UPSEE 2019 Paper 5

 PAPER-5 àíZnwpñVH$m H«$‘m§H$ àíZnwpñVH$m H$moS>
Question Booklet Sr. No.
AZwH«$‘m§H$ / Roll No.
AA
Q. Booklet Code

CÎma-erQ> H«$‘m§H$ / OMR Answer Sheet No.

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 
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No. of Pages in Booklet including title
24 Time 2 Hours 400 No. of Questions in Booklet
100

PAPER-5 àíZnwpñVH$m H«$‘m§H$/ Question Booklet Sr. No.

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àíZnwpñVH$m H$moS>
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Q. Booklet Code
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PAPER-5
[Aptitude Test for Lateral Entry in Engineering (BSc) / MCA]
Mathematics : Q. 1 to Q. 75
Computer Concepts : Q. 76 to Q. 100

PAPER 5 (MATHEMATICS)

001. The distance between the points of 001. aoImy =- x + 7 Am¡a nadb¶
y = ^ x - 1 h^ x - 2 h Ho$ à{VÀN>oX
intersection of the line y =- x + 7 and the 1
2
parabola y = ^ x - 1 h^ x - 2 h is
1
2 {~ÝXþAm| Ho$ ~rM H$s Xÿar h¡
(A) 2 (B) 3 2 (A) 2 (B) 3 2
(C) 5 2 (D) 7 2 (C) 5 2 (D) 7 2

002. If the parabola 002. ¶{X nadb¶ (parabola) y =- 12 x 2 + 3x + 10
1 EH$ nadb¶ y =- x 2 - x + k, H$mo ñne© H$aVm
y =- x 2 + 3x + 10 touches the parabola
2
y =- x 2 - x + k, then the value of k is h¡, V~ k H$m ‘mZ h¡
(A) 0 (B) 1 (A) 0 (B) 1

(C) 2 (D) 3 (C) 2 (D) 3

5-AA ] [2] [ Contd...

003. If f (x) =
x-1
, then the domain of 003. ¶{X f (x) = xx - 1
, V~ ^ f % f h (x) H$m àm§V
x+1 +1
^ f % f h (x) is (domain) h¡
(A) " x ! R x ! - 1} (A) " x ! R x ! - 1}
(B) " x ! R x ! 0} (B) " x ! R x ! 0}
(C) " x ! R x ! 0, - 1} (C) " x ! R x ! 0, - 1}
(D) " x ! R x ! 0, - 1, 1} (D) " x ! R x ! 0, - 1, 1}

004. Let f (x) = x + 2, x ! R and 004. ‘mZm {H$ f (x) = x + 2, x ! R Am¡a
h (x) = 3x - 1, x ! R . If g is a function such h (x) = 3x - 1, x ! R . ¶{X g EH$ Eogm ’$bZ h¡
that g % f = h , then Vm{H$, g % f = h , V~
(A) g(x) = 3x - 6 (B) g(x) = 3x - 7 (A) g(x) = 3x - 6 (B) g(x) = 3x - 7
(C) g(x) = 3x - 8 (D) g(x) = 3x - 9 (C) g(x) = 3x - 8 (D) g(x) = 3x - 9

1 1
005. If x = 3 + 2 2 then the value of x- 005. ¶{X x = 3 + 2 2 V~ x- H$m ‘mZ h¡&
x x
is
(A) 2 (B) - 2 (A) 2 (B) - 2
(C) 2 (D) – 1 (C) 2 (D) – 1

1-i i
006. Let z1 = 1 + i, z2 =
2
, z3 = 2 - i 006. ‘mZm {H$ z1 = 1 + i, z2 = 1 -
2
, z3 = 2 - i
z1 + z2 z +z
The imaginary part of
2z1 + 2z2 + z3
is V~ 2z +1 2z 2+ z H$m H$mën{ZH$ ^mJ h¡
1 2 3
1 1 1 1
(A) (B) (A) (B)
10 5 10 5
3 2 3 2
(C) (D) (C) (D)
10 5 10 5

007. The modulus of 3 - 4i is 007. 3 - 4i H$m ‘mnm§H$ (modulus) h¡
(A) 2 (B) 3 (A) 2 (B) 3
(C) 2 (D) 5 (C) 2 (D) 5

008. Let z = x + iy be a complex number. The 008. $‘mZm {H$ z = x + iy $EH$ gpå‘l g§»¶m (complex
equation z - i = z - 3 represents number) $h¡& g‘rH$aU z - i = z - 3 ${Zé{nV
H$amVr h¡&
(A) y = 4x + 3 (B) y = 4x - 3 (A) y = 4x + 3 (B) y = 4x - 3
(C) y = 3x + 4 (D) y = 3x - 4 (C) y = 3x + 4 (D) y = 3x - 4

5-AA ] [3] [ P.T.O.

009. The complex roots of x 3 + 1 = 0 are 009. x 3 + 1 = 0 $Ho$ gpå‘l ‘yb h¡
1 3 3 3 3
(A) !i (B) -1 !i (A)
1
!i (B) -1 !i
2 2 2 2 2 2 2 2
3 1 3 1 3 1 3 1
(C) !i (D) - !i (C) !i (D) - !i
2 2 2 2 2 2 2 2

010. Let P, Q be n × n matrices. Let O and I be 010. ‘mZm {H$ n × n Amì¶yh (matrix) P, Q h¢& ‘mZ
the zero and identity matrices of order n {H$ O Am¡a I H«$‘e… eyݶ Amì¶yh (zero matrix)
respectively. Suppose P – Q = I and PQ = O. VWm VËg‘H$ (identity matrix) h¢& ‘mZm {H$
P – Q = I Am¡a PQ = O. V~ {ZåZ {dH$ënm| ‘| go
Then which of the following options is
always CORRECT? H$m¡Zgm gX¡d g˶ h¡?
(A) P 3 + Q 3 = O (B) P3 + Q3 = I (A) P 3 + Q 3 = O (B) P3 + Q3 = I
(C) P 3 - Q 3 = O (D) P3 - Q3 = I (C) P 3 - Q 3 = O (D) P3 - Q3 = I

011. Let P be a 2 × 2 matrix such that 011. ‘mZm {H$ P EH$$ 2 × 2 Eogm Amì¶yh (matrix) h¡
P ; 0 E =-
1 ;1 E
and P ;1 E = ; 1 E
1 0 1 -1
2 1 2 Vm{H$ P ;10 E =- 1 ;11 E and P ;10 E = 12 ;-11 E
2
If O and I denote the zero and identity ¶{X O Am¡a I H«$‘e… H$mo{Q> (order) Ho$ eyݶ Amì¶yh
matrices of order 2 respectively, then which (zero matrix) VWm VËg‘H$ (identity matrix) h¢,
of the following options is CORRECT? V~ {ZåZ {dH$ënm| ‘| go H$m¡Z gm g˶ h¡?
(A) P 3 - P 2 - P = I (A) P 3 - P 2 - P = I
(B) P 3 - P 2 - P = O (B) P 3 - P 2 - P = O
(C) P 3 + P 2 - P = I (C) P 3 + P 2 - P = I
(D) P 3 + P 2 - P = O (D) P 3 + P 2 - P = O

012. Let a, b, c be real numbers such that b ≠ 0 and 012. ‘mZm {H$ a, b, c Eogr dmñV{dH$ g§»¶mE± h¡ Vm{H$
c ≠ 0. Suppose P = ; c 0 E and P -1 = P Then b ≠ 0 Am¡a c ≠ 0. ‘mZm {H$ P = ; c 0 E Am¡a
a b a b

(A) a = 0 and bc = 1 P -1 = P V~
(B) a ≠ 0 and bc = 1 (A) a = 0 Am¡a bc = 1
(C) a = 0 and bc = 2 (B) a ≠ 0 Am¡a bc = 1
(D) a = 0 and bc = –1 (C) a = 0 Am¡a bc = 2
(D) a = 0 Am¡a bc = –1

5-AA ] [4] [ Contd...

