BITSAT Maths 2010 Sample Paper Test

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Question

The equation of the normal to the circle x2 + y2 = a2 at point (x’ y’) will be :

Possible Answers

Selected	Possible Answer
	x’ y – xy’ = 0
	xx – yy’ = 0
	xy’ + xy’ = 0
	xx’ + yy’ = 0

Question

Equation of the bisector of the acute angle between lines 3x + 4y + 5 = 0 and 12x – 5y – 7 = 0 is :

Possible Answers

Selected	Possible Answer
	21x + 77y + 100 = 0
	99x – 27y + 30 = 0
	99x + 27y + 30 = 0
	21x – 77y – 100 = 0

Question

Equation to the line passing through the point (-4,5) and perpendicular to 3x = 4y = 7 :

Possible Answers

Selected	Possible Answer
	3x-4y+32=0
	4x+3y+1= 0
	3x+4y-8=0
	4x-3y+31=0

Question

If $\theta$ is the angle between two straight lines represented by $ax^2 \ + \ 2hxy \ + \ by^2$ = 0 then :

Possible Answers

Selected	Possible Answer
	$tan \ \theta =$ $\cfrac{2 \sqrt{h^2 + ab}}{a \ + \ b}$
	$cos \ \theta =$ $\cfrac{2 \sqrt{h^2 \ - \ ab}}{a \ + \ b}$
	$tan \ \theta =$ $\cfrac{\sqrt{h^2 \ - \ ab}}{a \ + \ b}$
	$tan \ \theta =$ $\cfrac{2 \sqrt{h^2 \ + \ ab}}{a \ + \ b}$

Question

The real part of cos h $(\alpha \ + \ i \beta )$ :

Possible Answers

Selected	Possible Answer
	$sin \ \alpha \ sin \ h \beta$
	$cos \ \alpha \ cos \ h \beta$
	$2 \ cos \ n \theta$
	$cos \ h \alpha \ cos \ \beta$

Question

If z = cos $\theta$ i sin $\theta,$ then the value of $z^n \ + \ \cfrac{1}{z^n}$ will be :

Possible Answers

Selected	Possible Answer
	$sin \ 2n\theta$
	$2 \ sin \ n\theta$
	$2 \ cos \ n\theta$
	$cos \ 2n\theta$

Question

If $\alpha \ and \ \beta$ are the roots of the equation x^2 – 2x + 4 = 0 then the value of $\alpha^n \ + \ \beta^n$ will be :

Possible Answers

Selected	Possible Answer
	$i2^{n+1} \ sin \ (n\pi/3)$
	$i2^{n+1} \ cos \ (n\pi/3)$
	$i2^{n-1} \ sin \ (n\pi/3)$
	$2^{n-1} \ cos \ (n\pi/3)$

Question

$[sin \ (\alpha \ + \ \theta ) -e^{ai}$ $sin \ \theta ]^n$ is equal to :

Possible Answers

Selected	Possible Answer
	$cos^n \ \alpha \ e^{in\theta}$
	$sin^n \ \alpha \ e^{in\theta}$
	$cos^n \ \alpha \ e-^{in\theta}$
	$sin^n \ \alpha \ e^{-in\theta}$

Question

If A is a skew symmetric matrix of second order and C is a column matrix of second order then CAC is equal to :

Possible Answers

Selected	Possible Answer
	[0]
	[1]
	$\left [\overset{0 \ 1}{1 \ 0} \right ]$
	$\left [\overset{1 \ 0}{0 \ 1} \right ]$

Question

If A = $\left [\overset{3 \ 1}{-1 \ 2} \right ]$ and I $\left [\overset{1 \ 0}{0 \ 1} \right ]$ then the correct statement is :

Possible Answers

Selected	Possible Answer

Question

If A and B are the two matrices of the same order and A^2-b^2 = (A+B ) (A-B) , then the correct statement will be :

Possible Answers

Selected	Possible Answer
	A’B’ = AB
	AB=BA
	$A^2+B^2 \ = \ A^2-B^2$
	none of these

