MATHEMATICS (Question Paper) 



General Instructions : (i) All Questions are compulsory (ii)The question paper consists of 31 questions divided into four sections A,B,C,D (iii) Section A comprises of 4 questions of 1 mark each, (iv) Section B Comprises of 6 questions of 2 marks each, (v) Section C comprises of 10 questions Of 3 marks each and Section D comprises of 11 questions of 4 marks each. (vi) Use of calculator is not permitted. 

SECTION – A 

Q.1.  Find the zeroes of polynomial X^{2} – 2X – 8 . 

Q.2.  A ladder 10 m long reaches a window 8 m above the ground. Find the distance of the foot of the ladder from base of the wall. 

Q.3.  If sin A =, calculate cos A . 

Q.4.  Find the class mark of 15.5 – 20.5 

SECTION  B 

Q.5.  If α and β are zeroes of the Polynomial 3x^{2}+5x+2, Find the value of 

Q.6.  For what value of a and b will the following system of linear equations have infinitely many solutions 2x +3 y =7 (ab)x + (a+b)y = 3a+b2 

Q.7.  If ΔABC ∼ ΔDEF and their areas be respectively 64 cm^{2} and 121 cm^{2}.If EF = 15.4 cm, Find BC. 

Q.8.  If sin4A = cos(A20^{0}) , where 4A is an acute angle, find the value of A. 

Q.9.  Convert the following frequency distribution table into a less than type cumulative frequency distribution table:


Q.10. 
Evaluate cos48^{0} – sin42^{0} 

SECTION  C 

Q.11.  Given HCF ( 306, 657 ) = 9. Find the LCM ( 306, 657 ). 

Q.12.  Find the zeroes of the quadratic polynomial 6x^{2} – 7x – 3 and verify the relationship between the zeroes and the coefficients. 

Q.13.  Solve: 3x – 5y =4 9x – 2y = 7 by using Elimination method. 

Q.14.  If the areas of two similar triangles are equal then show that the triangles are congruent. 

Q.15.  ABC is an isosceles triangle right angled at C. Prove that AB^{2} = 2AC^{2}  
Q.16.  Prove that (sinA + cosecA)^{2} + (cosA + secA)^{2} = 7 + tan2A + cot^{2}A 

Q.17.  Without using trigonometric table evaluate the following 3cos68^{0} cosec22^{0}  tan43^{0} tan47^{0} tan12^{0} tan60^{0} tan78^{0} 

Q.18.  If tan(A + B) = 3 and tan(A – B) Find A and B 

Q.19.  Find the median of the following distribution 

Q.20. 
If the mean of the following distribution is 6 , find the value of p


SECTION  D 

Q.21.  Prove that √3 is irrational. 

Q.22.  Find all the zeroes of the polynomial 2x^{4} 3x^{3}3x^{2}+6x2 if two of its zeroes are √2 and √2 

Q.23.  8 men and 12 boys can finish a piece of work in 10 days while 6 men and 8 boys can finish it in 14 days. Find the time taken by one man and by one boy alone to finish the Work. What value is depicted? 

Q.24.  If tanA = 2 Evaluate secAsinA + tan^{2}A – cosecA The marks obtained by 30 students of class X of certain school in Mathematics paper Consisting of 100 marks are presented in the table below. Find the mode of this data 

Q.25. 


Q.26. 
In an equilateral triangle ABC , D is a point on side BC such that BD = 1/3 BC Prove that 9 AD^{2} = 7 AB^{2} 

Q.27.  Prove that the ratios of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. 

Q.28.  Divide : 2t^{4} + 3t^{3} 2t^{2} – 9t 12 by t^{2} – 3 

Q.29.  The median of the following data is 525 Find the values of x and y if the total Frequency is 100 

Q.30. 
Prove that 

Q.31. 
For a morning walk three persons step off together. There steps measure 80cm, 85cm, and 90cm respectively. What is the minimum distance each should walk so that they can cover the distance in complete steps? 