013. Let A & B be two n × n invertible matrices. 013. ‘mZm {H$ A & B Xmo n × n ì¶wËH«$‘ Amì¶yh
Which of the following options is always (invertible matrix) h¢& {ZåZ {dH$ënm| ‘| go H$m¡Z
correct ? gm gX¡d g˶ h¡?
(A) det ^ A + B h = det A + det B (A) det ^ A + B h = det A + det B
(B) det ^ AB h = det ^ BA h (B) det ^ AB h = det ^ BA h
(C) det ^ AB h = det (B -1) det (A -1) (C) det ^ AB h = det (B -1) det (A -1)
(D) det ^ mA h = m det ^ A h, m (D) det ^ mA h = m det ^ A h, m EH$ dmñV{dH$
is a real number g§»¶m h¡

014. The number of real solutions of the equation 014. g‘rH$aU 9 + 8 2x - 2 = 5 Ho$ dmñV{dH$
9 + 8 2x - 2 = 5 is ‘ybm| H$s g§»¶m h¡
(A) 0 (B) 1 (A) 0 (B) 1
(C) 2 (D) 3 (C) 2 (D) 3

x + x-1 = +
015. If a, b are the roots of
x-2 2
x 1, 015. ¶{X a, b x -x 2 + x -2 1 = x + 1, Ho$ ‘yb h¢ V~
then the equation with roots a , b is a , b ‘ybm| dmbr g‘rH$aU h¡
2
(A) x - 3x + 2 = 0 (A) x 2 - 3x + 2 = 0
(B) x 2 - 4x + 3 = 0 (B) x 2 - 4x + 3 = 0
(C) x 2 - 5x + 6 = 0 (C) x 2 - 5x + 6 = 0
(D) x 2 - 6x + 8 = 0 (D) x 2 - 6x + 8 = 0

x+2 + 3 = x+2 + 3 =
016. Sum of the roots of
4 x-1
7 is 016. 7 Ho$ ‘ybm| H$m ¶moJ h¡
4 x-1
(A) 26 (B) 27 (A) 26 (B) 27
(C) 28 (D) 29 (C) 28 (D) 29

017. Let a1, a2, a3, ..... be in arithmetic progression 017. ‘mZm {H$ EH$ g‘m§Va loUr
a1, a2, a3, .....
such that its 1st, 10th, and 22th terms are (arithmetic progression) ‘| Bg Vah go h¢ {H$
consecutive terms of some geometric BgH$s nhbo, Xgd| Am¡a ~mB©gd| nX {H$gr JwUmoÎma
progression. The common ratio of the loUr (geometric progression) Ho$ nX h¢& JwUmoÎma
geometric progression is loUr H$m gmd© AZwnmV (common ratio) h¡
4 5 4 5
(A) (B) (A) (B)
3 3 3 3
(C) 2 (D) 3 (C) 2 (D) 3

5-AA ] [5] [ P.T.O.

018. Let a1, a2, a3, ..... be in arithmetic progression 018. ‘mZm {H a1, a2, a3, ..... EH$ g‘m§Va loUr
such that a4 + a8 + a12 + a16 = 224 . The (arithmetic progression) ‘| Bg Vah go h¢ Vm{H$
sum of the first 19 terms of the arithmetic a4 + a8 + a12 + a16 = 224 . g‘m§Va loUr Ho$ nhbo
progression is 19 nXm| H$m ¶moJ h¡
(A) 1058 (B) 1060 (A) 1058 (B) 1060
(C) 1062 (D) 1064 (C) 1062 (D) 1064

019. Let a1, a2, a3, ..... be in arithmetic progression 019. ‘mZm {H a1, a2, a3, ..... EH$ g‘m§Va loUr ‘| h¢
{OgH$m gmd© A§Va (common difference) Aeyݶ
with nonzero common difference. It is given
13
(non zero) h¡& {X¶m J¶m h¡ {H$
that / ai = 88 and ak = 8 for some k. Then 13
/ ai = 88 Am¡a {H$gr k Ho$ {bE ak = 8 V~ k
i=3
i=3
the value of k is H$m ‘mZ h¡
(A) 5 (B) 6 (A) 5 (B) 6
(C) 7 (D) 8 (C) 7 (D) 8

x
020. It is given that 020. {X¶m J¶m h¡ {H$ xlim
"0
ae - bx - a =
2 . V~
x2
lim ae x - bx - a =
x"0 2 . The value of a + b a + b H$m ‘mZ h¡
x2
is
(A) 4 (B) 6 (A) 4 (B) 6

(C) 8 (D) 10 (C) 8 (D) 10

021. The sum of intercepts on the axes of the 021. dH«$ x + y = 2 H$s (1, 1) na ñne©aoIm
tangent to the curve x + y = 2 at (1, 1) (tangent) Ho$ Ajm| (axes) na A§V:I§S>
is (intercepts) H$m ¶moJ h¡
(A) 1 (B) 2 (A) 1 (B) 2
(C) 3 (D) 4 (C) 3 (D) 4

022. If the function 022. ¶{X ’$bZ

f (x) = * ax - bx + 3; if 2 # x < 3 f (x) = * ax - bx + 3; if 2 # x < 3
x + 2; if x < 2 x + 2; if x < 2
2 2

2x - a + b; if x $ 3 2x - a + b; if x $ 3
is continuous, then the value of (a + b) is g§VV (continuous) h¡, V~ (a + b) H$m ‘mZ h¡
(A) 0 (B) 1 (A) 0 (B) 1
(C) 2 (D) 3 (C) 2 (D) 3

5-AA ] [6] [ Contd...

023. If the function 023. ¶{X ’$bZ
f (x) = ) 2 f (x) = )
x + 1; x # c x + 1; x # c
x , x > c is continuous then the x 2, x > c g§VV (continuous) h¡,
possible values of c are V~ c Ho$ gå^m{dV ‘mZ h¢
1! 2 1! 3 1! 2 1! 3
(A) (B) (A) (B)
2 2 2 2
1! 5 1! 6 1! 5 1! 6
(C) (D) (C) (D)
2 2 2 2

024. Suppose f is differentiable function such that 024. ‘mZm {H$ f EH$ Eogm AdH$bZr¶ ’$bZ h¡ {H$ f (g
f (g (x)) = x and f ' (x) = 1 + (f (x))2. The value (x)) = x Am¡a f ' (x) = 1 + (f (x))2. V~ g'(1) H$m
of g'(1) is ‘mZ h¡
1 1 1 1
(A) (B) (A) (B)
2 3 2 3
1 1 1 1
(C) (D) (C) (D)
4 5 4 5

If the function f (x) = ) ¶{X ’$bZ f (x) = ) ax
ax 2 + b; if x # 2 2
+ b; if x # 2
025.
4x - 4, if x > 2
is 025.
4x - 4, if x > 2
g~ OJh
differentiable everywhere then the value of AdH$bZr¶ h¡, V~ ^ a + b hH$m ‘mZ h¡
^ a + b h is
(A) 0 (B) 1 (A) 0 (B) 1

(C) 2 (D) 3 (C) 2 (D) 3

026. Let f be a differentiable function with 026. ‘mZm {H f ‘mZm {H$ EH$ AdH$bZr¶ ’$bZ h¡
f (0) = 1, f l(0) = 1 ,and f (a + b) = f (a) f (b), VWm f (0) = 1, f l(0) = 1 h¡ Am¡a g^r dmñV{dH$
for all real numbers a & b. Which of the g§»¶mAm| a & b Ho$ {bE f (a + b) = f (a) f (b), h¡&
following options is correct? V~ {ZåZ {dH$ënm| ‘| go H$m¡Z gm g˶ h¡?
(A) f (x) - f l(x) = 0 (A) f (x) - f l(x) = 0
(B) f l(x) f (x) = 1 (B) f l(x) f (x) = 1
(C) 2f (x) - f l(x) = 1 (C) 2f (x) - f l(x) = 1
(D) 3f (x) - f l(x) = 2 (D) 3f (x) - f l(x) = 2

027. For which of the following values of k does 027. k Ho$ {ZåZ{bpIV ‘| go {H$g ‘mZ Ho$ {bE g‘rH$aU
the equation loge x = kx 2, k 2 0 have exactly loge x = kx 2, k 2 0 H$m Ho$db hr EH$ hb
one solution? h¡?
1 1 1 1
(A) (B) (A) (B)
e 2e e 2e
2 3 2 3
(C) (D) (C) (D)
e e e e

5-AA ] [7] [ P.T.O.