Question

The value of the determinant $\Bigg |\overset{a-b-c}{\underset{2c}{2b}}$ $\overset{2a}{\underset{2c}{b-c-a}}$ $\overset{2a}{\underset{c-a-b}{2b}}\Bigg |$ will be :

Possible Answers

Selected	Possible Answer
	$(a-b-c) \ (a^2+b^2+c^2)$


	none of these

Question

If (1 + x)^n $= \ C_0 + C_1 x + C_2 x^2$ + …+ C_nx^n, then $C_0-C_1+C_2-C_3 \ +....+(-1)^n \ C_n$ is equal to :

Possible Answers

Selected	Possible Answer

Question

The term independent of x in the expansion $\Bigg [of x + \cfrac{1}{x} \Bigg ]^{2n}$ is :

Possible Answers

Selected	Possible Answer
	$\cfrac{1.3.5........(2n-1)}{n!} \ . 2^{n-1}$
	$\cfrac{1.3.5........(2n-1)}{n!} \ . 2^n$
	$a.3.5......(2n-1)} \ . 2^n$
	none of these

Question

is equal to :

Possible Answers

Selected	Possible Answer

Question

If n $\in$ N then $\overset{n}{m=1}$ m2 is equal to :

Possible Answers

Selected	Possible Answer
	$\cfrac{m(m+1)(2m+1)}{6}$
	$\cfrac{n(n-1)(2n-1)}{6}$
	$\cfrac{m((m-1)(2m-1)}{6}$
	$\cfrac{n(n+1)(2n+1)}{6}$

Question

If A.M. and H.M. between two numbers are 27 and 12 respectively then their G.M. is:

Possible Answers

Selected	Possible Answer
	9
	18
	24
	36

Question

If $\cfrac{1}{q+r} \ , \cfrac{1}{r+p} \ ,$ $\cfrac{1}{p+q} \ ,$ are in A.P. then :

Possible Answers

Selected	Possible Answer
	p2,q2, r2 are in A.P.
	p,q,r are in A.P.
	p,q,r are in G.P.
	$\cfrac{1}{p} \ , \cfrac{1}{q} \ ,$ $\cfrac{1}{r} , \ are \ in \ A.P.$

Question

If $\alpha \ and \ \beta$ are the roots of the equation x^2 – ax + b = 0 and $v_2 \ = \ \alpha^n \ + \ \beta^n$ then :

Possible Answers

Selected	Possible Answer
	$v_n+1 = av_n + bv^{n-1}$
	$v_{n+1} = bv_n - av_{n-1}$
	$v^{n+1} = av_n - bv_{n-1}$
	$v^{n+1} = bv_n + av_{n-1}$

Question

If $\alpha \ and \ \cfrac{1}{\alpha\alpha}$ are the roots of the equation 5x^2+13x+k = 0 then k will be:

Possible Answers

Selected	Possible Answer
	5
	-5
	13
	1

Question

The value $i^3-i^5-i^{10}-i^{16}$ will be :

Possible Answers

Selected	Possible Answer
	0
	i
	– 2 – 2i
	2 – 2i

Question

A coin tossed m + n (m > n) , times then the probability that the head appears m times continuosly is :

Possible Answers

Selected	Possible Answer
	$\cfrac{m+n}{2^{m+n}}$
	$\cfrac{n+2}{2^{m+1}}$
	$\cfrac{m}{2^{m+n}}$
	$\cfrac{m+2}{2^{n+1}}$

Question

For any two events A and B if P $(A \cup B)$ = 5/6, P $(A \cap B)$ = 1/3, P(B) = ½ then P(A) is :

Possible Answers

Selected	Possible Answer
	½
	2/3
	1/3
	none of these

Question

If M and N are any two events , then the probability of happening exactly one event is:

Possible Answers

Selected	Possible Answer
	P(M) + P(N) – P(MN)
	P(M) + P(N) – 2P(MN)
	P(M) + P(N) + 2P(MN)
	none of these

Question

A bag contains 3 white and 5 black balls. One ball is drawn at random. Then the probability that it is black is :

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{8}$
	$\cfrac{3}{8}$
	$\cfrac{5}{8}$
	$\cfrac{3}{5}$

Question

A box contains 100 bulbs, out of these 10 are used. 5 bulbs are choosen at random. Then the probability that no one is fused is :

