## Sunday, February 14, 2016

• Sunday, February 14, 2016
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Roll No…………..
Total No. of .Questions :07

Paper ID [BB102 ]
BBA (Sem.-1st)
Time :03 Hrs                                                                Max Marks :60
Instruction to Candidates :
1.       Section –A is Compulsory .
2.       Attempt any Four question from Section –B .
Section –A
Q1.
a)       For any two sets A and B show that ,A  B  A  B
b)      Construct the truth for p v  q
c)       If 8C r -7 C 3 = 7C 2 , find r .
d)      Using Binomial theorem , evaluate (99 )5.
e)       If a ,b ,c are in AP show that  b + c , c + a, a + b are also in A.P.
f)       A function is defined as ,f(x)=  for x ≠ 1=2 for x =1
Test its continuity at x= 1 .
g)       Find the maximum value of 1-x2.
h)      State Cramer`s rule to solve  simultaneous equations .
i)       If the sum of the series 2,5,8,11,…...is 60100, then find n .
j)       Which is greater ; log 23 or log 5.
Section –B
Q2.    a)       For any two sets A and B , show that ,(A ∩ B)c =Ac  Bc .
b)      For any logical statements p ,q and r show that ,p v (q  ^  r)=(p v q) ^ (p v r ).
Q3.    a)       Solve x2 -   =4x+6 .
b)      How many different words can be formed out of the letters of the
word ALLAHABAD ?In how many of them the  vowels occupy the
even positions ?
Q4.    a)      Prove that the coefficient of  x n  in the expansion of (1+x )2x-1.
b)      Sum to n terms the series ,. 7+ . 77 + .777+ ….
Q5.    a)      If in an A.P . , the sum of p terms in equal to the sum of q terms ,
then prove that the sum of p + q terms is zero .
b)      If a ≠ 0 then evaluate
Q6.    a)      If  xy =yx , prove that  = .
b)      Divide 64 into two parts such that the sum of the cubes of two
parts is minimum .
Q7.    a)      Apply Gauss elimination method to solve the equations , x+ 4y
-z=-5 ; x+ y -6z = - 12; 3x –y-z =4 .
b)      Find the value of ,