028. The area bounded by the graphs of functions 028. ’$bZ f (x) = x 2 + 2x Am¡a g (x) = x + 2 Ho$
f (x) = x 2 + 2x and g (x) = x + 2 is AmboIm| go {Kam joÌ’$b h¡
(A) 3/2 (B) 5/2 (A) 3/2 (B) 5/2
(C) 7/2 (D) 9/2 (C) 7/2 (D) 9/2

029. If the lines y = b divides the region bounded 029. ¶{X aoIm y = b dH«$m| (curves) y = 4 - x 2 Am¡a
by the curves y = 4 - x 2 and y = 0 into y = 0 go {Kao hþE joÌ (region) H$mo g‘mZ joÌ’$b
regions of equal area, then the value of b (area) dmbo joÌ ‘| {d^m{OV H$amVr h¡ V~ b H$m
is........ ‘mZ h¡
(A) ^ 2 - 3 2 h (B) 2 ^ 2 - 3 2 h (A) ^ 2 - 3 2 h (B) 2^ 2 - 3 2 h
(C) 3 ^ 2 - 3 2 h (D) 4 ^ 2 - 3 2 h (C) 3 ^ 2 - 3 2 h (D) 4^ 2 - 3 2 h

030. If [y] denotes the greatest integer less than or 030. ¶{X y ! R , y go H$‘ ¶m ~am~a ‘hÎm‘ nyUmªH$
equal to y for all y ! R , then the value of the J«hU H$aZo dmbo ’$bZ H$mo [y] go {Zé{nV {H$¶m J¶m
8 8

integral 6 x @ dx is
w hmo Vmo g‘mH$bZ (integral) w 6 x @ dx H$m ‘mZ h¡
0 0
(A) 8 (B) 9 (A) 8 (B) 9
(C) 10 (D) 11 (C) 10 (D) 11

r 2 r 2
dx dx
031. The value of w x3is 031. w x3H$m ‘mZ h¡
-r 2
e + 1 -r 2
e +1
r r
(A) (B) π (A) (B) π
2 2
(C) 0 (D) 1 (C) 0 (D) 1
2r 3 2r 3
2r 3 2r 3
032. If . = we sin x
dx then w x e sin x dx is 032. ¶{X . = w e sin x
dx V~ w x e sin x dx
r 3 r 3
r r
~am~a h¡ r 3 r 3

(A) . (B) . r r
2 3 (A) . (B) .
2 3
2r
(C) . (D) r. 2r
3 (C) . (D) r.
3
033. If [y] denotes the greatest integer less than or 033. ¶{X y ! R , go H$‘ ¶m y Ho$ ~am~a ‘hÎm‘ nyUmªH$
equal to y for all y ! R , then the value of the J«hU H$aZo dmbo ’$bZ H$mo [y] go {Zé{nV {H$¶m J¶m
3r 2
hmo Vmo g‘mH$bZ (integral) integral
integral w [sin x] dx is 3r 2

-r
r 2
r
w [sin x] dx H$m ‘mZ h¡
(A) (B) r 2
2 2 -r r
(A) (B)
(C) 0 (D) π 2 2
(C) 0 (D) π

5-AA ] [8] [ Contd...

034. If the solution of the differential equation 034. ¶{X AdH$b g‘rH$aU (differential equation)
dy 2x
dy 2x
+ = kx , represents a family of circles + = kx , H$m hb d¥Îmm| Ho$ Hw$b (family of
dx y y dx y y
circles) {OZH$m H|$Ð (0, 0) na h¡ H$mo {Zé{nV H$aVm
with centers at (0, 0), then the value of k is
h¡, V~ k H$m ‘mZ h¡
(A) 0 (B) 1 (A) 0 (B) 1
(C) 2 (D) 3 (C) 2 (D) 3

035. The solution of the differential equation 035. AdH$b g‘rH$aU (differential equation)
dy
^ y2 - x2h
dy
+ 2xy = 0 represents the family ^ y2 - x2h + 2xy = 0 H$m hb CZ dH«$m| Ho$ Hw$b
dx dx
(family of curves) H$mo {Zé{nV H$aVm h¡ {OZH$s
of curves given by the equation g‘rH$aU Xr OmVr h¡
(A) x 2 + y 2 = k 2 (A) x 2 + y 2 = k 2
(B) x 2 + ^ y - k h2 = k 2 (B) x 2 + ^ y - k h2 = k 2
(C) (x - k) 2 + (y - k) 2 = k 2 (C) (x - k) 2 + (y - k) 2 = k 2
(D) ^ x - k h2 + y 2 = k 2 (D) ^ x - k h2 + y 2 = k 2

036. A curve is drawn such that the slope at a 036. EH$ dH«$ Bg Vah ItMm OmVm h¡ {H$ EH$ q~Xþ
point P ^ x, y h is equal to x. Then the curve P ^ x, y h na {OgH$s T>mb x Ho$ ~am~a h¡& V~ dH«$
represents a family of {H$g Hw$b H$mo {Zé{nV H$aVm h¡
(A) circles (A) d¥Îm (circles)
(B) parabolas (B) nadb¶ (parabolas)
(C) ellipses (C) XrK©d¥Îm (ellipses)
(D) hyperbolas (D) A{Vnadb¶ (hyperbolas)

dy dy
037. If y (x) satisfies x
dx
+ x + y = 0, y (1) = 1, 037. ¶{X y (x) x dx + x + y = 0, y (1) = 1, H$mo
then y (2) is g§Vwï> H$aVm h¡ y (2) V~ h¡
(A) 0 (B) -1 (A) 0 (B) -1
4 4
3 3
(C) - (D) -e (C) - (D) -e
4 4

038. Area of the triangle formed by 9x 2 - 4y 2 = 0 038. 9x 2 - 4y 2 = 0 Am¡a x = 2 go ~Zo {Ì^wO H$m
and x = 2 is joÌ’$b h¡
(A) 3 (B) 6 (A) 3 (B) 6
(C) 9 (D) 12 (C) 9 (D) 12

5-AA ] [9] [ P.T.O.

039. If ax 2 + 2hxy + by 2 + 2gx + 2fy + c = 0 039. ¶{X ax 2 + 2hxy + by 2 + 2gx + 2fy + c = 0
represents two parallel straight lines then Xmo g‘mZm§Va gab aoImAm| H$mo {Zé{nV H$aVr h¡ V~
which of the following statements is always {ZåZ {dH$ënm| ‘| go H$m¡Z gm gX¡d g˶ h¡? (g^r
TRUE? (all coefficients are assumed to be JwUm§H$ Aeyݶ ‘mZo {bE JE h¢)
non-zero)
(A) g 2 = ab, ah 2 = bf 2 (A) g 2 = ab, ah 2 = bf 2
(B) f 2 = hg, c 2 = ab (B) f 2 = hg, c 2 = ab
(C) h 2 = ab, bg 2 = af 2 (C) h 2 = ab, bg 2 = af 2
(D) h 2 = ab, b 2 g = a 2 f (D) h 2 = ab, b 2 g = a 2 f

040. The radius of the incircle of the triangle 040. aoIm 5x + 12y = 60 Am¡a {ZX}em§H$ Ajm|
formed by the line 5x + 12y = 60 and the (coordinate axes) go ~Zo {Ì^wO Ho$ A§V:d¥Îm
coordinate axes is (incircle) H$s {ÌÁ¶m h¡
(A) 1 (B) 2 (A) 1 (B) 2
(C) 3 (D) 4 (C) 3 (D) 4

