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

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(x⁴ - 16); q(x) = 12(x³ - 8)  (Marks 2)

Q3) If b is the mean proportional between a and c, prove that
(a² - b² + c²)/(a^-2 - b^-2 + c^-2) = b⁴  (Marks 2)

Q4) Find the values of k so that the quadratic equation
x² - 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/tan² ))(1 + (1/cot² ) = 1/(sin² - sin⁴ )  (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 x₁, x₂, x₃, ..., x_n is , prove that the mean of the observations x₁ + a, x₂ + a, x₃ + 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)

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)

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