The number of constant functions from a set containing m elements to a set containing n elements is

(a)

mn

(b)

m

(c)

n

(d)

m+n

The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

(a)

one-to-one

(b)

on to

(c)

bijection

(d)

cannot be defined

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f is

(a)

an one-to-one function

(b)

an onto function

(c)

a function which is not one-to-one

(d)

not a function

For real numbers x and y, define xRy if x - y + √2 is an irrational number. Then the relation R is __________

(a)

reflexive

(b)

symmetric

(c)

transitive

(d)

none of these

Let R be the relation over the set of all straight lines in a plane such that l₁Rl₂ ⇔ l₁丄l₂ . Then  R is __________

(a)

symmetric

(b)

reflexive

(c)

transitive

(d)

an equivalent relation

The number of relations on a set containing 3 elements is

(a)

9

(b)

81

(c)

512

(d)

1024

If \(f:R\rightarrow R\) is defined by \(f(x)=2x-3\) __________

(a)

\({1\over 2x-3}\)

(b)

\({1\over 2x+3}\)

(c)

\({x+3\over 2}\)

(d)

\({x-3\over 2}\)

\(n(A\cap B)=4\) and \((A\cup B)=11\) then \(n(p(A\triangle B))\) is __________

(a)

44

(b)

256

(c)

64

(d)

128

Let f and g be two odd functions then the function of f o g is ___________

(a)

an even function

(b)

an odd function

(c)

neither even nor odd

(d)

a periodic function

For any four sets A, B, C and D, which of the following is not true?

(a)

A x C ⊂  B x D

(b)

(A x B) ∩ (C x D) = (A ∩ C) x (B ∩ D)

(c)

A x (B U,C) = (A x B) U (A x C)

(d)

A x (B ∩ C) = (A x B) ∩ (A x C)

If A and B are any two finite sets having m and n elements respectively then the cardinality of the power set of A \(\times\) B is ___________

(a)

2^m

(b)

2ⁿ

(c)

mn

(d)

2^mn

The domain and range of the function \(f(x)={|x-4|\over x-4}\)

(a)

R, [-1, 1]

(b)

R \ {4};{-1,1}

(c)

R \ {4};{-1,l}

(d)

R, (-1,1)

The unit vector parallel to the resultant of the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(\hat{i}-2\hat{j}+\hat{k}\) is

(a)

\({\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

(b)

\({2\hat{i}+\hat{j}\over\sqrt{5}}\)

(c)

\({2\hat{i}-\hat{j}+\hat{k}\over\sqrt{5}}\)

(d)

\({2\hat{i}-\hat{j}\over\sqrt{5}}\)

A vector \(\overrightarrow{OP}\) makes 60° and 45° with the positive direction of the x and y axes respectively.  Then the angle between \(\overrightarrow{OP}\)and the z-axis is

(a)

45°

(b)

60°

(c)

90°

(d)

30°

Two vertices of a triangle have position vectors \(3\hat{i}+4\hat{j}-4\hat{k}\) and \(2\hat{i}+3\hat{j}+4\hat{k}\) . If the position vector of the centroid is \(\hat{i}+2\hat{j}+3\hat{k}\), then the position vector of the third vertex is

(a)

\(-2\hat{i}-\hat{j}+9\hat{k}\)

(b)

\(-2\hat{i}-\hat{j}-6\hat{k}\)

(c)

\(2\hat{i}-\hat{j}+6\hat{k}\)

(d)

\(-2\hat{i}+\hat{j}+6\hat{k}\)

If \(|\overrightarrow{a}+\overrightarrow{b}|=60,\) \(|\overrightarrow{a} - \overrightarrow{b}|=40\)  and \(|\overrightarrow{b}|=46\) , then \(|\overrightarrow{a}|\) is

(a)

42

(b)

12

(c)

22

(d)

32

If \(\overrightarrow{a}=\hat{i}+2\hat{j}+2\hat{k},|\overrightarrow{b}|=5\) and the angle between \(\overrightarrow{a}\) and \(\overrightarrow{b}\) is \({\pi\over 6},\) then the area of the triangle formed by these two vectors as two sides, is

(a)

\(7\over4\)

(b)

\(15\over4\)

(c)

\(3\over4\)

(d)

\(17\over4\)

\(\int \tan ^{-1} \sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}} d x\) is

(a)

x²+c

(b)

2x²+c

(c)

\({x^2\over2}+c\)

(d)

\(-{x^2\over2}+c\)

\(\int \sin \sqrt{x} d x\) is

(a)

\(2(-\sqrt{x}cos\sqrt{x}+sin\sqrt{x})+c\)

(b)

\(2(-\sqrt{x}cos\sqrt{x}-sin\sqrt{x})+c\)

(c)

\(2(-\sqrt{x}sin\sqrt{x}-cos\sqrt{x})+c\)

(d)

\(2(-\sqrt{x}sin\sqrt{x}+cos\sqrt{x})+c\)

The condition that the equation ax² + bx + c = 0 may have one root is the double the other is ___________

(a)

2b² = 9ac

(b)

b² = ac

(c)

b² = 4ac

(d)

9b² = 2ac