041. Tangents are drawn from the point P(7,1) to 041. q~Xþ go P(7,1) d¥Îm (circle) x 2 + y 2 = 25 na
the circle x 2 + y 2 = 25 intersect y-axis at ñne© aoImE§ (tangents) ItMr J¶r h¢ Omo y-Aj
points Q and R respectively. The perimeter of H$mo H«$‘e… Q Am¡a R na H$Q>Vr h¢& {Ì^wO PQR H$s
the triangle PQR is n[a{Y h¡
(A) 25 (B) 30 (A) 25 (B) 30
(C) 35 (D) 40 (C) 35 (D) 40

042. A chord of the circle x 2 + y 2 = 9 has midpoint 042. d¥Îm x 2 + y 2 = 9 H$s EH$ Ordm H$m ‘ܶq~Xþ
(1, 2). The chord intersects x-axis and y-axis (midpoint) (1, 2) h¡. ¶h Ordm x-Aj Am¡a
y-Aj H$mo H«$‘e… q~Xþ P Am¡a Q na à{VÀN>oX
at P and Q respectively. If O denotes the
H$aVr h¡& ¶{X O ‘ybq~Xþ (origin) H$mo Xem©Vm h¡, Vmo
origin, then the area of the triangle OPQ is
{Ì^wO OPQ H$m joÌ’$b h¡
15 15
(A) 5 (B) (A) 5 (B)
2 2
25 25
(C) 10 (D) (C) 10 (D)
4 4

043. A tangent to the parabola y 2 = 2x at the point 043. q~Xþ P(2, 2) na nadb¶ y 2 = 2x H$s EH$ ñne©
P(2, 2) intersects x-axis at point Q. Then PQ aoIm (tangent) x-Aj H$mo q~Xþ Q na H$mQ>Vr h¡& V~
equals ~am~a h¡
(A) 5 (B) 2 5 (A) 5 (B) 2 5
(C) 3 5 (D) 4 5 (C) 3 5 (D) 4 5

5-AA ] [ 10 ] [ Contd...

044. The normal to the ellipse x 2 + 4y 2 = 8 at the 044. q~Xþ P(2, 1) na XrK©d¥Îm x 2 + 4y 2 = 8 H$m A{^b§~
point P(2, 1) intersects the ellipse at another (normal) XrK©d¥Îm H$mo EH$ Xÿgao q~Xþ Q na H$mQ>Vm
point Q. Then the coordinates of Q are h¡& V~ Q Ho$ {ZX}em§H$ h¢
(A) c 1,
7 m
(A) c 1,
7 m
(B) c 2, 3 m
(B) c 2, 3 m
2 2 2 2
(C) ` , -
25 j ` 14 , - 23 j (C) ` , -
12 12 25 j ` 14 , - 23 j
(D) (D)
17 17 17 17 17 17 17 17

045. The tangent to the hyperbola x 2 - 9y 2 = 9 045. q~Xþ ` 5, - 34 j na A{Vnadb¶ x 2 - 9y 2 = 9 H$s
at the point ` 5, - j intersects the line
4
3 EH$ ñne© aoIm (tangent), aoIm 6x - 3y = 5 H$mo
6x - 3y = 5 at the point P. Then the
coordinates of P are q~Xþ P na H$mQ>Vr h¡& V~ P Ho$ {ZX}em§H$ h¢
(A) `1,
1j ` 5 ,0 j
(A) `1, j (B) ` , 0 j
1 5 (B)
3 6 3 6

(C) ` , 1 j (D) ` , j (C) ` , 1 j ` 7, 2 j
4 7 2 4
(D)
3 6 3 3 6 3
2
x2 + y =
046. The tangents at points (3, 0) and (0, 2) to the 046. XrK©d¥Îm 9 4
1 Ho$ q~Xþ (3, 0) Am¡a (0, 2)
2
x + y =
2
na ItMr J¶r ñne© aoImAm| (tangents) H$m Am§V[aH$
ellipse 1 have an internal angle
9 4 H$moU (internal angle) h¡
(A) 30° (B) 45° (A) 30° (B) 45°
(C) 60° (D) 90° (C) 60° (D) 90°

047. The volume of the parallelepiped whose 047. EH$ g‘mÝVafQ>’$bH$ (parallelepiped) {OgHo$ {H$Zmao
edges are represented by the vectors (edges) g{Xe a = 2it - 3tj + 4kt, b = it + 2tj - kt
a = 2it - 3tj + 4kt, b = it + 2tj - kt ,and Am¡a c = 3it - tj + 2mkt go {Zé{nV {H$¶o JE h¢ H$m
c = 3it - tj + 2mkt is 7 units. The possible Am¶VZ (volume) 7 BH$mB© (units) h¡& V~ ‘m’ Ho$
values of ‘m’ are g§^m{dV ‘mZ h¢
(A) 1 & –1 (B) 1&2 (A) 1 & –1 (B) 1&2
(C) 2 & 4 (D) 3 & 5 (C) 2 & 4 (D) 3 & 5

048. Let a be a unit vector. Then the value of 048. ‘mZm {H a EH$ EH$H$ g{Xe (unit vector) h¡&
it # (a # it) + tj # (a # tj) + kt # (a # kt) is equal V~ it # (a # it) + tj # (a # tj) + kt # (a # kt) H$m
to ‘mZ ~am~a h¡
(A) 1 (B) 2 (A) 1 (B) 2
(C) 3 (D) 4 (C) 3 (D) 4

5-AA ] [ 11 ] [ P.T.O.

049. A unit vector a is parallel to yz plane 049. EH$ EH$H$ g{Xe (unit vector), a , yz-Vb Ho$
and perpendicular to it - 4tj + 3kt . Let g‘m§Va VWm it - 4tj + 3kt Ho$ bå~dV h¡& ‘mZm {H$ .
b = it + 2tj - kt Then a $ b equals b = it + 2tj - kt V~ a $ b ~am~a h¡
1 2 1 2
(A) (B) (A) (B)
2 3 2 3
2 3 2 3
(C) (D) (C) (D)
5 7 5 7

050. Which of the following statements is NOT 050. {ZåZ H$WZm| ‘| go H$m¡Z gm H$WZ g˶ Zht h¡
correct?
(A) ¶{X a Am¡a b EH$H$ g{Xe (unit vector)
(A) If a and b are unit vectors and θ
is the angle between them, then h¢ VWm CZHo$ ~rM H$m H$moU θ h¡, V~
i 1 i =1 -
sin = a - b sin a b
2 2 2 2
(B) If a + b = a - b then a and b are (B) ¶{X a + b = a - b V~ a Am¡a b bå~dV
perpendicular vectors.
g{Xe h¢
(C) a ×(b + c ) + b ×( c + a ) + c ×(a +b )=0
(C) a ×(b + c ) + b ×( c + a ) + c ×(a +b )=0
(D) If a ×b = c × d and a × c =b × d , then
the vectors a – d and b – c are (D) ¶{X a ×b = c × d Am¡a a × c =b × d , V~
perpendicular. g{Xe a – d Am¡a b – c bå~dV h¢

051. Let a , b , c be any three vectors. Then 051. ‘mZm {H a, b, c VrZ g{Xe h¢& V~
[a + b , b + c , c + a ] equals [a + b , b + c , c + a ] ~am~a h¡
(A) 2[ a , b , c ] (A) 2[ a , b , c ]
(B) [ a , b , c ] (B) [ a , b , c ]
(C) 1 (C) 1
(D) 0 (D) 0

052. Let a = 3it - 2tj + kt , b = it - 3tj + 5kt , and 052. ‘mZm {H a = 3it - 2tj + kt , b = it - 3tj + 5kt , Am¡a
c = 2it + tj - 4kt . Then the triangle formed by c = 2it + tj - 4kt . V~ g{Xe a , b , c Ûmam ~Zm
the vectors a , b , c is {Ì^wO h¡
(A) scalene (A) {df‘~mhþ (scalene)
(B) equilateral (B) g‘~mhþ (equilateral)
(C) isosceles but not right angled (C) g‘{Û~mhþ (isosceles) bo{H$Z g‘H$moU Zhr
(D) right angled (D) g‘H$moU (right angled)

5-AA ] [ 12 ] [ Contd...