Possible Answers

Selected	Possible Answer
	$\left [\cfrac{9}{10} \right ]^5$
	$\cfrac{^{90}C_5}{^{100}C_5}$
	$\left [\cfrac{1}{2} \right ]^5$
	$10^{-5}$

Question

For any two events A and B the correct statement is :

Possible Answers

Selected	Possible Answer
	$P \ (A \cap B) \le P (A) + P \ (B)$
	$P \ (A \cap B) \le P (A) + P \ (B) \ - 1$
	$P \ (A \cap B) \ge P (A) + P \ (B) \ - 1$
	$P \ (A \cap B) \ge P (A) + P \ (B)$

Question

For any non zero vector $\overset{\rightarrow \rightarrow}a the$ correct statement is :

Possible Answers

Selected	Possible Answer
	$\overset{\rightarrow \rightarrow}a.a \le 0$
	$\overset{\rightarrow \rightarrow}a.a = 0$
	$\overset{\rightarrow \rightarrow}a.a > 0$
	$\overset{\rightarrow \rightarrow}a.a \ge 0$

Question

$\overrightarrow{a.(}$ $\overrightarrow{b}\overrightarrow{X}$ $\overrightarrow{c)} = 0$ then the correct statement is :

Possible Answers

Selected	Possible Answer
	out of $\overrightarrow{a,}$ $\overrightarrow{b,}$ $\overrightarrow{c,}$ any two vectors are parallel
	$\overrightarrow{a,}$ $\overrightarrow{b,}$ $\overrightarrow{c,}$ are coplanar
	any two are equal $\overrightarrow{a,}$ $\overrightarrow{b,}$ $\overrightarrow{c,}$
	at least one above statement is correct

Question

If $\overrightarrow{A}$ $\overrightarrow{X}$ $\overrightarrow{B}$ $\overrightarrow{=}$ 0 where $\overset{\rightarrow \rightarrow}A$ $and \ \overset{\rightarrow \rightarrow}B$ are non zero vectors then :

Possible Answers

Selected	Possible Answer
	$\overset{\rightarrow}A\ and \$ $\overset{\rightarrow}B$ are perpendicular to each other
	the angle between $\overset{\rightarrow}A\$ $and\ \overset{\rightarrow}B\ is\ \pi$
	$\overset{\rightarrow}A\$ $and \ \overset{\rightarrow}B$ parallel vectors
	$\overset{\rightarrow}B$ is unit vector

Question

If 2i + j – k and i – 4j + $\lambda$ k are perpendicular to each other then $\lambda$ is equal to:

Possible Answers

Selected	Possible Answer
	– 3
	– 2
	– 1
	0

Question

If $\cfrac{d}{dx} \ \ \Phi$ (x) = f(x) then $\overset{2}{1}$ f(x) dx is equal to :

Possible Answers

Selected	Possible Answer

	$\Phi (1) \ - \ \Phi(2)$

	$\Phi (2) \ - \ \Phi(1)$

Question

If f (a – x) = f(x), then $\overset{a}{0}$ xf(x) dx is equal to :

Possible Answers

Selected	Possible Answer
	$\overset{a}{0} \ f(X)dX$
	$a \overset{a/2}{0} \ f(X)dX$
	$a \overset{a}{0} \ f(X)dX$
	none of these

Question

$\overset{a}{-a}$ f(x)dx = 2 $\overset{a}{0}$ f(x)dx when :

Possible Answers

Selected	Possible Answer
	f(2a-x) = – fx
	f(2a-x)=f(x)
	f(-x)=-f(x)
	f(-x)=f(x)

Question

$\overset{2}{0}$ | 1 – x|dx is equal to :

Possible Answers

Selected	Possible Answer


	$\cfrac{3}{2}$
	$\cfrac{1}{2}$

Question

For any integer n the value of $\overset{\pi \pi}{0}$ $e^{cos2} \ cos^3$ (2n+1)x dx will be:

Possible Answers

Selected	Possible Answer

	0
	1
	e

Question

$\cfrac{sin \ 2X}{sin^4 X + \ cos^4 \ X}$ dx is equal to :

