Free Printable FORMULA QUIZ 2 : 27 DEC

1.

$at\ -a\ -\ point\ \left(x_0,\ y_0\right)$
$\ \frac{dy}{dx\ }\ ,\ is\ -\ zero,\$
$then\ -\ equation\ \ -of\$
$normal\ -\ is$

a)

$x\ =\ x_0$

b)

$y\ =\ y_0$

c)

$\frac{x_0}{y_0}=\ 1$

d)

$\frac{x_0}{y_0}=-\ 1$

2.

$\frac{d}{dx}\operatorname{cosec}^{-1}x\ =$

a)

$\frac{1}{1+x^2}$

b)

$\frac{1}{x\sqrt{1-x^2}}$

c)

$\frac{1}{\sqrt{1-x^2}}$

d)

$-\ \frac{1}{x\sqrt{1-x^2}}$

3.

matrix "A" is

non - singular, if

a)

$\left|A\right|=0$

b)

$\left|A\right|\ne0$

c)

$\ A\ =\ A'$

d)

$A\ =\ -\ A'$

4.

$Element,\ \left(-1\right)^{1+3}M_{13}$
is - cofactor - of

a)

$a_{31}$

b)

$a_{12}$

c)

$a_{21}$

d)

$a_{13}$

5.

$If\ A\ =\ \left[a_{ij}\right]_{3\times3}\ ,\ then$
$\left|k.A\right|=$

a)

$k\left|A\right|$

b)

$k^2\left|A\right|$

c)

$k^3\left|A\right|$

d)

$3k\left|A\right|$

6.

$\ A\ ,\ is\ -\ square\ -\ matrix,\ of$
$order\ ,\ 3\$
$then,$
$\left|adj\ A\right|=$

a)

$\left|A\right|$

b)

$\left|A\right|^2$

c)

$\left|A\right|^3$

d)

0

7.

The - ratio - of - cofactor & minor
of - element , $a_{23}$
of - any - matrix - is

a)

1

b)

- 1

c)

0

d)

$2\ \times\ 3$

8.

$Matrix,\ A\ =\ \left[a_{ij}\right]_{m\times n}\ ,\ with$
$a_{ij}=\ 1,\ when,\ i\ =\ j\ and\$
$a_{ij}=\ 0,\ when,\ i\ \ne\ j\ is\$

a)

Null matrix

b)

Row matrix

c)

Column Matrix

d)

Identity matrix

9.

A + A' is a

a)

$symmertic\ -\ matrix$

b)

$skew\ -\ symmertic\ -\ matrix$

c)

$null\ -\ matrix$

d)

$row\ -\ matrix$

10.

A - matrix , has, 8, elements,

then - which - of,

its - order - is

not - possible

a)

$1\times8$

b)

$2\times4$

c)

$3\times2$

d)

$8\times1$

11.

$\cos^{-1}\left(-x\right)=$

a)

$\cos^{-1}\left(x\right)$

b)

$\pi\ +\cos^{-1}\left(x\right)$

c)

$\pi\ -\ \cos^{-1}\left(-x\right)$

d)

$\pi\ -\ \cos^{-1}\left(x\right)$

12.

In, a - probability - distribution

for - all - given, probabilities

p_{1,\ \ }p_{2,}\ \ p_{3\ ,...\ }p_i

\Sigma p_i=\

a)

0

b)

1

c)

- 1

d)

2

13.

A - bag, contains, 2 white & 1 red
balls. Two - balls, are, drawn. if
X - denotes, the - numbers

of - red - balls,
then

a)

X = 0,1, 2

b)

X = 0, 1, 2, 3

c)

X = 0, 1

d)

X = 1,2,3

14.

$P\left(at\ \ -\ least,\ one\ ,\ of,\ A\ \&\ B\right)=$

a)

1 - P(A)P(B)

b)

1 - P(A' )P(B' )

c)

1 - P(A)P(B')

d)

1 - P(A').P(B)

15.

$Events,\ \ E\ \&\ F\ ,\ \ are$
$\ dependent\ ,\ then$
$P\left(A\cap B\right)$

a)

$=\ P\left(A\right)P\left(B\right)$

b)

$\ne P\left(A\right)P\left(B\right)$

c)

$P\left(\frac{B}{A}\right)$

d)

$P\left(\frac{A}{B}\right)$

16.

