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CHAPTER # 1
NUMBER SYSTEM
I. CHOOSE THE CORRECT ANSWERS. __
1. 2 is a __________ number.
(a) Rational (b) irrational (c) Prime (d) None
2. Circumference of any circle = .en!t" of its diameter
(a) # $ 2 (b) % # (c) # (d) 2 #
&. # is a .
(a) '"ole number (b) Natural number
(c) Rational Number (d) Irrational number
. odulus of com*le+ number & , i is .
(a) (b) % - (c) - () /
-. 0dditie inerse of (a b) is ..
(a) (a% b) (b) (% a b) (c) (%a %b) (d) None
. 3 , 3 = ..
(a) Real number (b) Com*le+ number(c) / (d) %1
4. 3 5 3 = .
(a) Real number (b) Com*le+ number
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(c) / (d) None6. 3. 3 = .
(a) 737 (b) 737
2
(c) / (d) None8. 9"e set :I %1; *osses closur *ro*erty
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SHORT QUESTIONS
1. Proe t"at 3 5 3 is real.
2. If 3 = a 5 ? b t"en *roe t"at 3 % 3 is ima!inary.
&. If 3 = a 5 ? b t"en *roe t"at A. A = 7372.
. Proe t"at 3 = A iff 3 is real.
-. Bind t"e multi*lication Inerse of 2 5 & ?.
__ __. +*ress ( 5 %&) (& 5 %& in t"e form of a 5 bi.__
4. +*ress & 5 ? in *olar form.
6. +*ress 1 , ? in *olar form.
8. BactoriAe a25 8 b2.
1/. (BactoriAe) 4+25 4y2
11. im*lify (1 %2)/(& ).__
12. "o< t"at & is an irrational number.
1&. Proe t"at (31/32) = 31 $ 32 Bor all 3 D C.
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CHAPTER # 2
(SETS, FUNCTION & GROUP)
1. 0 set "as obEects.
(a) Identical (b) Not
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6. If 0 = : ; t"en P (0) =
(a) m*ty set (b) :/; (c) :O; (d) None
8. If n(s) = m t"en nP(s) =..
(a) 2m (b) 2 m%1 (c) 2 m51 (d) & m
1/. 0 MG is defined as .
(a) :+ $ + 0 + G; (b) :+ $ + 0 J + G;
(c) :+ $ + 0 J + G; (d) None
11. 0G is defined as
(a) :+ $ + 0 + G; (b) :+ $ + 0 Q G;
(c) :+ $ + 0 + G; (d) None
12. 9"e com*lement of a set 0 is defined as ..
(a) 0$= :+ $ + M + 0; (b) 0$= :+$+ M+ 0;
(c) 0$= :+ $ + M + 0; (d) None
1&. 0 M O =.
(a) 0 (b) O (c) u (d) None
1. 0 O =
(a) 0 (b) O (c) 0$ (d) None
1-. 0 , O =..
(a) 0 (b) O (c) 0$ (d) None
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1. (0MG)$= .
(a) 0$ MG$ (b) 0$ MG (c) 0$G$ (d) 0G$
14. If 0+G = G+0 t"en .
(a) 0 = G (b) 0G = O (c) 0 = G (d) None
16. 9"e function f 0G is 0 into G function
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SHORT QUESTION
1. 'rite do
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CHAPTER # 3
(MCQs)
1. 9riial solution of "omo!eneous linear e@uation is
(a) (1 / /) (b) (/ 1 /) (c) (/ / 1) (d) (///)
2. Bor non%triial solution 707 is
(a) 707 U / (b) 707 V / (c) 707 = / (d) None
&. Bor triial solution 707 is..(a) 707 U / (b) 707 V / (c) 707 = / (d) None
. ystem o linear e@uations is Inconsistent if
(a) ystem "as no solution (b) ystem "as many solution
(c) ystem "as uni@ue solution (d) None
-. inimum number of e@uation for any system of e@uations
(a) 2 (b) & (c) (d) 1/
. 9"e matri+ 0 is Wermitian
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8. 0 s@uar matri+ 0 = :aiE; is u**er trian!ular matri+
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SHORT QUESTION
1 %1 1 /1. If 0 = a b and 02= / 1 t"en find t"e alue a [ b
- 2 2 12. Bind t"e matri+ \+] if %2 1 + = %2 1
- &&. If 0 = 1 1 erifies t"at 0 0%1= I2
bc ac ab. 'it"out e+*ansion s"o< t"at 1$a 1$b 1$c = / a b c
mn l l2 1 l2 l&
-. "o< t"at nl m m2 = 1 m2 m&
m n n2 1 n2 n&
. "o< t"at (0%1)%1= 0
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CHAPTER #
(MCQs)
1. ystem of simultaneous e@uation inoles .. or more e@uations.