Possible Answers

Selected	Possible Answer
	$2 \ tan^{-1} (tan^2 X ) + C$
	$tan^{-1} (X \ tan^2 X ) + C$
	$tan^{-1} (tan^2 X ) + C$
	$none \ of \ these$

Question

$\cfrac{1}{X^5}$ dx is equal to :

Possible Answers

Selected	Possible Answer
	$- \ \cfrac{1}{5X^4} + C$
	$- \ \cfrac{1}{5X^6} + C$
	$- \ \cfrac{1 \ + \ C}{4X^4} + C$
	$\cfrac{-5}{X^6} + C$

Question

The function sin x + cos x is maximum when x is equal to :

Possible Answers

Selected	Possible Answer
	$\cfrac{\pi}{6}$
	$\cfrac{\pi}{4}$
	$\cfrac{\pi}{3}$
	$\cfrac{\pi}{2}$

Question

If the normal to a curve is parallel to axis of x, then the correct statement is :

Possible Answers

Selected	Possible Answer
	$\cfrac{dX}{dy} = - 1$
	$\cfrac{dX}{dy}$
	$\cfrac{dX}{dy} = 0$
	$\cfrac{dy}{dX} = 0$

Question

$\cfrac{d}{dX} \ sin^{-1}$ x is equal to :

Possible Answers

Selected	Possible Answer
	$- \cfrac{1}{\sqrt{X^2 \ - 1}}$
	$\cfrac{1}{\sqrt{X^2 \ - 1}}$
	$\cfrac{1}{\sqrt{1 - X^2}}$
	$- \ \cfrac{1}{\sqrt{1 - X^2}}$

Question

The differential coefficient of $e^{x-3}$ is :

Possible Answers

Selected	Possible Answer
	$2X^{3} e^{x3}$
	$3X (e^{x3})$
	$e^{x3}$
	$3X^{2} e^{x3}$

Question

$\cfrac{d}{dX} \ (X^X)$ is equal to :

Possible Answers

Selected	Possible Answer
	$X^X \ log \ (e/X)$
	$X^X \ log \ eX$
	$log \ eX$
	$X^X \ log \ X$

Question

$\overset{lim}{X \rightarrow a}$ [f(x),g(x)] will exist, when :

Possible Answers

Selected	Possible Answer
	$\overset{lim}{X \rightarrow a}$ $\cfrac{f(X)}{g(X)}$ is exists
	$\overset{lim}{X \rightarrow a}$ $[f(X)]^{g(X)}$ is exists
	$\overset{lim}{X \rightarrow a}$ f (x) or lim g(x) is exists
	$\overset{lim}{X \rightarrow a}$ f (x) and $\overset{lim}{X \rightarrow a}$ g(x) both exists

Question

$\overset{lim}{X \rightarrow 0}$ $\cfrac{sin \ X}{X}$ is equal to :

Possible Answers

Selected	Possible Answer
	2
	- 1
	1
	0

Question

If f(x) = sin [x] , [x] $\ne$ 0 where [x] is a greatest integer less or equal to x then $\overset{lim}{X \rightarrow 0}$ f(x) is equal to :

Possible Answers

Selected	Possible Answer
	- 1
	0
	1
	does not exist

Question

If A = {-2, -1, 0, 1,2} and f: $A \rightarrow R$ such that f(X) = X^2 + 1, then the range of f will be:

Possible Answers

Selected	Possible Answer
	$\Big\{$ $1, \overset{+}{-} \ 2, \overset{+}{-} 5$ $\Big\}$
	{1,2,5}
	{-2, -1, 0, 1,2}
	none of these

Question

The point (at3, at2) will lies on the curve :

Possible Answers

Selected	Possible Answer
	$X^3 \ = \ ay^2$
	$X^3 \ = \ ay$
	$y^2 \ = \ ac$
	$y^2 \ = \ aX^2$

Question

The diameter of the circle $X^2 \ + \ y^2$ + 4x – 6y = 0, is :

Possible Answers

Selected	Possible Answer
	$\sqrt{52}$
	$\sqrt{13}$
	$\sqrt{26}$
	$\sqrt{20}$

Question

The pole of the line $\tau x$ + my + n = 0 w.r.t. the circle $X^2 \ + \ y^2 \ = \ a^2$ is :