If , F , is - a - event - of,
sample - space , S

then\ ,\ P\left(\frac{S}{F}\right)=

a)

0

b)

P(F)

c)

1

d)

P(S)

17.

Distance - between - lines

\overrightarrow{r\ }\ =\ \overrightarrow{a_1}\ +\ \lambda\overrightarrow{b\ _{ }}

&

\overrightarrow{r\ }\ =\ \overrightarrow{a_2}\ +\ \mu\ \overrightarrow{b_{ }}

is

a)

0

b)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{a_1\ }\right|}\right|$

c)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{a_2}\right|}\right|$

d)

$\left|\frac{\overrightarrow{b\ }\times\left(\overrightarrow{a_2}-\ \overrightarrow{a_1}\right)}{\left|\overrightarrow{b\ }\right|}\right|$

18.

$If\ ,\ l,\ m\ \ \&\ ,\ n\ are$

direction - cosines - of - line

them,\ \left(l^2+1\right)+

\left(m^2+1\right)+

\left(n^2+1\right)=

a)

0

b)

1

c)

3

d)

4

19.

$Equation\ -\ of\ -\ plane$
$pas\sin g\ \ -\ though,\ \ \overrightarrow{a\ }\ \ \&$
$perpendicular\ ,\ \ to\ \ \overrightarrow{N\ }\ is$

a)

$\overrightarrow{r\ }.n\ \ =\ a$

b)

$\left(\overrightarrow{r\ }\ +\ \overrightarrow{a\ }\right).\overrightarrow{N\ }\ =\ 0$

c)

$\left(\overrightarrow{r\ }\ -\ \overrightarrow{a\ }\right).\overrightarrow{N\ }\ =\ 0$

d)

$\left(\overrightarrow{r\ }\ -\ \overrightarrow{N\ }\right).\overrightarrow{a\ }\ =\ 0$

20.

$Line\ -\ pas\sin g\ -\ through$
$\overrightarrow{a\ }\ \ \&\ \ \overrightarrow{b\ }\ is$

a)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\ \overrightarrow{b\ }$

b)

$\overrightarrow{r\ }\ =\ \overrightarrow{b\ }+\ \lambda\ \overrightarrow{a\ }$

c)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\left(\ \overrightarrow{b\ }+\ \ \overrightarrow{a\ }\right)$

d)

$\overrightarrow{r\ }\ =\ \overrightarrow{a\ }+\ \lambda\left(\ \overrightarrow{b\ }-\ \ \overrightarrow{a\ }\right)$

21.

Direction - cosines - of,

z - axis, are

a)

1, 0 ,0

b)

0, 1, 0

c)

0, 0, 1

d)

1, 1, 1

22.

In - a - parallelogram,
$"the\ \ -vector\ -\ sum\ -\ of"$
two - co initial - vectors,
(adjacent - sides )
represents

a)

any - side - of $\parallel\ gram$

b)

$diagonals\ \ -\ of,\ \ \parallel\ gram$

c)

$Orthocentre\ -\ of,\ \parallel\ gram$

d)

$Centroid\ -\ of,\ \parallel\ gram$

23.

$\overrightarrow{a\ }\ \times\ \overrightarrow{b\ }\ is$

a)

$\perp\ to\ \overrightarrow{a\ }$

b)

$\perp\ to\ \overrightarrow{b\ }$

c)

$\parallel\ \ to\ \overrightarrow{a\ }$

d)

$\perp\ ,\ \ to\ -\ both\ \ -\ \overrightarrow{a\ }\ \&\ \overrightarrow{b\ }$

24.

$If,\ \ \overrightarrow{a\ }\ \times\ \overrightarrow{b\ }\ =\ 0$
then

a)

$\overrightarrow{a\ }\ \perp\ \overrightarrow{b\ }$

b)

$\overrightarrow{a\ }\ \parallel\ \overrightarrow{b\ }$

c)

Both

d)

None of these

25.