053. The difference in the sums of coefficients 053. ^1 + x hn + 2 Ed§ ^1 + x hn Ho$ àgma ‘| JwUm§H$m| Ho$
in the expansion of ^1 + x hn 2 and ^1 + x hn
+
¶moJm| ‘| A§Va 768 h¡& V~ ^1 + x hn Ho$ àgma ‘| x5
is 768. Then the coefficient of x5 in the
H$m JwUm§H$ h¡
expansion of ^1 + x h is
n

(A) 56 (B) 84 (A) 56 (B) 84
(C) 7 (D) 210 (C) 7 (D) 210

054. The sum 054. ¶moJ’$b
^ C0 h
50 2+
2 # ^ 50 C1 h2 + 3 # ^ 50 C2 h2 + ... + 51 # ^ 50 C50 h2 ^ 50 C0 h2 + 2 # ^ 50 C1 h2 + 3 # ^ 50 C2 h2 + ... + 51 # ^ 50 C50 h2
equals ~am~a h¡
(A) 25 # 100 C50 (B) 26 # 100 C50 (A) 25 # 100 C50 (B) 26 # 100 C50
(C) 26 # 101 C50 (D) 25 # 101 C51 (C) 26 # 101 C50 (D) 25 # 101 C51

055. The sum 055. ¶moJ’$b
20 C 20 C 20 C 20 C 20 C 20 C 20 C 20 C
1 2 3 20 1 2 3 20
20 C + 2 # 20 C + 3 # 20 C + ... + 20 # 20 C 20 C + 2 # 20 C + 3 # 20 C + ... + 20 # 20 C
0 1 2 19 0 1 2 19
equals ~am~a h¡
(A) 840 (B) 630 (A) 840 (B) 630
(C) 420 (D) 210 (C) 420 (D) 210

056. Let A, B, C be independent events with 056. ‘mZm {H A, B, C ñdV§Ì KQ>ZmE± h¢ VWm
1 1 1
1 1
P (A) = , P (B) = , P (C) = .
1 P (A) = , P (B) = , P (C) =
2 3 4
h¡& V~
2 3 4
^ ^ h
Then P A - B , C is h P ^ ^ A - B h , C h h¡
2 3 2 3
(A) (B) (A) (B)
3 4 3 4
1 1 1 1
(C) (D) (C) (D)
3 2 3 2

057. Which of the following statement is NOT 057. {ZåZ H$WZm| ‘| go H$m¡Z gm H$WZ g˶ Zht h¡
TRUE?
(A) If A and B are independent events, then (A) ¶{X A Am¡a B ñdV§Ì KQ>ZmE± h¢ V~
P (A , B) = P (A) + P (B) - P (A + B) . P (A , B) = P (A) + P (B) - P (A + B)
(B) If A and B are mutually exclusive events,
(B) ¶{X A Am¡a B nañna AndOu KQ>ZmE± h¢, V~
then P (A - B) = P (A)
P (A - B) = P (A)
(C) If A and B are independent events
and P (A) 1 1 , then P (A - B) = (C) ¶{X A Am¡a B ñdV§Ì KQ>ZmE± h¢ VWm P (A) 1 1
P ( A) - P ( B) . V~ P (A - B) = P (A) - P (B)
(D) If 0 < P (B) < 1 , (D) ¶{X 0 < P (B) < 1 , V~
C
then P (A | B) + P (A | B) = 1 . P (A | B ) + P (A C | B ) = 1 .

5-AA ] [ 13 ] [ P.T.O.

058. Players P1 and P2 play a game against each 058. pIbm‹S>r P1 Am¡a P2 EH$ Xÿgao Ho$ pIbm’$ Iob
3
other and the probability that P1 will win is
5 IobVo h¢ Am¡a P1 Ho$ OrVZo H$s àm{¶H$Vm 53 h¡& do
They play five games. Then probability that nm§M Iob IobVo h¢& V~ P2 Ho$ A{YH$ go A{YH$ Xmo
P2 will win at most two games is Iob OrVZo H$s àm{¶H$Vm h¡
1349 1428 1349 1428
(A) (B) (A) (B)
3125 3125 3125 3125
1867 2133 1867 2133
(C) (D) (C) (D)
3125 3125 3125 3125

059. A room has two night lamps. A collection of 059. EH$ H$‘ao ‘| Xmo ZmBQ> b¢n h¢& 8 ~ë~m| Ho$ g§J«h ‘| 2
8 bulbs has 2 defective bulbs. Two bulbs are Iam~ ~ë~ h¢& Xmo ~ë~m| H$mo Bg g§J«h go ¶mÑpÀN>H$
selected at random from this collection and na MwZm J¶m h¡ Am¡a b¢n ‘| bJm¶m J¶m h¡& V~ XmoZm|
placed in lamps. Then the probability that b¡ånm| ‘| Iam~ ~ë~ bJmZo H$s àm{¶H$Vm h¡
both lamps get defective bulbs is
1 1
1 1 (A) (B)
(A) (B) 14 28
14 28
2 4
2 4 (C) (D)
(C) (D) 31 35
31 35

060. The coefficients a and b in the quadratic 060. {ÛKmV g‘rH$aU ax 2 + 4x + b = 0 Ho$ JwUm§H$ a
equation ax 2 + 4x + b = 0 are determined
Am¡a b ñdV§Ì ê$n go Xmo ~ma EH$ {Zînj nmgm ’|$H$H$a
by throwing an unbiased dice two times
{ZYm©[aV {H$E OmV| h¡& V~ g‘rH$aU Ho$ dmñV{dH$
independently. Then the probability that the
equation will have real and equal roots is Am¡a g‘mZ ‘yb hmoZo H$s àm{¶H$Vm h¡
1 1 1 1
(A) (B) (A) (B)
6 8 6 8
1 1 1 1
(C) (D) (C) (D)
12 16 12 16

061. An urn contains 4 white and 3 red balls. Two 061. EH$ H$be ‘| 4 g’o$X Am¡a 3 bmb J|X| h¢& H$be go
balls are drawn at random without replacement
à{VñWmnZ Ho$ {~Zm ¶mÑpÀN>H$ ê$n go Xmo J|X| {ZH$mbr
OmVr h¢& H$‘ go H$‘ EH$ Ho$ bmb hmoZo H$s àm{¶H$Vm
from the urn. Then the probability that at least
h¡
one is red is
3 4
3 4 (A) (B)
(A) (B) 7 7
7 7 5 6
5 6 (C) (D)
(C) (D) 7 7
7 7

5-AA ] [ 14 ] [ Contd...

062. The value of 062. ^ cos 75° - cos 15° h2 + ^ sin 75° - sin 15° h2
^ cos 75° - cos 15° h2 + ^ sin 75° - sin 15° h2 is
H$m ‘mZ kmV h¡
1 3 1 3
(A) (B) (A) (B)
2 4 2 4
7 7
(C) 1 (D) (C) 1 (D)
4 4

063. The sum of all solutions of the equations 063. g‘rH$aU 2^ cos 2 i - sin 2 i h = 1 Ho$ A§Vamb
2 ^ cos 2 i - sin 2 i h = 1 in the interval [0, π] is [0, π] ‘| g^r ‘ybm| H$m ¶moJ h¡
r r r r
(A) (B) (A) (B)
3 2 3 2
4r 4r
(C) π (D) (C) π (D)
3 3

064. In ΔABC, let + B=90° and AB=15, BC=20. 064. ΔABC, ‘| + B = 90° VWm AB = 15, BC =
20. h¡& ‘mZm {H$ B go AC na S>mbm J¶m bå~
Let the perpendicular from B on AC intersect
(perpendicular) BgH$mo D na à{VÀN>oX H$aVm h¡&
at D. Then the length of BD is
V~ BD H$s bå~mB© h¡
(A) 8 (B) 10 (A) 8 (B) 10
(C) 12 (D) 15 (C) 12 (D) 15