Possible Answers

Selected	Possible Answer
	$\Big[- \cfrac{n}{1} \ a^2 \ ,$ $- \cfrac{n}{m} \ a^2 \Big]$
	$\Big[- \cfrac{a}{na^2} ,$ $\cfrac{m}{ma^2} \Big]$
	$\Big[- \cfrac{1}{n} \ a^2 \ ,$ $\cfrac{m}{n} \ a^2 \Big]$
	$\Big[- \cfrac{1}{n} \ a^2 \ ,$ $- \cfrac{m}{n} \ a^2 \Big]$

Question

Two dice thrown together then the probability of getting a sum of 7, is :

Possible Answers

Selected	Possible Answer
	$\cfrac{7}{36}$
	$\cfrac{6}{36}$
	$\cfrac{5}{36}$
	$\cfrac{8}{36}$

Question

For any two events A and B, P $(A \cap B)$ is equal :

Possible Answers

Selected	Possible Answer
	$P(A) - P(A \cap B)$
	$P (A) - \overset{\cap}{P(A \cap B)}$
	$P(A) - P(A \cup B)$
	$P (A) + \overline{(A} \ \overline{\cap B})$

Question

If A and B are two events, then $P \overline{(A \ / \ B)}$ is equal to :

Possible Answers

Selected	Possible Answer
	$P \overline{(A)} \ /P \overline{(B)}$
	$\cfrac{1-P(A+B)}{\overline{P(B)}}$
	$\underline{1- P(AB)}$

Question

If A $\le B,$ then $B \cup A$ will be :

Possible Answers

Selected	Possible Answer
	[0]
	$\Phi$
	A
	B

Question

$P \Bigg[$ $\cfrac{\overline{A}}{A \cup B}$ $\Bigg]$ is equal :

Possible Answers

Selected	Possible Answer
	$\cfrac{P(A)}{P(A \cup B)}$
	$\cfrac{P (\overline A \cap B)}{P(A \cap B)}$
	$\cfrac{P \overline{(A)}}{P(A \cup B)}$
	$\cfrac{P \overline{(B)}}{P(A \cup B)}$

Question

The period of $sin^4 \ X+cos^4$ x will be :

Possible Answers

Selected	Possible Answer
	$\cfrac{3 \pi}{2}$
	$2 \pi$
	$\pi$
	$\cfrac{\pi}{2}$

Question

$\overrightarrow{a} \overrightarrow{X}$ $\overrightarrow{(b} \overrightarrow{X}$ $\overrightarrow{c)} \overrightarrow{is}$ equal to :

Possible Answers

Selected	Possible Answer
	$\overrightarrow{(a} . \overrightarrow{c)}$ $\overrightarrow{b} - \overrightarrow{(a} .$ $\overrightarrow{b)} . \overrightarrow{c}$
	$\overrightarrow{(a} . \overrightarrow{c)}$ $\overrightarrow{b} + \overrightarrow{(a} .$ $\overrightarrow{b)} . \overrightarrow{c}$
	$\overrightarrow{(a} . \overrightarrow{b)}$ $\overrightarrow{c} + \overrightarrow{(a} .$ $\overrightarrow{b)} . \overrightarrow{c}$
	$\overrightarrow{(a} . \overrightarrow{b)}$ $\overrightarrow{c} - \overrightarrow{(a} .$ $\overrightarrow{c)} . \overrightarrow{b}$

Question

The angle between the vectors (i+j) abd (j+k) is :

Possible Answers

Selected	Possible Answer
	$\cfrac{\pi}{4}$

	$\cfrac{\pi}{-4}$
	$\cfrac{\pi}{3}$

Question

The area of the region bounded by the curves y = x sin x, axis of x, x= 0 and $X \ = \ 2 \pi$ will be :

Possible Answers

Selected	Possible Answer
	$8 \pi$
	$4 \pi$
	$2 \pi$
	$\pi$

Question

$\overset{\pi^{/2}}{0}$ log sin x dx is equal to :

