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7/18/2019 Math Set a Question and Solution in DU
http://slidepdf.com/reader/full/math-set-a-question-and-solution-in-du 1/6
1. If g(x) = thenb x
x
x
a x,
−+
− ?)
2( =
+ ba g
a)2
2
a
ab b)
22
4
ba
ab
− c)
2
4
b
ad)
22
2
ba
ab
−
Solution:
2. Find the square root of ( )312
1−+−
(a) )31(2
1i+± (b) )31(
2
1i+± (c) )31(
2
1−+± (d) )31(
2
1i−±
Solution:
3. If A =
−
−
−
311
122
11
and !=
−
−−
131
312
321
, then A!=?
(a)
−−
312
2"#
33
(b)
−
−−
11"$
1"#
#%1
(c)
− 312
%42
#31
(d)
−
−−
312
1"#
33
Solution:
&sing 'acuator e get,
A! =
−
−−
312
1"#
33
4. If n*4 = 14 (n+1)*3 , then n = ?
(a) $ (b) " (c) (d) a and c
7/18/2019 Math Set a Question and Solution in DU
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Solution:
)4)(3)(2(14)3)(2)(1( −−−=−−− nnnnnnn
#%1#2 =+−⇒ nn
))($( =−−⇒ nn
,$=⇒ n
#. -he 'oefficient of # x and 1# x are equa for the exansion of
1
3
22
+
x
p x , hat is the
ositi/e /aue of ?
(a)3
1(b) 3 (c)
3
1(d) 3
Solution:
%. -he 0idoint of the ine oining the oints A(1,2) and !(a,b) is (%,"), hat is the coordinate of
oint !?
(a) (1,%) (b) (11, 1%) (c) (11,+1%) (d) (+1, +%)
oution
%2
1=
+ a"
2
2=
+ b
11=⇒ a 1%=⇒ b
)%,11(=∴ B
$. Find the equation of a circe assing through the oint (1, +2) and has center at (",4).
(a) 3122 =−−−+ y x y x (b) 3122 =−−−+ y x y x
(c) 122 =−−+ y x y x (d) "22 =+ y x
Solution:
-he circe assing through the oint (1,+2) i satisf the equation of circe.
7/18/2019 Math Set a Question and Solution in DU
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. A force of # 0agnitude is acting in east direction5 another 2 force is acting at %2
o
incination to east direction. 6hat is the ange beteen the resutant and # force?
(a) .11% (b) .21 (c) .
32 (d) .#1%
Solution:
". 13
#=θ Sin
and
∠∠θ
2 . ?
)(coscot
)sec(tan=
−+
−+
θ θ
θ θ
ec
(a)1
3− (b)
3
1− (c)
2##
11 (d)
1
3
Solution: use cacuator for required /aues.
1. ?cos
3
i0 =+→ X SinX
x7
(a) (b) 3 (c) 4 (d) 2
Solution:
11. If θ θ 3,cos Sin y x == then ?
2
2
=dx
yd
(a) θ 2cos3− (b)θ
θ
sin
2cos3 (c) θ 2sin
2
3− (d) none of these
Solution:
7/18/2019 Math Set a Question and Solution in DU
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12. ∫ =−1
2?)1( dx x x
(a) 1 (b) (c)3
1 (d) +1
Solution:
13. 6hat is the soution of ?)( 44=− ya D (89 %4)
(a) = )sincos( 4321 axcaxcecec axax +++ −
(b) =ax xaxax ecececec sin
#
cos
421 ( +++ −
)
(c) = xa xaecec
22
21
−+
(d) one of these
Solution:
Auxiiar equation : 44 =− a D
( )22 a D +⇒ ( ) 22 =− a D
aia D ±±=⇒ ,
( )axcaxcecec y axax
sincos, 432 +++=∴ −
14. If .$12 ≤+ x hich one is correct?
(a) 34 ≤≤− x (b) 2≤ x (c) ## ≤≤− x (d) none of these
Solution:
( ) $12$ ≤+≤− x
1$21$ −≤≤−−⇒ x
%2 ≤≤−⇒ x
34 ≤≤−⇒ x
1#. 6hat is the correct binar con/ersion of 4%?
(a) 111111 (b) 111111 (c) 111111 (d) 1111111
7/18/2019 Math Set a Question and Solution in DU
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Solution:
&sing scientific cacuator (4%)1= (111111)2
1%. 9quations of robabiit for e/ents A and ! are reated b ( ) ,3
1=∩ B A P ,
%
#)( =∪ B A P
,2
1)( = A P then ?)( = B P
(a)3
2 (b)
#
2 (c)
$
2 (d)
"
2
Solution:
( ) )()()( B A P B P A P B A P ∩−+=∪
3
1)(
2
1
%
#−+=⇒ B P
3
2
%
4
%
23#
3
1
2
1
%
#)( ==+−=+−=⇒ B P
1$. ∫ =+
?)2sin1( θ θ d
2
(a) 12−
(b) 1+
2
(c)
2
(d)
2
3
Solution:
using cacuated e get, I = 12
#$" −=⋅
o, Anser is (a).
1. For hat /aue of ;a<, tangent dran at (,) oint on the cur/e )1( xax y −= i 0ae an
ange % ith x+axis
(a) 2
1
(b) 2
3
(c) 3 (d) 2
1
Solution:
axaaxaxdx
d
dx
dy2)(
2 −=−=
7/18/2019 Math Set a Question and Solution in DU
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at (,) ointdx
dy = a+2a. = a
soe = tan% 3=
According to question, a = 3
Ans: (c)
1". If ( ) x
a x x f += 2
has 0ini0u0 /aue at 2= x oint, then a=?
(a) (b) 1 (c) 1% (d) none of these.
Solution:
For 0ini0u0 /aue,
=dx
dy
3
2
2
2
2
2
xa
x x
a
x
a x
=⇒
=⇒
=−⇒
at 2= x int, po 1%22 3 =×=a
2. 8o0ain of tangent function is?
(a) R ( )
∈+− N nn Rb
212)( [ ]1,1)( −− Rc (d) R+(+1,1)
Solution:
tangent function is undefined at2
and odd 0utie of
2
>ence, do0ain is R
+ ( )
∈+ N nn
212