## Class: XI Mathematics

Posted: July 6, 2013 in Questions of class-11

ARNIKO AWASIYA HIGHER SECONDARY SCHOOL

Class: XI      Mathematics        F.M.:50

Time: 1:30 Hour                       P.M.:20

Candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.

Group “A”

1. a) If A = { l, o, v, e } and B = {r, o, s , e}, find the symmetric difference of set A and set B.                                                  

b) A, B and C are the subsets of a universal set U. Prove that .                                                

1. a) If the equation (1 + m2) x2 + 2mcx + (c2 – a2) = 0 has equal roots, show that c2 = a2 (1+m2).                                                           

b) If and be in H.P., show that x, y, z are in G.P. 

c) a) By mathematical induction, prove that

.                                  

1. a) What are the standard forms of equation of a straight line? Find the slope of the line .                                                 

b) What do you mean by the left hand limit and right hand limit of a function? What is the condition for the limit of a function to exist at a point?                                                                                             

Group “B”

i)         How many students are there in the group?

ii)       How many read all the three subjects?                             

b) Prove that a quadratic equation ax2 + bx + c = 0 can not have more than two roots.

1. a) If a, b, c are rational and a + b + c = 0, show that the roots of        (b + c – a) x2 + (c + a – b) x + (a + b – c) = 0 are rational.

b) Evaluate:

1. a) A function f(x) is defined as

f(x) =

Find the value k so that f(x) is continuous at x=2

b) From first principle, find the derivative of y =3x2 – 2x

Group “C”

1. The three sides of a triangle have the equations 7x – y + 11 = 0,

x + y – 15 = 0 and 7x + 17y + 65 = 0. Find the equation of the straight line through a vertex and parallel to the opposite side with the equation   x + y – 15 = 0.                                                                       

1. Find the nth term and the sum of the first n terms of the series.



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