Possible Answers

Selected	Possible Answer
	$\pi \ log \Bigg[\cfrac{1}{-2} \Bigg]$
	$\pi \ log \ 2$
	$\pi \ log \Bigg[\cfrac{1}{2} \Bigg]$
	$\cfrac{\pi}{2} \ log \ 2$

Question

$\overset{b}{a}$ f(x) dx is equal to :

Possible Answers

Selected	Possible Answer
	$\overset{b}f (X-a-b) dX$
	$\overset{a}f(a-X )dX$
	$\overset{b}f(a+b-X )dX$
	noneof these

Question

$\overset{\pi^{/2}}{0}$ sin 2x log tan x dx is equal to :

Possible Answers

Selected	Possible Answer
	$2 \pi$
	$\pi$

	$\pi /2$

Question

$\overset{\pi \pi}{0} \ cos^3$ x dx is equal to :

Possible Answers

Selected	Possible Answer
	$4 \pi$
	$2 \pi$
	$\pi$

Question

cot x dx is equal to :

Possible Answers

Selected	Possible Answer
	log tan x + C
	log sec x + C
	log cosec x + C
	log sin x + C

Question

If z = x + y iy then |z – 5| is equal to :

Possible Answers

Selected	Possible Answer
	$\sqrt{(X - y)^2 \ + \ 5^2}$
	$\sqrt{(X - 5)^5 \ + \ y^2}$
	$\sqrt{X^2 \ + (y \ - \ 5)^2}$
	$\sqrt{(X - 5)^5 \ + (y \ - \ 5)^2}$

Question

If $\alpha \ and \ \beta$ are the roots of the equation $4X^2 \ + \ 3X \ + \ 7 = 0$ then $\cfrac{1}{\alpha \alpha}$ $+ \cfrac{1}{\beta \beta}$ is equal is :

Possible Answers

Selected	Possible Answer
	$\cfrac{7}{3}$
	$\cfrac{2}{7}$
	$\cfrac{-3}{7}$
	$\cfrac{3}{7}$

Question

2,357 is equal to :

Possible Answers

Selected	Possible Answer
	$\cfrac{2379}{999}$
	$\cfrac{2355}{999}$
	$\cfrac{2355}{997}$
	none of these

Question

If the second term of a G.P. is 2 and the sum of its infinite terms is 8, then its first therm is :

Possible Answers

Selected	Possible Answer
	2
	4
	6
	8

Question

(1+2+3+….+n) is equal to :

Possible Answers

Selected	Possible Answer
	$\Bigg[\cfrac{n(n \ + \ 1)}{2} \Bigg]^2$

	$\cfrac{n(n \ + \ 1)}{2}$
	$\cfrac{n(n \ - \ 1)}{2}$

Question

For an $\in N \ 2^{3 \ n}$ – 7n – 1 is divisible by :

Possible Answers

Selected	Possible Answer
	50
	49
	51
	48

Question

If x = 2 + $2^{1/3} \ +\ 2^{2/3}$ , then $X^3 \ - \ 6X^2$ + 6x is equal to :

Possible Answers

Selected	Possible Answer
	0
	1
	2
	3

Question

If $(1 - X)^n = C_0 \ + \ C_1X$ + ….+ C_nX^n then $C_1 \ + \ 2C_2 \ + \ 3C_3$ ….. nC_n is equal is :

Possible Answers

Selected	Possible Answer
	$n.2^{n-1}$
	$(n - 1)^ \ {2n-1}$
	$(n + 1)^ \ {2n}$
	$2^{n-1} \ - \ 1$

Question

Determinate $\overset{c \ - \ id}{\underset{1 \ + \ ib}}$ $\overset{a \ - \ id}{\underset{c \ + \ id}}$ is equal to :

Possible Answers

Selected	Possible Answer


	$(a^2+b^2) \ (c^2+d^2)$
	$(a+b) \ (a-b)$

Question

$\Bigg |\overset{43}{\underset{17}{35}}$ $\overset{1}{\underset{3}{7}}$ $\overset{6}{\underset{2}{4}}\Bigg |$

is equal to :

Possible Answers

Selected	Possible Answer
	- 6
	- 110
	0
	150

Question

If A = $\bigg[ \overset{1}{0} \overset{0}{1} \bigg]$ then A2 is equal to:

Possible Answers

Selected	Possible Answer
	$\bigg[ \overset{0}{0} \overset{0}{0} \bigg]$
	$\bigg[ \overset{0}{0} \overset{0}{1} \bigg]$
	$\bigg[ \overset{1}{0} \overset{0}{1} \bigg]$
	$\bigg[ \overset{1}{1} \overset{1}{1} \bigg]$

Question

If A = $\bigg[ \overset{1}{0} \overset{1}{1} \bigg]$ then $A^ \ n$ is equal to :

Possible Answers

Selected	Possible Answer
	$\bigg[\overset{1}{0} \overset{n^n}{1} \bigg]$
	$\bigg[\overset{n}{0} \overset{n}{n} \bigg]$
	$\bigg[\overset{1}{0} \overset{n}{1} \bigg]$
	$\bigg[\overset{1}{0} \overset{1}{1} \bigg]$

Question

If A and B are the invertible matrix of the required order then the value of $(AB)^{-1}$ will be :

Possible Answers

Selected	Possible Answer
	$[(AB)']^{-1}$
	$A^{-1} B^{-1}$
	$B^{-1}A^{-1}$
	$(BA)^{-1}$

Question

The value of sin 3x is :

Possible Answers

Selected	Possible Answer
	$4 \ sin \ X \ - \ 3 sin^3 \ X$
	$4 \ sin \ X \ + \ 3 sin^3 \ X$
	$3 \ sin \ X \ - \ 4 \ sin^3 \ X$
	$3 \ sin \ X \ + \ 4 \ sin^3 \ X$

Question

The imaginary roots of $(-1)^{1/3}$ is :

Possible Answers

Selected	Possible Answer
	$\cfrac{1 \ \underline{+}\ \sqrt{3i}}{4}$
	$\underline{+} \ i$
	$\cfrac{-\ 1 \ \underline{+}\ \sqrt{3}}{2}$
	$\cfrac{1 \ \underline{+}\ \sqrt{3i}}{2}$

Question

The argument and modulus of the $e^\ {sin\ i \theta}$ is :

Possible Answers

Selected	Possible Answer
	$1, \ sin\ h \theta$
	$1, \ \pi/2$
	$e^\ {cos} \ \theta ,\ sin\ h \theta$
	$e^\ {sin} \ \theta ,\ sin\ h \theta$

Question

The minimum distance of a point (x, y) from a line ax + by + c = 0, is :

Possible Answers

Selected	Possible Answer
	$\cfrac{\|aX1 + by1 + c\|}{\sqrt{a^2 + b^2}}$
	$\cfrac{\|aX1 + by1 + c\|}{\sqrt{a^2 + b^2-c}}$
	$\cfrac{\|aX1 + by1 + c\|}{\sqrt{a^2 + b^2+c^2}}$
	$\cfrac{\|aX1 + by1 + c\|}{\sqrt{a^2 + b^2+c}}$

Question

A straight line through ( 1, 1) and parallel to the line 2x + 3y – 7 = 0 is :

Possible Answers

Selected	Possible Answer
	2x + 3y + 5 = 0
	3x – 2y + 7 = 0
	3x + 2y – 8 = 0
	2x + 3y – 5 = 0

Question

Equation of the straight line passing through the points (-1, 3) and (4, -2) is :

Possible Answers

Selected	Possible Answer
	x- y = 3
	x + y = 3
	x – y = 2
	x + y = 2

Question

The general equation of circle passing through the point of intersection of circle S = 0 and line P = 0, is :

Possible Answers

Selected	Possible Answer
	$S\ +\ \lambda P = 0, \lambda \in R$
	6S + 4P = 0
	3S + 4P = 0
	4S + 5P = 0

Question

The equation of the radial axis of two circle X^2 + y^2 + 2g_1X + 2f_1y + c_1 = 0 and X^2 + y^2 + 2g_2X + 2f_2y + c_2 = 0 , is :