$\frac{\overrightarrow{a\ }.\ \overrightarrow{b\ }}{\left|\overrightarrow{a\ }\right|}=$

a)

$angle,\ between,\ \ \overrightarrow{a\ }\ \&\ \overrightarrow{b\ }$

b)

$area\ -\ of\ -\ triangle$

c)

$\Pr ojection\ \ -\ of,\ \ \overrightarrow{a\ }-\ on\ -\overrightarrow{b\ }$

d)

$\Pr ojection\ -\ of,\ \overrightarrow{b\ }\ -on\ -\ \overrightarrow{a\ }$

26.

$If,\ \overrightarrow{a\ }.\ \overrightarrow{b\ }\ =\ -\ \left|\overrightarrow{a\ }\right|\overrightarrow{\left|b\right|}$
$then\ ,\ \ angle\ -between$
$\overrightarrow{a\ }\ and\ \overrightarrow{b\ }\ is$

a)

$0^0$

b)

$\frac{\pi}{2}$

c)

$\frac{\pi}{6}$

d)

$\pi$

27.

$\overrightarrow{AB}+\overrightarrow{BC}+\ \overrightarrow{CA}=$

a)

$\overrightarrow{AC}$

b)

0

c)

$2\ \overrightarrow{AB}$

d)

$\overrightarrow{CB}$

28.

$\left(x+3y^2\right)\ \frac{dy}{dx}\ =y$
is of

a)

$variable\ -\ separable\ -\ form$

b)

homogeneous form

c)

$\frac{dy}{dx}+Py\ =\ Q,\ form$

d)

$\frac{dx}{dy}+Px=\ Q,\ form$

29.

$The\ -\ solution\ -\ of\$

$\frac{dy}{dx}+Py\ =\ Q,\ is$

a)

$y\ =\ \int_{\ \ }Q.\left(I.F\ \right)dx\ +\ c$

b)

$x.\left(I.F.\right)\ =\ \int_{\ \ }Q.\left(I.F\ \right)dy\ +\ c$

c)

$y.\left(I.F.\right)\ =\ \int_{\ \ }Q.\left(I.F\ \right)dx\ +\ c$

d)

$x.\left(I.F.\right)\ =\ \int_{\ \ }Q.\left(P\ \right)dy\ +\ c$

30.

$Equation\$

\left(1+\ e^{\frac{x}{y}}\right)dx+\ e^{\frac{x}{y}}\left(1\ -\ \frac{x}{y}\right)dy\ =0

will - be, solved - through

a)

variable- separable - method

b)

$Linear\ -\ equation\ -method$

c)

$\ substituting\ ,\ y\ =\ vx$

d)

$substituting\ ,\ x\ =\ vy$

31.

$Is,\ \ differential\ -\ equation\$

\frac{dy}{dx}\ =\ \sin\ x+\ \cos\ y

is - homogeneous

a)

Yes

b)

No

c)

not - a - differential - equation

d)

$None\ -\ of\ -\ these$

32.

$\int_{ }^{ }\ \frac{dx}{\sqrt{x^2-a^2}}=\$

a)

$\log\left|x+\sqrt{x^2-\ a^2}\right|\ +C$

b)

$\log\left|x+\sqrt{x^2+\ a^2}\right|\ +C$

c)

$\frac{1}{a}\tan^{-1\ }\frac{x}{a}+c$

d)

$\frac{1}{a}\sin^{-1\ }\frac{x}{a}+c$

33.

$\int_{ }^{ }A.B\ dx\ =\ A\int_{ }^{ }B\ dx\ -\ \int_{ }^{ }\left[\Delta\right]\ dx$
then $\Delta\ =$

a)

$\frac{d}{dx}B\int_{ }^{ }A\ dx$

b)

$\frac{d}{dx}\int_{ }^{ }A.B\ dx$

c)

$\frac{d}{dx}A\int_{ }^{ }B\ dx$

d)

$\frac{d}{dx}A\int_{ }^{ }A\ dx$

34.

$\int_{ }\ \frac{dx}{x^2+a^2}\ =$

a)

$\tan^{-1\ }\left(\frac{x}{a}\right)+c$

b)

$\frac{1}{a}\sin^{-1\ }\left(\frac{x}{a}\right)+c$

c)

$\frac{1}{a}\tan^{-1\ }\left(\frac{x}{a}\right)+c$

d)

$\sin^{-1\ }\left(\frac{x}{a}\right)+c$

35.