065. In ΔABC, let a = 13, b = 14 and c = 15. Then 065. ‘mZm {H$ ΔABC, ‘o§ a = 13, b = 14 Am¡a c = 15.
B
tan is
2 h¡& V~ tan B2 h¡
(A) 2/5 (B) 4/7 (A) 2/5 (B) 4/7
(C) 5/9 (D) 6/11 (C) 5/9 (D) 6/11

066. The number of solutions of the equation 066. g‘rH$aU sin i + sin 5i = sin 3i Ho$ A§Vamb
sin i + sin 5i = sin 3i in the interval 8 0, B
r
2 8 0, r B ‘| ‘ybm| H$s g§»¶m h¡
2
are
(A) 0 (B) 1 (A) 0 (B) 1
(C) 2 (D) 3 (C) 2 (D) 3

067. The largest angle of the triangle with sides 4, 067. {Ì^wO {OgH$s ^wOmE§ 4, 5, 6 h¢, H$m g~go ~‹S>m
5, 6 is H$moU h¡
(A) cos -1 `
3j
sin -1 `
3j
(A) cos -1 `
3j
sin -1 `
3j
(B) (B)
8 4 8 4

sin -1 `
1j
sin -1 `
1j
(C) cos -1 `
1j
(C) cos -1 `
1j
(D) (D)
8 4 8 4

5-AA ] [ 15 ] [ P.T.O.

068. The angles of elevation to the top of a tower 068. EH$ ‘rZma Ho$ nX go 100 ‘rQ>a H$s Xÿar na EH$ q~Xþ
from a point at 100 meter distance from the go CgH$s MmoQ>r H$m CÞ¶Z H$moU 60° h¡& Vmo ‘rZma H$s
foot of the tower is 60°. Then the height of D$±MmB© h¡
the tower is
(A) 25 3 (B) 50 3 (A) 25 3 (B) 50 3

(C) 75 3 (D) 100 3 (C) 75 3 (D) 100 3

tan -1 `
1 j+
tan -1 ` j H$m ‘mZ h¡
1
The value of tan -1 `
1 j+
tan -1 ` j is
1 069.
069. 2 3
2 3
r r r r
(A) (B) (A) (B)
4 3 4 3
2r r 2r r
(C) (D) (C) (D)
3 2 3 2

070. The distance (in meters) of a point travelling 070. EH$ gab aoIm ‘| MbZo dmbo {H$gr H$U (particle)
in a straight line after t seconds from a fixed H$s aoIm na {H$gr {Z¶V q~Xþ (fixed point) go
t goH§$S> ‘| Mbr Xÿar (‘rQ>a ‘|) s = 2t 4 - 3t 2 - 1
point is represented by s = 2t 4 - 3t 2 - 1 .
go {Zé{nV h¡& Xmo goH§$S> Ho$ ~mX H$U H$m ËdaU
The acceleration after 2 seconds is (acceleration) h¡
(A) 70 m/s2 (B) 80 m/s2 (A) 70 m/s2 (B) 80 m/s2
(C) 90 m/s2 (D) 100 m/s2 (C) 90 m/s2 (D) 100 m/s2

071. A ball falling from the top of a tower reaches 071. EH$ ‘rZma H$s MmoQ>r go EH$ J|X {dam‘mdñWm go {JaVr
earth in 20 seconds. The height of the tower hþB© àÏdr na 20 goH§$S> ‘| nhþ§MVr h¡& ‘rZma H$s$
is (assume g = 9.8 m/s2) D$§MmB© h¡ (‘mZm {H$ g = 9.8 m/s2 )
(A) 1960 meters (B) 2240 meters (A) 1960 meters (B) 2240 meters

(C) 2380 meters (D) 2460 meters (C) 2380 meters (D) 2460 meters

072. A ball is thrown vertically upwards. If it 072. EH$ J|X D$na H$s Amoa (vertically upwards) ’|$H$s
has the same height after 8 seconds and 12 OmVr h¡& ¶{X 8 Am¡a 12 goH§$S> Ho$ nümV² dh g‘mZ
seconds, then the initial velocity is D$§MmB© na h¡ Vmo J|X H$m àma§{^H$ doJ h¡
(assume g = 9.8 m/s2) (‘mZm {H$ g = 9.8 m/s2)
(A) 49 m/s (B) 98 m/s (A) 49 m/s (B) 98 m/s
(C) 147 m/s (D) 196 m/s (C) 147 m/s (D) 196 m/s

5-AA ] [ 16 ] [ Contd...

073. Let PQ be a uniform rod of length 120 cm. 073. ‘mZm {H PQ 120 cm ‘mZm {H$ b§~mB© H$m EH$
Two weights of masses 1 kg and 3 kg are g‘ê$n S§>S>m h¡& 1 {H$J«m Am¡a 3 {H$J«m Ho$ Xmo dµOZ
placed at a distance 10 cm from P and 40
H«$‘e… P go 10 go‘r Am¡a Q go 40 go‘r H$s Xÿar
cm from Q respectively. If x is the distance
na aIo OmVo h¢& ¶{X 2 {H$bmoJ«m‘ Ho$ Vrgao dµOZ H$s
(in cm) of the third weight of mass 2 kg from
P go Xÿar x cm h¡ Vm{H$ Bg ì¶dñWm H$m JwéËd H|$Ð
P so that the center of gravity of the system

is at the middle of the rod PQ, then the value
S§>S>o PQ Ho$ ‘ܶ ‘| hmo, Vmo x H$m ‘mZ h¡

of x is

(A) 50 (B) 55 (A) 50 (B) 55
(C) 60 (D) 65 (C) 60 (D) 65

074. Two forces of equal magnitude are acting at 074. Xmo g‘mZ n[a‘mU dmbo ~b EH$ q~Xþ na bJ aho h¢&
a point. If the square of the magnitude of the ¶{X n[aUm‘r ~b Ho$ n[a‘mU H$m dJ© CZHo$ n[a‘mU
resultant is three times of the product of their Ho$ JwUZ’$b H$m VrZ JwZm h¡ Vmo XmoZm| ~bm| Ho$ ~rM
magnitude then the angle between the two H$m H$moU h¡
forces is

(A) 150° (B) 120° (A) 150° (B) 120°
(C) 60° (D) 90° (C) 60° (D) 90°

075. Let one of the two forces acting on a particle
075. ‘mZm {H ‘mZm {H$ EH$ H$U na H$m‘ H$aZo dmbo Xmo
be double in magnitude than the other. If the
~bm| ‘| go EH$ Xÿgao H$s VwbZm ‘| n[a‘mU ‘| XmoJwZm
angle between the directions of the of the
h¡& ¶{X n[aUm‘r ~b Am¡a ~‹S>o ~b H$s {XemAm| Ho$
resultant and the greater force is 30°, then the
~rM H$m H$moU 30°, h¡, Vmo Xmo ~bm| Ho$ ~rM H$m H$moU
angle between the two forces is
h¡
(A) 30° (B) 60°
(A) 30° (B) 60°
(C) 90° (D) 120°
(C) 90° (D) 120°

5-AA ] [ 17 ] [ P.T.O.

