius of the
circle is 10 cm, find the area of the rhombus. **(Marks 2)**

**Q6) **Lata goes to a shop to
buy a leather coat, costing Rs. 654. The rate of sales tax is 9%. She tells the
shopkeeper to reduce the price of the coat to such an extent that she has to pay
Rs. 654, inclusive of sales tax. Find the reduction needed in the price of the
coat. **(Marks 2)**

**Q7) **If cos
+ sin = 2cos
, show that

cos - sin
= 2sin .
**(Marks 2)
**

**Q8) **Show that

(1 + (1/tan^{2} ))(1
+ (1/cot^{2} ) =
1/(sin^{2} - sin^{4}
) **(Marks 2)**

**Q9) **In Fig. 1, ABCD is a
rectangle with AD = 12 cm and DC = 20 cm. Line segment DE is drawn making an
angle of 30^{o} with AD, intersecting AB in E. Find the lengths of DE
and AE. **(Marks 2)
**

**Q10) **If the diagonal BD of a
quadrilateral ABCD bisects both B
and D, show that AB/BC =
AD/CD. **(Marks 2)
**

**Q11) **In Fig. 2, ABC is a
triangle in which BAC =
30^{o}. Show that BC is the radius of the circum-circle of ABC,
whose centre is O. **(Marks 2)
**

**Q12) **In two similar triangles
ABC and PQR, if their corresponding altitudes AD and PS are in the ratio of 4 :
9, find the ratio of the area of ABC
to that of PQR. **(Marks
2)**

**Q13) **If the mean of n
observations x_{1}, x_{2}, x_{3}, ..., x_{n} is ,
prove that the mean of the observations x_{1} + a, x_{2} + a, x_{3}
+ a, ..., x_{n} + a is
+ a. **(Marks 2)
**

**Q14) **Flow Chart. Omitted
being out of Syllabus. **(Marks 2)**

**Q15) **Fill in the blanks in
the following table and find the Crude Death Rate (CDR) for the data: **(Marks
2)**

Age group (in years) |
Population | Number of Deaths |

0 - 15 | 4,000 | 200 |

15 - 25 | - | 120 |

25 - 40 | 1,500 | 100 |

40 - 50 | 3,000 | 150 |

Above 50 | 2,000 | - |

Total | 13,000 | 700 |

**Section - B**

**Q16) **Solve graphically the
following system of linear equations:

x + y = 3, 2x + 5y = 12 **(Marks 4)**

**Q17) **Factorise. Omitted,
being out of Syllabus. **(Marks 4)**

**Q18) **A part of monthly
expenses of a family is constant and the remaining varies with the price of
wheat. When the rate of wheat is Rs. 250 a quintal, the total monthly expenses
of the family are Rs. 1,000 and when it is Rs. 240 a quintal, the total monthly
expenses of the family are Rs. 980. Find the total monthly expenses of the
family when the cost of wheat is Rs. 350 a quintal. **(Marks 4)**

**Q19) **A piece of cloth costs
Rs. 200. If the piece were 5 m longer, and each metre of cloth costed Rs. 2
less, the cost of the piece would have remained unchanged. How long is the piece
and what is its original rate per metre ? **(Marks 4)**

**Q20) **A sphere of diameter 6
cm is dropped in a right circular cylindrical vessel partly filled with water.
The diameter of the cylindrical vessel is 12 cm. If the sphere is completely
submerged in water, by how much will the level of water rise in the cylindrical
vessel ? **(Marks 4)**