$If\ ,\ f\left(2a-x\right)\ =\ f\left(x\right)$

then

\int_0^{2a}f\left(x\right)\ dx\ =

a)

0

b)

$\frac{\pi}{4}$

c)

$2\int_0^af\left(x\right)\ dx\$

d)

$\int_0^af\left(a-x\right)\ dx\ =$

36.

If , f(- x) = - f(x)

then, f(x) is

a)

odd

b)

even

c)

prime

d)

composite

37.

$\frac{d}{dx}\left(u.v\right)=$

a)

$u.\ \frac{d}{dx}v\ -\ v\ \frac{d}{dx}u$

b)

$u.\ \frac{d}{dx}v\ +\ u\ \frac{d}{dx}v$

c)

$u.\ \frac{d}{dx}v\ +\ v\ \frac{d}{dx}u$

d)

$v.\ \frac{d}{dx}u\ -\ u\ \frac{d}{dx}v$

38.

$\int_{\ }^{ }\cot\ x\ dx\ =\$

a)

log(tanx )+C

b)

log (secx+ tanx) +c

c)

log cos x+c

d)

log sinx +c

39.

$Anti\ \ -\ derivative\ -\ of\$
$x^2,\ \ is$

a)

$2x$

b)

$\frac{x^3}{3}+c$

c)

$x^2$

d)

1

40.

$value\ -\ of,\ \ \int\ \ x_{ }^n\ dx\$

where,\ \ n\ =\ -1\ ,\ is

a)

$\frac{x^0}{0}+c$

b)

$\frac{x^2}{2}+c$

c)

$\log x+c$

d)

secx .tan x +c

41.

Universal - relation - is

a)

$A\ \times\ B$

b)

$B\times\ A$

c)

$\phi$

d)

$A\times A$

42.

Onto - function,

is - also - called

a)

Injective

b)

Bijective

c)

Objective

d)

Surjective

43.

If both (a, b) and (b, a)

are in R.

Then "R" is

a)

One - one

b)

Onto

c)

Reflexive

d)

Symmetric

44.

$In\ -\ its\ -\ domain$
$\sin^{-1}\ \frac{1}{x}=$

a)

$\operatorname{cosec}^{-1}x$

b)

$\tan^{-1}x$

c)

$\cot^{-1}x$

d)

$\sec^{-1}x$

45.

$\tan^{-1}x+\ \cot^{-1}x\ =$

a)

1

b)

0

c)

$\frac{\pi}{2}$

d)

$\frac{\pi}{4}$

46.

$2\tan^{-1}x\ =$

a)

$\sin^{-1}\left(\frac{2x}{1+x^2}\right)$

b)

$\cos\ ^{-1}\left(\frac{1-\ x^2}{1+x^2}\right)$

c)

$\tan^{-1}\left(\frac{2x}{1-x^2}\right)$

d)

All - of - these

47.

$\Pr incipal\ -\ value\ \ -of$
$\cos^{-1}x\ ,\ lies\ -\ between$

a)

$\left[-\ \frac{\pi}{2}\ ,\ \frac{\pi}{2}\right]$

b)

$\left(-\ \frac{\pi}{2},\ \frac{\pi}{2}\right)$

c)

$\left[0,\ \pi\right]$

d)

$\left(0,\ \pi\right)$

48.

If - both, A & B are

symmetric - matrices, then

AB - BA, is

a)

Skew Symmetrix

b)

Symmetric

c)

Zero matrix

d)

Identity matrix

49.

$For\ -\ two\ -\ matrices,$

A\ \&\ B

AB\ =\ BA\ =\ I\ ,\ then

a)

A is inverse of B

b)

B is inverse of A

c)

Both

d)

None of these

50.

$\frac{d}{dt}\left(a^{t+\ \frac{1}{t}}\right)=$

a)

$a^{t+\ \frac{1}{t}}\left(1-\frac{1}{t^2}\right)$

b)

$a^{t+\ \frac{1}{t}}\left(1-\frac{1}{t^2}\right)\log\ a$

c)

$\left(1-\frac{1}{t^2}\right)\log\ a$

d)

$a^{t+\ \frac{1}{t}}\left(1+\frac{1}{t^2}\right)\log\ a$

FORMULA QUIZ 2 : 27 DEC

Total questions: 50

Worksheet time: 50mins

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