(a) 1 (b) 2 (c) & (d)
2. '"en discriminant = / t"en t"e roots are.
(a) Real and e@ual (b) Rational
(c) Irrational and une@ual (d) None
&. If roots of t"e e@uation +25 R+ 5 1 = / are e@ual t"e alue of X
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(a) +25 + 5 P = / (b) +25 + , P = /(c) +2% + 5 P = / (d) +2, + , P = /
6. Bor
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SHORT QUESTIONS
1. ole by factoriAation 8+2, 12+ , - = /
2. ole by com*letin! s@uare +2, 2+ , 688 = /
&. ole by uadratic formula -+2, 1&+ 5 = /
. ole +%2, 1/ = &+%1
-. aluate (1 5 < , ) (b) (%> $ 2. > $ 2)(c) (%1 2) (d) None of t"ese
. Inerse sine function is ) (d) (%>$2 >$2)
4. 9"e inerse cosine function can be
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(a) (%1 1) (b) (%g g) (c) (/ >) (d) (%>$2 >$2)
8. 9"e ran!e of y = cos%1+ function is
(a) (%1 1) (b) (%g g) (c) (/ >) (d) (%>$2 >$2)
1/. Inerse tan!ent function can be 5 Cos%1+ (b) > , Cos%1 +(c) > 5 in%1+ (d) > , in%1+
1. 9an%1(%+) = .
(a) 9an%1+ (b) Cot %1+ (c) % 9an%1+ (d) % Cot %1+
14. If in%1 = >$2 , + t"en + = ..
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(a) / (b) > $ & (c) > $ (d) > 5 +
16. in
%1
0 5 in
%1
G = .._____ _____ ____ ____(a) in%1(01 ,G2, G1 % 02) (b) in%1(01 , G2= G1 , 02)
_____ _____ _____ _____(c) in%1(01 , G25 G1 5 02 (d) in%1(021 , G25 G21 , 02)
18. in%10 , in%1G = ._____ _____ _____ _____
(a) in%1(01 ,G25 G1 % 02) (b) in%1(01 , G2% G1 , 02)_____ _____ _____ _____
(c) in%1(01 , G25 G1 5 02 (d) in%1(021 , G25 G21 , 02)
2/. Cos%10 5 Cos%1G = .._____________ ____________
(a) Cos%1Y0G % (1 , 02)(1 , G2)Z (b) Cos%1Y0G 5 (1 , 02)(1 , G2)Z_____________ _____________
(c) Cos%1Y0G % (1 5 02)(1 , G2)Z (d) Cos%1Y0G % (1 , 02)(1 5 G2)Z
21. Cos%1 0 , Cos%1 G =
_____________ ____________ (a) Cos%1Y0G % (1 , 02)(1 , G2)Z (b) Cos%1Y0G 5 (1 , 02)(1 , G2)Z_____________ _____________
(c) Cos%1Y0G % (1 5 02)(1 , G2)Z (d) Cos%1Y0G % (1 , 02)(1 5 G2)Z
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SHORT QUESTION
1. 'it" out usin! tables $ calculators ealuate_
(i) in%1 (ii) in%1(%1) (iii) Cos%1(&$2)_ _
(i) 9an%1(%1 $ &) () Cosec%1 (%2 $ &)
2. Bind t"e alue of _(i) in YCos%1(& $ 2) (ii) ec Yin%1(1$2)Z
(iii) ec YCos%1(1$2)Z (i) 9an Yin%1(%1$2)Z
&. "o< t"at Cos%112 $ 1& = in %1 - $ 1&
. "o< t"at Cos%1 $ - = Cot %1 $ &
-. "o< t"at Cos (2 in%1 +) 1 , 2+2____
. Cos (in%1 +) = 1 , +2
____4. Cos in (2 Cos%1 +) = 2+ 1 , +2
6. "o< t"at tan%1(%+) = % tan%1+
8. "o< t"at in%1 (%+) = % in%1+
____1/. "o< t"at tan (in%1) = + $ 1 , +2
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CHAPTER # 1
1. 9ri!onometric e@uation contain .. tri!onometric function.
2. 9ri!onometric functions are function.
