For any two sets A and B, (A - B) \(\cup\) (B - A)=_____.

1

(a)

(A - B) \(\cup\) A

(b)

(B - A) \(\cup\) B

(c)

(A \(\cup\) B) - (A \(\cap\) B)

(d)

(A \(\cup\) B) \(\cap\) (A \(\cap\) B)

If tan \(\theta={\alpha\over \alpha+1}\) and tan \(\phi ={1\over 2\alpha+1}\) , then (A+ B) is equal to ______.

1

(a)

0

(b)

\(\pi\over4\)

(c)

\(\pi\over6\)

(d)

\(\pi\over2\)

If Sn denote the sum of n terms of an  AP. whose first term is a and common difference is d given by is d given by d = S_n - kS_n-1 + S_n-2 then K is equal to ______.

1

(a)

5

(b)

2

(c)

3

(d)

4

The locus of the points of trisection of the double ordinates of a parabola is a ______.

1

(a)

pair of lines

(b)

parabola

(c)

circles

(d)

none of these

State which of the following sets are finite and which are infinite?
D = {x : x \(\in\) Z and x > -10}

2

(a)

Find the equation of the hyperbola satisfying the given condition.
Foci (± 4, 0), e =2

2

(a)

For the function f,given by f(x)=x²- 6x + 8,prove that f^'(5)-3f^'(2)=f^'(8)

2

(a)

A and B are mutually exclusive events of an experiment. If P(not A)=0.65, \(P(A\cup B)=0.65\) and P(B) = p, then find the value of p.

2

(a)

Find the range of each of the following functions 
(i) f(x) = 2 - 3x, x \(\in\) R, x > 0
(ii) f (x) = x² + 2, x is a real number.
(iii) f (x) = x, x is a real number.

2

(a)

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

2

(a)

Solve \(3{ x }^{ 2 }-4x+\frac { 20 }{ 3 } =0\)

2

(a)

Compute \(\frac { 8! }{ 4! } \). is \(\frac { 8! }{ 4! } \) = 2!?

2

(a)

In the arithmetic progressions 2, 5, 8,....upto 50 terms and 3, 5, 7, 9,.... upto 60 terms, find how many terms are identical.

4

(a)

Find the equation of hyperbola, if length of transverse axis is 10 and conjugate axis is 8.

4

(a)

Evaluate  \(\lim _{x \rightarrow \frac{1}{2}} \frac{4 x^{2}-1}{2 x-1}\)

4

(a)

Solve \(\sqrt { 3 } cos\theta +sin\theta =\sqrt { 2 } \)

4

(a)

Solve the inequality \(|\frac { 2 }{ x-4 } |>1;x\neq 4.\)

4

(a)

Evaluate (1.025)^-1/3 correct to three places of decimal.

4

(a)

If a line passes through (2,2) and is perpendicular to the line 3x + y = 3, then find its y-intercept.

4

(a)

Write down the negation
x = 2 \(\Rightarrow \)x² = 4

4

(a)

The frequency distribution

x	A	2A	3A	4A	5A	6A
f	2	1	1	1	1	1

Where, A is a positive integer, has a variance of 160. Determine the value of A. 

4

(a)

1. Which of the following pairs of sets are disjoint
   {a, e, i, o u} and { c, d, e, f }

   4

   (a)

2. If x and y are any two distinct integers, then prove by mathematical induction that \(\left( { x }^{ n }-{ y }^{ n } \right) \) is divisible by (x-y), for all \(n\in N\)

   4

   (a)

1. Show that the points P(0,7,10), Q(-1,6,6)and R(-4,9,6) form a right angled isosceles triangle.

   4

   (a)

2. Two students Anil and Ashima appeared in an examination.The probability that Anil will qualify the examination.The probability that Anil will qualify the examination is 0.05 and that Ashima will qualify the examination is 0.10.The probability that both will qualify the examination is 0.02.Find the probability that
   atleast one of them will not qualify the examination

   4

   (a)

Prove the following: tan x = \({4\tan x(1-\tan^2 \ x)\over 1-6\ \tan^2 \ x+\tan^4 \ x}\)

6

(a)

Solve the inequalities graphically 2x - y >1, 2y < -1

6

(a)

Find the sum to n terms of the series \(\frac{1}{1\times 2}+\frac{1}{2\times 3}+\frac{1}{3\times 4}+....\)

6

(a)

Find what the following equation become when the origin is shifted to (1, 1). (i) x²+xy-3y²-y+2=0, (ii) xy-y²-x+y=0, (iii) xy-x-y+1=0 

6

(a)

Find the derivative of (x+a) (it is to be understood that a, b, c, d, p, q, rand s are fixed non-zero constants and m and n are integers)

6

(a)

Find the C.V of the following data:

Size (in m)	10-15	15-20	20-25	25-30	30-35	35-40
No.of items	2	8	20	35	20	15

6

(a)