PAPER 5 (COMPUTER CONCEPTS)

076. Collecting personal information and 076. ì`{º$JV OmZH$mar EH$Ì H$aZm Am¡a à^mdr T>§J go
effectively posing as another individual is Xygao ì`{º$ Ho$ ê$n ‘| àñVwV H$aZm AnamY Ho$ ê$n ‘|
known as the crime of: OmZm OmVm h¡:
(A) Spooling (B) Identity theft (A) ñnyqbµJ (B) AmBS|>{Q>Q>r WoµâQ>
(C) Spoofing (D) Hacking (C) ñnyqµ’$J (D) h¡qH$J

077. PARAM is an example of: 077. PARAM CXmhaU h¡ :
(A) Super computer (B) PC
(A) gwna H$åß`yQ>a (B) PC
(C) Laptop (D) PDA
(C) b¡nQ>mon (D) PDA

078. .......... are set of rules and procedures to 078. .......... B§Q>aZoQ> na So>Q>m Q´m§g{‘eZ H$mo {Z`§{ÌV H$aZo
control the data transmission over the internet Ho$ {bE {Z`‘m| Am¡a à{H«$`mAm| H$m goQ> h¡
(A) IP address (B) Domains (A) IP ES´og (B) S>mo‘oZ
(C) Protocol (D) Gateway (C) àmoQ>moH$m°b (D) JoQ>do

079. The following numbers are inserted into an 079. {XE JE H«$‘ ‘| {ZåZ{bpIV g§»`mAm| H$mo EH$ Imbr
empty binary search tree in the given order: ~mBZar gM© Q´r ‘| S>mbm J`m h¡: 10,1,3,5,15,12,16.
10,1,3,5,15,12,16. What is the height of Bg ~mBZar gM© Q´r H$s D$§MmB© Š`m hmoJr?
binary search tree?
(A) 3 (B) 4
(A) 3 (B) 4
(C) 5 (D) 6
(C) 5 (D) 6

080. Which one of the following is the most 080. {ZåZ{bpIV ‘| go H$m¡Z gm bm°{OH$ Bg dmŠ` H$m
appropriate logical formula to represent the à{V{Z{YËd H$aZo Ho$ {bE g~go Cn`wº$ h¡: ""Gold
statement? ‘‘Gold and silver ornaments are and silver ornaments are precious.’’
precious’’. The following notations are used: The following notations are used: G(x):
G(x): x is a gold ornament S(x): x is a silver x is a gold ornament, S(x): x is a silver
ornament P(x): x is precious ornament, P(x): x is precious
(A) 6x (P (x) → (G(x) / S(x))) (A) 6x (P (x) → (G(x) / S(x)))
(B) 6x ((G (x) / S(x)) → P(x)) (B) 6x ((G (x) / S(x)) → P(x))
(C) 7x ((G (x) / S(x)) → P(x)) (C) 7x ((G (x) / S(x)) → P(x))
(D) 6x ((G (x) 0 S(x)) → P(x)) (D) 6x ((G (x) 0 S(x)) → P(x))

5-AA ] [ 18 ] [ Contd...

081. The following postfix expression with single 081. ñQ>¡H$ H$m Cn`moJ H$aHo$ EH$b A§H$m| Ho$ Am°na|S> Ho$
digit operands is evaluated using a stack: gmW {ZåZ{bpIV nmoñQ>{’$Šg EŠgàoeZ H$m ‘yë`m§H$Z
823^/23*+51*–
H$[a`o: 8 2 3 ^ / 2 3 * + 5 1 * –
Note that ^ is the exponentiation operator.
ZmoQ>: EŠgnmoZ|{e`b Am°naoQ>a h¡& nhbo * ‘yë`m§H$Z
The top two elements of the stack after the
first * is evaluated are:
Ho$ ~mX ñQ>¡H$ Ho$ erf© Xmo VËd Š`m h¢:
(A) 6, 1 (B) 5, 7 (A) 6, 1 (B) 5, 7
(C) 3, 2 (D) 1, 5 (C) 3, 2 (D) 1, 5

082. A poultry farm has only chickens and dogs. 082. EH$ nmoëQ´r ’$m‘© ‘| Ho$db ‘w{J©`m§ Am¡a Hw$Îmo h¢. O~
When the manager of the poultry counted the nmoëQ´r Ho$ à~§YH$ Zo ’$m‘© ‘| ñQ>m°H$ Ho$ hoS²g H$mo {JZm,
heads of the stock in the farm, the number Vmo Hw$b g§»`m 200 Wr & hmbm§{H$, O~ n¡am| H$s
totaled up to 200. However, when the number g§»`m {JZm J`m, Vmo Hw$b g§»`m 540 Wr & Hw$Îmo Ho$
of legs was counted, the number totaled up to ‘wH$m~bo IoV ‘| Am¡a {H$VZo ‘w{J©`m± Wt. ZmoQ>: IoV
540. How many more chickens were there in ‘|, àË`oH$ Hw$Îmo Ho$ 4 n¡a Wo Am¡a àË`oH$ ‘wJ} Ho$ 2 n¡a
the farm? Note: In the farm, each dog had 4
Wo&
legs and each chicken had 2 legs.
(A) 130 (B) 60 (A) 130 (B) 60
(C) 70 (D) 120 (C) 70 (D) 120

083. Which of the following is true about merge 083. ‘O© gm°Q>© Ho$ ~mao ‘| {ZåZ{bpIV ‘| go H$m¡Z gm ghr
sort? h¡?
(A) Merge Sort works better than quick sort (A) ‘O© gm°Q>© Ëd[aV H«$‘~ÕVm go ~ohVa H$m‘ H$aVm
if data is accessed from slow sequential h¡ `{X So>Q>m H$mo Yr‘r AZwH«${‘H$ ‘o‘moar go
memory. EŠgog {H$`m OmVm h¡&
(B) Merge Sort is stable sort by nature (B) ‘O© gm°Q>© ñd^md go pñWa gm°Q>© h¡
(C) Merge sort outperforms heap sort in (C) A{YH$m§e à¡pŠQ>H$b pñW{V`m| ‘| ‘O© gm°Q>©, hrn
most of the practical situations. gm°Q>© go ~ohVa àXe©Z H$aVm h¡
(D) All of the above. (D) D$na Ho$ g^r&

084. Which one of the following in NOT 084. {ZåZ{bpIV ‘| go {H$gH$m EH$ g‘yh H$m JwU hmoZm
necessarily a property of a Group? µOê$ar Zht h¡?
(A) Commutativity (A) Commutativity
(B) Associativity (B) Associativity
(C) Existence of inverse for every element (C) Existence of inverse for every element
(D) Existence of identity (D) Existence of identity

5-AA ] [ 19 ] [ P.T.O.

085. In a competition, a school awarded medals in 085. EH$ à{V`mo{JVm ‘|, ñHy$b Zo {d{^Þ lo{U`m| ‘| nXH$
different categories. 36 medals in dance, 12 go gå‘m{ZV {H$`m. Z¥Ë` ‘| 36 nXH$, ZmQ>H$s`Vm ‘|
medals in dramatics and 18 medals in music.
12 nXH$ Am¡a g§JrV ‘| 18 nXH$ h¢²& `{X `o nXH$
If these medals went to a total of 45 persons
and only 4 persons got medals in all the three
Hw$b 45 ì`{º$`m| Ho$ nmg JE Am¡a VrZm| lo{U`m| ‘|
categories, how many received medals in Ho$db 4 ì`{º$`m| H$mo nXH$ {‘bo, BZ‘| go {H$VZm| H$mo
exactly two of these categories? BZ‘| go Xmo lo{U`m| ‘| nXH$ àmá hþE?
(A) 5 (B) 3 (A) 5 (B) 3
(C) 6 (D) 4 (C) 6 (D) 4

086. Let P(E) denote the probability of the 086. P(E) H$mo KQ>Zm E H$s KQ>Zm H$s g§^mdZm H$m g§Ho$V
occurrence of event E. If P(A) = 0.5 and P(B) XoVo h¢²& `{X P(A) = 0.5 Ed§ P(B) = 1, {’$a H«$‘e…
= 1, then the values of P(A/B) and P(B/A) P(A/B) Ed§ P(B/A) Ho$ ‘yë` h¢:
respectively are
(A) 0.5, 0.25 (B) 0.25, 0.5 (A) 0.5, 0.25 (B) 0.25, 0.5
(C) 0.5, 1 (D) 1, 0.5 (C) 0.5, 1 (D) 1, 0.5

087. The total number of prime implicants of the 087. The total number of prime implicants of the
function f (w, x, y, z) = Σ(0, 2, 4, 5, 6, 10) function f (w, x, y, z) = Σ(0, 2, 4, 5, 6, 10)
is .................... is .................
(A) 2 (B) 3 (A) 2 (B) 3
(C) 4 (D) 5 (C) 4 (D) 5