&. If in + %= Cos + t"en t"e !eneral solution is
(a) n > $ 5 2n > ) are
(a) > $ & 2> $ & (b) > $ > $ &
(c) > $ & - > $ & (d) None of t"ese
-. eneral solution of t"e e@uation 1 5 Cos + = / is
(a) : >$2 5 2n>; (b) :% >$2 5 2n>;
(c) :> 5 2n>; (d) None of t"ese
. olution of t"e e@uation 1 5 Cos + = / is
(a) >$2 (b) > (c) 2 > (d) None of t"ese
4. Cos + = "as solution
(a) >$2 (b) >$& (c) >$ (d) >$
6. 9"e solution set of tan 2+ = 1 in (/ >) is
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(a) :>$6 ->$6; (b) : >$ ->$;
(c) : >$ &>$; (d) None of t"ese
8. 9"e solution set of sec + = % 2 in (/ >) is(a) 2>$& >& (b) >$& 2>$&
(c) >$& >$& (d) None of t"ese
1/. 9"e solution set of sin + = / is
(a) 2n> n D 3 (b) n > n D 3
(c) 2n> n D (d) None of t"ese
11. 9"e solution of tan2 + = & ) is
(a) >$& ->$& (b) >$& 2>$&
(c) >$& >$& (d) None of t"ese
12. If tan (+$2) = & and + lies in (/ 2>) t"en + is e@ual to
(a) / and + (b) >$& and ->$&
(c) >$ and ->$ (d) None of t"ese
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SHORT QUESTION
1. Bind t"e solution of t"e follo
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CHAPTER # 1
ANSWERS '
1. b2. c&. d. c-. c. b4. a6. b8. c1/. a11. b12. a1&. c
1. c
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CHAPTER # 2
ANSWERS '
1. c2. c&. d
. a-. b. c4. a6. c8. a1/. a11. b12. a1&. a1. b1-. a1. c14. a16. b18. a2/. c
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CHAPTER # 3
ANSWERS '
1. d2. c&. d. a-. a. a4. b6. c8. c1/. a11. b12. a
1&. c
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CHAPTER #
ANSWERS '
1. b2. a&. b
. c-. b. a4. c6. b8. d1/. b11. c12. c1&. d
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CHAPTER # !
ANSWERS '
1. d2. c&. a. b-. a. b4. b6. b8. c1/. a
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CHAPTER # "
As*+s '
1. a2. b&. a. d
-. c. b4. b6. b8. b1/.a11.c12.d1&.c
1.a1-.c1.d14.c16.b18.a2/.d21.b22.a2&.c
2.a2-.b2.a24.c26.d
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CHAPTER #
As*+s '
1. b2. a&. a. a
-. b. c4. a6. c8. b1/. d11. b12. c1&. d
1. a1-. a1. b14. c16. a18. c2/. d21. c22. d2&. a
2. d2-. d2. b24. a26. a28. a&/. d
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&1. a&2. a&&. b&. b
&-. c CHAPTER #
As*+s'
1. a2. b&. d. b-. c. d4. a6. c8. a1/. b11. d
12. d1&. c1. d1-. c1. d14. d16. c18. c2/. a
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CHAPTER # $
As*+ '
1. c2. b&. d
. b-. a. c4. b6. c8. a1/. b11. c12. d1&. b1. a1-. c1. c14. b16. a18. d2/. c21. c22. b
2&. a2. c2-. b2. d24. a26. c28. b
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&/. b&1. d&2. a&&. a
&. d CHAPTER # 1%
ANSWERS '
1. a2. c&. b. a-. d. b4. c6. d8. d1/. b11. c12. b
1&. a1. d1-. b1. a14. d16. c18. a2/. b21. c
22. b2&. b2. d2-. b2. c24. c
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CHAPTER # 11
ANSWERS '
1. c2. a
&. d. d-. c. a4. b6. a8. a1/. b
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CHAPTER # 12
As*+s '
1. c2. b&. c. a-. a. a4. d6. d8. d1/. c11. a12. c
1&. b1. b1-. c1. a14. a16. b18. a2/. d21. b
22. c2&. c2. b2-. a2. c24. b26. c
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28. a&/. c
CHAPTER # 13
As*+s '
1. a2. a&. b. c
-. a. d4. c6. a8. c1/. c11. d12. a1&. b
1. a1-. b1. c14. b16. b18. b2/. a21. b
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CHAPTER # 1
As*+s '
1. a2. c&. c. a
-. c. b4. d6. a8. a1/. b11. d12. b
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