The range of the function \(f(x) = \left| \left\lfloor x \right\rfloor - x \right| ,x \in R\)  is 

(a)

[0, 1]

(b)

[0, ∞)

(c)

[0, 1)

(d)

(0, 1)

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

If \(\alpha\) and \(\beta\) are two values of θ obtained from the equation a cos θ + b sin θ = c then the value of \(tan(\frac{\alpha+\beta}{2})\) is _______________

(a)

\(\frac{a}{b}\)

(b)

\(\frac{b}{a}\)

(c)

\(\frac{c}{a}\)

(d)

\(\frac{c}{b}\)

a polygon has 44 diagonals, then the number of its sides are _________

(a)

22

(b)

88

(c)

8

(d)

11

\(\frac{1}{q+r},\frac{1}{r+p},\frac{1}{p+q}\) are in A.P., then ______________

(a)

p,q,r are inA.P

(b)

p²,q²,r² are inA.P

(c)

\(\frac{1}{p},\frac{1}{q},\frac{1}{r}\)

(d)

p,q,r are in H.P.

Equation of the straight line that forms an isosceles triangle with coordinate axes in the I-quadrant with perimeter 4 + 2\(\sqrt{2}\) is

(a)

x + y + 2 = 0

(b)

x + y - 2 = 0

(c)

\(x+y-\sqrt{2}=0\)

(d)

\(x+y+\sqrt{2}=0\)

If \(\left( \begin{matrix} 2 & \lambda & -3 \\ 0 & 2 & 5 \\ 1 & 1 & 3 \end{matrix} \right) \) is a singular matrix, then \(\lambda \) is_____________

(a)

\(\lambda \)=2

(b)

\(\lambda \)≠2

(c)

\(\lambda =\frac { -8 }{ 5 } \)

(d)

\(\lambda \neq \frac { -8 }{ 5 } \)

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)

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

\(\lim _{ x\rightarrow \infty }{ \left( \frac { 1 }{ x } +2 \right) } \)is equal to

(a)

\(\infty \)

(b)

0

(c)

1

(d)

2

Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log \left(\frac{1-x^2}{1+x^2}\right)\) then \(\frac{dy}{dx}\) is ______

(a)

\(\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)

(b)

\(-\frac { 4x }{ 1-{ x }^{ 4 } } \)

(c)

\(\frac { 1 }{ 4-{ x }^{ 4 } } \)

(d)

\(\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)