The value of a when x³- 2x²+ 3x + a is divided by (x - 1), the remainder is 1, is ___________

(a)

-1

(b)

1

(c)

2

(d)

-2

If ⁿC_r-1 = 36, ⁿC_r = 84 and ⁿC_r+1 = 126 then r = _________

(a)

2

(b)

2

(c)

3

(d)

4

2^1/4 4^1/8 8^1/16 16^1/32 . . . = ______________

(a)

1

(b)

2

(c)

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

(d)

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

If the co-ordinates of a variable point p be \((t+\frac{1}{t},t-\frac{1}{t})\) where t is the parameter then the locus of p ______________

(a)

xy = 1

(b)

x²+ y² = 4

(c)

x²- y² = 4

(d)

x²- y² = 8

If A is a matrix 3 \(\times\) 3, then \({ { (A }^{ 2 }) }^{ -1 }\) =____________

(a)

\(\frac { 1 }{ { A }^{ 2 } } \)

(b)

A^-2

(c)

\({ { (A }^{ -1 }) }^{ 2 }\)

(d)

I

Find the odd one out of the following

(a)

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

(b)

\(2\hat { i } +4\hat { j } +6\hat { k } \)

(c)

\(7\hat { i } +14\hat { j } +21\hat { k } \)

(d)

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

\(\lim _{ x\rightarrow \frac { \pi }{ 2 } }{ \frac { \sin { x } }{ x } } =\)

(a)

\(\pi \)

(b)

\(\frac { \pi }{ 2 } \)

(c)

\(\frac { 2 }{ \pi } \)

(d)

1

The slope of the graph of \(f\left( x \right) =\frac { \left| x \right| }{ x } ,x>0\quad is\)

(a)

1

(b)

0

(c)

-1

(d)

undefined

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 f(x) is an odd function, then  f^'(x) is an ______ function

(a)

even

(b)

odd

(c)

even or odd

(d)

neither even nor odd