If A = {(x,y) : y = e^x, x∈R} and B = {(x,y) : y = e^-x, x ∈ R} then n(A∩B) is

(a)

Infinity

(b)

0

(c)

1

(d)

2

If A = {x / x is an integer, x² \(\le\) 4} then elements of A are ___________

(a)

A = {-1, 0, 1}

(b)

A = {-1, 0, 1, 2}

(c)

A = {0, 2, 4}

(d)

A = {- 2, - 1, 0, 1, 2}

Solve \(\sqrt{7+6x-x^2}=x+1\)

(a)

(1, -3)

(b)

(3, -1)

(c)

(1, -1)

(d)

(3, -3)

The value of log 1 is

(a)

1

(b)

0

(c)

\(\infty\)

(d)

-1

If \(\Sigma n=210\) then \(\Sigma { n }^{ 2 }\)= ______________

(a)

2870

(b)

2160

(c)

2970

(d)

none of these

If a vertex of a square is at the origin and its one side lies along the line 4x + 3y - 20 = 0, then the area of the square is

(a)

20 sq. units

(b)

16 sq. units

(c)

25 sq. units

(d)

4 sq.units

The vector in the direction of the vector\(\hat{i}-2\hat{j}+2\hat{k}\) that has magnitude 9 is _________ .

(a)

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

(b)

\(\frac { \hat { i } -2\hat { j } +2\hat { k } }{ 3 } \)

(c)

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

(d)

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

Assertion (A) : \(\overset { \rightarrow }{ a } ,\overset { \rightarrow }{ b } ,\overset { \rightarrow }{ c } \) are the position vector three collinear points then 2 \(\overset { \rightarrow }{ a }=\overset { \rightarrow }{ b } +\overset { \rightarrow }{ c } \)
Reason (R): Collinear points, have same direction

(a)

Both A and R are true and R is the correct explanation of A

(b)

Both A and R are true and R is not a correct explantion of A

(c)

A is true but R is false

(d)

A is false but R is true

If P(A)=\(\frac { 1 }{ 2 } \), P(B)=\(\frac { 1 }{ 3 } \) and P(A/B) = \(\frac { 1 }{ 4 } \), then \(P(\bar { A } \cap \bar { B } )\) =

(a)

\(\frac { 1 }{ 12 } \)

(b)

\(\frac { 3 }{ 4 } \)

(c)

\(\frac { 1 }{ 4 } \)

(d)

\(\frac { 3 }{ 16 } \)

Two dice are thrown. It is known that the sum of the numbers on the dice was less than 6, the probability of getting a sum 3 is

(a)

\(\frac { 1 }{ 18 } \)

(b)

\(\frac { 5 }{ 18 } \)

(c)

\(\frac { 1 }{ 5 } \)

(d)

\(\frac { 2 }{ 5 } \)