The number of relations from a set containing 4 elements to a set containing 3 elements is:

(a)

2¹⁶

(b)

2⁵

(c)

2⁷

(d)

2¹²

\((\sqrt { 5 } -2)(\sqrt { 5 } +2)\) is equal to ___________

(a)

1

(b)

3

(c)

23

(d)

21

2 sin 5x cos x _______________

(a)

sin 6x + cos 4x

(b)

sin 6x + sin 4x

(c)

cos 6x + sin 4x

(d)

cos 6x + cos 4x

If 15C_3r = 15 C_r+3 , then r is equal to _________

(a)

5

(b)

4

(c)

3

(d)

2

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

(a)

2870

(b)

2160

(c)

2970

(d)

none of these

The equation x²+ kxy + y²- 5x - 7y + 6 = 0 represents a pair of straight lines then k = ______________

(a)

\(\frac{5}{3}\)

(b)

\(\frac{10}{3}\)

(c)

\(\frac{3}{2}\)

(d)

\(\frac{3}{10}\)

Choose the correct or the most suitable answer from the given four alternatives.
\(If\sin { (x+y)= } \log { (x+y) } \) then \(\frac { dy }{ dx } \) is _____

(a)

2

(b)

-2

(c)

1

(d)

-1

Choose the correct or the most suitable answer from the given four alternatives.
If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then ____

(a)

\(\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

(b)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)

(c)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0\)

(d)

\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

\(\int { \frac { 4\left( sin^{ -1 }x \right) ^{ 3 } }{ \sqrt { 1-{ x }^{ 2 } } } } \) dx = ________+c.

(a)

log (sin ^-1x)

(b)

(sin ^-1 x)⁴

(c)

4 (sin^-1 x)⁴

(d)

\(\frac { \left( { sin }^{ -1 }x \right) ^{ 4 } }{ 4 } \)

Choose the incorrect pair :

(a)

P(A) + P (B) -2P(A∩B) - Exactly one of them occur

(b)

P(A∩B) - Simultaneous occurrence of A and B

(c)

peA) + P (B) - P(A∩B) - Occurrence of either A or B or both

(d)

1 - P(A∪B) - Occurrence of only A