If \({ log }_{ \sqrt { x } }\) 0.25 = 4, then the value of x is

(a)

0.5

(b)

2.5

(c)

1.5

(d)

1.25

\(\frac { sin(A-B) }{ cosAcosB } +\frac { sin(B-C) }{ cosBcosC } +\frac { sin(C-A) }{ cosCcosA } \) is

(a)

sin A + sin B + sin C

(b)

1

(c)

0

(d)

cos A + cos B + cos C

The number of five digit telephone numbers having at least one of their digits repeated is

(a)

90000

(b)

10000

(c)

30240

(d)

69760

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 A =\(\begin{bmatrix} 1& 2 &2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}\) is a matrix satisfying the equation AA^T = 9I, where I is 3 \(\times\) 3 identity matrix, then the ordered pair (a, b) is equal to

(a)

(2, - 1)

(b)

(- 2, 1)

(c)

(2, 1)

(d)

(- 2, - 1)

If \(\overrightarrow{a}, \overrightarrow{b}, \overrightarrow{c}\) are the position vectors of three collinear points, then which of the following is true?

(a)

\(\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}\)

(b)

\(2\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}\)

(c)

\(\overrightarrow{b}=\overrightarrow{c}+\overrightarrow{a}\)

(d)

\(4\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0\)

If f(x) = x(-1)^{\(\left\lfloor 1\over x \right\rfloor \)}, \(x\le0\), then the value of \(lim_{x\rightarrow 0}f(x)\) is equal to

(a)

-1

(b)

0

(c)

2

(d)

4

If x = a sin \(\theta\) and y = b cos \(\theta\), then \({d^2y\over dx^2}\)is

(a)

\({a \over b^2}sec^2 \theta\)

(b)

\(-{b \over a}sec^2 \theta\)

(c)

\(-{b \over a^2}sec^3 \theta\)

(d)

\(-{b^2\over a^2}sec^3 \theta\)

\(\int 2^{3 x+5} d x\) is

(a)

\({3(2^{3x+5})\over log 2}+c\)

(b)

\({2^{3x+5}\over 2log (3x+5)}+c\)

(c)

\({2^{3x+5}\over 2log 3}+c\)

(d)

\({2^{3x+5}\over 3log 2}+c\)

A man has 3 fifty rupee notes, 4 hundred rupees notes, and 6 five hundred rupees notes in his pocket. If 2 notes are taken at random, what are the odds in favour of both notes being of hundred rupee denomination?

(a)

1:12

(b)

12:1

(c)

13:1

(d)

1:13