Maths Class X 1996(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) Find the value of k for which the system of equations has no solution :
3x - 4y + 7 = 0
kx + 3y - 5 = 0  (Marks 2)

Q2) Find the g.c.d. of the following polynomials :
2x² - x - 1 and 4x² + 8x + 3  (Marks 2)

Q3) If A = (x + 1)/(x - 1), find A - 1/A in the simplified form.  (Marks 2)

Q4) Form the quadratic equation in x whose roots are 2 + 5 and 2 - 5.  (Marks 2)

Q5) The base radii of two right circular cones of the same height are in the ratio 3 : 5. Find the ratio of their volumes.  (Marks 2)

Q6) A colour T.V. is available for Rs. 13,440 inclusive of sales tax. If the original cost of T.V. is Rs. 12,000 find the rate of sales tax.  (Marks 2)

Q7) Evaluate : cot 54^o/tan 36^o + tan 20^o/cot 70^o - 2  (Marks 2)

Q8) Simplify : (1 + tan² )(1 - sin )(1 + sin )  (Marks 2)

Q9) Prove that : sin /(1 - cos ) = cosec + cot .  (Marks 2)

Q10) In Fig. 1, ABC and DEF are similar. The area of ABC is 9 sq.cm and area of DEF is 16 sq.cm. If BC = 2.1 cm, find the length of EF.  (Marks 2)
  

Q11) In Fig. 2, O is the centre of the circle and AB is a chord of the circle. Line QBS is a tangent to the circle at B. If AOB = 110^o, find APB and ABQ.  (Marks 2)

Q12) In Fig. 3, chords AB and CD intersect at P. If AB = 5 cm, PB = 3 cm and PD = 4 cm, find the length of CD.  (Marks 2)

Q13) Calculate the median of the following data :
83, 37, 70, 29, 45, 63, 41, 70, 30, 54  (Marks 2)

Q14) Find the Crude Death Rate (CDR) for the following data:  (Marks 2)

Q15) Flow Chart. Omitted being out of Syllabus.  (Marks 2)

Section - B

Q16) Solve for the following system of equations graphically  :
2x + y - 3 = 0
2x - 3y - 7 = 0  (Marks 4)

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

Q18) A man has only 20 paise coins and 25 paise coins in his purse. If he has 50 coins in all totaling Rs. 11.25, how many coins of each does he have?  (Marks 4)

Q19) Divide 29 into two parts so that the sum of the squares of the parts is 425.  (Marks 4)

Q20) The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of 28 cm diameter. Find the length of the wire.  (Marks 4)

 

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