Possible Answers

Selected	Possible Answer
	$2\ (g_1 - g_2)\ X + 2$ $(f_1 - f_2)\ y - c_1 - c_2 =0$
	$2\ (g_2 - g_1)\ X + 2$ $(f_1 - f_2)\ y + c_1 - c_2 =\ 0$
	$2\ (g_1 - g_2)\ X + 2$ $(f_1 - f_2)\ y + c_1 - c_2 =\ 0$
	$2\ (g_1 - g_2)\ X + 2$ $(f_1 - f_2)\ y + c_2 - c_1 =\ 0$

Question

If f (x) = cos (log x), then f(x) f(y) – 1 $[f \overset{(\underline X)}{y} - f (Xy) ]$ is equal to :

Possible Answers

Selected	Possible Answer
	0
	f(x+y)
	$f \overset{(\underline X)}{y}$
	f(xy)

Question

If f(x) = $\cfrac{X}{X - 1}$ = y, then the value of f(y) is :

Possible Answers

Selected	Possible Answer
	1 –x
	x + 1
	x – 1
	x

Question

$\overset{lim}{n \rightarrow \infty}$ $\bigg[\cfrac{1^2}{13 + n3}$ $+ \cfrac{2^2}{23 + n3}$ $+ \cfrac{1}{2n} \bigg]$ is equal to :

Possible Answers

Selected	Possible Answer
	$\cfrac{1}{2} \ log \ 2$
	$3 \ log \ 2$
	$\cfrac{1}{3} \ log \ 2$
	$\cfrac{1}{2} \ log \ 3$

Question

$\overset{lim}{X \rightarrow \infty}$ $\cfrac{X2 - a2}{X - a}$ is equal to :

Possible Answers

Selected	Possible Answer
	$\infty$
	0
	a
	2a

Question

$\cfrac{d}{dX} \ (2^X)$ is equal to :

Possible Answers

Selected	Possible Answer
	1
	$2^X \ log \ 2$
	x log 2
	0

Question

Differential coefficient of $X^3\ w.r.t. \ X^2$ will be :

Possible Answers

Selected	Possible Answer
	$\cfrac{3}{2_X}$
	$\cfrac{2}{3_X}$
	$\cfrac{3}{2} \ X$
	$\cfrac{3X^2}{2}$

Question

$\cfrac{d}{dX}$ (tan x ) is equal to :

Possible Answers

Selected	Possible Answer
	$cosec^2 \ X$
	sec x tan x
	cosec x cot x
	$sec^2 \ X$

Question

The coordinates of the point where the tangent to the curve x2 + y2 – 2x – 3 = 0 is parallel to the axis of x is :

Possible Answers

Selected	Possible Answer
	$1. \ \underline{+} \ \sqrt{3}$

	$1, \ \underline{+} \ 2$
	$(1. \ \underline{+} \sqrt{2} )$

Question

The point at which tangent to the curve y = $\tau^{2X}$ at the point (0, 1) meets the x-axis is :

Possible Answers

Selected	Possible Answer
	(1, 0)
	(- ½, 0)
	(2, 0)
	(0, 2)

Question

Maximum value of slope of a tangent to the curve y = $- X^3 \ +\ 3X^2$ + 2x – 27 will be :

Possible Answers

Selected	Possible Answer
	11
	- 4
	5
	2

Question

m $\cfrac{sin\ \sqrt{X}}{\sqrt{X}}$ dx is equal to :

Possible Answers

Selected	Possible Answer
	$-\ 2\ cos \ \sqrt{X} \ + \ C$
	$2\ cos \ \sqrt{X} \ + \ C$
	$2\ sin \ \sqrt{X} \ + \ C$
	$sin \ \sqrt{X+} C$

Question

Correct statement is :

Possible Answers

Selected	Possible Answer
	$(AB)^{-1} \ = \ B^{-1} A^{-1}$
	$(AB)^{-1} \ = \ A^{-1} B^{-1}$
	$(AB)^T \ = \ A^T B^T$
	$(AB)^1 \ = \ A^1 B^1$

Question

If the matrix P = $\bigg[\overset{1}{-3}\ \underset{0}{2} \bigg]$ and Q $\bigg[\overset{-1}{2}\ \underset{3}{0} \bigg]$ then the correct statement is :

Possible Answers