088. Which of the following statements is/are 088. {ZåZ{bpIV ‘| go H$m¡Z gm H$WZ A§{S>aoŠQ>oS> J«m’$ Ho$
TRUE for undirected graphs? {bE TRUE h¡ /?
P: Number of odd degree vertices is even. P: Number of odd degree vertices is even.
Q: Sum of degrees of all vertices is even. Q: Sum of degrees of all vertices is even.
(A) P only (B) Q only (A) P only (B) Q only
(C) Both P and Q (D) Neither P nor Q (C) Both P and Q (D) Neither P nor Q

089. Consider the following statements: 089. {ZåZ{bpIV H$WZm| na {dMma H$a|:
S1: The sum of two singular n × n matrices S1: The sum of two singular n × n matrices
may be non-singular may be non-singular
S2: The sum of two n × n non-singular S2: The sum of two n × n non-singular
matrices may be singular. matrices may be singular.
Which of the following statements is correct? {ZåZ{bpIV H$WZm| ‘| go H$m¡Z ghr h¡?
(A) S1 and S2 are both true (A) S1 Am¡a S2 XmoZm| gË` h¢
(B) S1 is true, S2 is false (B) S1 gË` h¢ , S2 AgË` h¢
(C) S1 is false, S2 is true (C) S1 Ag˶ h¢ , S2 gË` h¢
(D) S1 and S2 are both false (D) S1 Am¡a S2 XmoZm| AgË` h¢

5-AA ] [ 20 ] [ Contd...

090. Given the function F = P′ + QR, where F is a 090. {XE JE ’$bZ F = P′ + QR, Ohm§ F VrZ ~y{b`Z
function in three Boolean variables P, Q and R Ma ‘| EH$ ’$bZ h¡ : P, Q, R Ed§ P′ = !P
and P′ =!P, consider the following statements. {ZåZ{bpIV H$WZm| na {dMma H$a|&
S1: F = Σ (4, 5, 6) S1: F = Σ (4, 5, 6)
S2: F = Σ (0, 1, 2, 3, 7) S2: F = Σ (0, 1, 2, 3, 7)
S3: F = Π (4, 5, 6) S3: F = Π (4, 5, 6)
S4: F = Π (0, 1, 2, 3, 7) S4: F = Π (0, 1, 2, 3, 7)
Which of the following is true? BÝ‘o go ghr Š`m h¡?
(A) S1-False, S2-True, S3-True, S4-False (A) S1-False, S2-True, S3-True, S4-False
(B) S1-True, S2-False, S3-False, S4-True (B) S1-True, S2-False, S3-False, S4-True
(C) S1-False, S2-False, S3-True, S4-True (C) S1-False, S2-False, S3-True, S4-True
(D) S1-True, S2-True, S3-False, S4-False (D) S1-True, S2-True, S3-False, S4-False

091. Which of the following is true? 091. {ZåZ{bpIV ‘| go gË` h¡?
(A) Static methods cannot be overloaded. (A) Static methods cannot be overloaded.
(B) Static data members can only be (B) Static data members can only be
accessed by static methods. accessed by static methods.
(C) Non-static data members can be (C) Non-static data members can be
accessed by static methods. accessed by static methods.
(D) Static methods can only access static (D) Static methods can only access static
members (data and methods) members (data and methods)

092. Because the configuration information for 092. Š`m|{H$ DHCP ŠbmB§Q> Ho$ {bE H$m°pݵ’$JaoeZ H$s
a DHCP client is received dynamically, you OmZH$mar J{Verb ê$n go àmá hmoVr h¡, AmnH$mo goqQ>½g
must use which utility to read the current
H$mo gË`m{nV H$aZo Ho$ {bE dV©‘mZ H$m°pݵ’$JaoeZ H$mo
n‹T>Zo Ho$ {bE H$m¡Z gr Cn`mo{JVm H$m Cn`moJ H$aZm
configuration to verify the settings?
Mm{hE?
(A) PING (B) TRACERT
(A) PING (B) TRACERT
(C) ARP (D) IPCONFIG (C) ARP (D) IPCONFIG

093. In .............., the bodies of the two loops 093. .............. ‘|, Xmo bynm|
Ho$ ~m°S>rµO H$mo EH$ gmW
are merged together to form a single loop
{‘bH$a EH$ EH$b byn ~Zm`m OmVm h¡, ~eV} {H$ do
provided that they do not make any references
to each other.
EH$-Xygao H$mo g§X{^©V Zht H$aVo h¢
(A) Loop unrolling (A) byn AZamoqbJ
(B) Loop jamming (B) byn O¡q‘J
(C) Loop concatenation (C) byn H$mZH¡$Q>ZoeZ
(D) Strength reduction (D) ñQ´|W [aS>ŠeZ

5-AA ] [ 21 ] [ P.T.O.

094. “typedef” in C basically works as an alias. 094. C ‘| “typedef” ‘yb ê$n go EH$ alias Ho$ ê$n ‘|
Which of the following is correct for H$m‘ H$aVm h¡& {ZåZ{bpIV ‘| go H$m¡Z gm “typedef”
“typedef”? Ho$ {bE ghr h¡?
(A) typedef can be used to alias compound (A) typedef can be used to alias compound
data types such as struct and union. data types such as struct and union.
(B) typedef can be used to alias both (B) typedef can be used to alias both
compound data types and pointer to compound data types and pointer to
these compound types. these compound types.
(C) typedef can be used to alias a function (C) typedef can be used to alias a function
pointer and an array. pointer and an array.
(D) All of the above. (D) All of the above.

095. ‘ptrdata’ is a pointer to a data type. The 095. ‘‘ptrdata’’ EH$ nm°B§Q>a So>Q>m àH$ma H$m g§Ho$VH$ h¡&
expression *ptrdata++ is evaluated as (in A{^ì`{º$ *ptrdata ++ H$m ‘yë`m§H$Z (C ++ ‘|)
C++) : Ho$ ê$n ‘| {H$`m OmVm h¡:
(A) *(ptrdata++) (A) *(ptrdata++)
(B) (*ptrdata)++ (B) (*ptrdata)++
(C) *(ptrdata)++ (C) *(ptrdata)++
(D) Depends on compiler (D) {S>n|S>g Am°Z H$ånmBba

096. Define the connective * for the Boolean 096. ¶{X ~y{b¶Z d¡[a¶odbg X Ed§ Y Ho$ {bE
variables X and Y as: X * Y = XY + X' Y'. connective * H$mo Eogo n[a^m{fV {H$¶m OmVm h¡…
Let Z = X * Y. X * Y = XY + X' Y', Let Z = X * Y.
Consider the following expressions P, Q and Vmo P, Q Am¡a R Ho$ {bE {ZåZ{bpIV A{^ì`{º$`m|
R. na {dMma H$a| &
P: X = Y * Z P: X = Y * Z
Q: Y = X * Z Q: Y = X * Z
R: X * Y * Z=1 R: X * Y * Z=1
Which of the following is TRUE? BZ‘| go g˶ Š`m h¡?
(A) Only P and Q are valid (A) Ho$db P Ed§ Q hr ‘mÝ` h¢&

(B) Only Q and R are valid. (B) Ho$db Q Ed§ R hr ‘mÝ` h¢&

(C) Only P and R are valid. (C) Ho$db P Ed§ R hr ‘mÝ` h¢&

(D) All P, Q, R are valid. (D) g^r P, Q, R ‘mÝ` h¢&

5-AA ] [ 22 ] [ Contd...

097. Consider the following relations: 097. {ZåZ{bpIV relations na {dMma H$a|:
R1 (a,b) iff (a + b) is even over the set of R1 (a,b) iff (a + b) is even over the set of
integers integers
R2 (a,b) iff (a + b) is odd over the set of R2 (a,b) iff (a + b) is odd over the set of
integers integers
R3 (a,b) iff a . b > 0 over the set of non-zero R3 (a,b) iff a . b > 0 over the set of non-zero
rational numbers rational numbers
R4 (a,b) iff |a – b| ≤ 2 over the set of natural R4 (a,b) iff |a – b| ≤ 2 over the set of natural
numbers numbers
Which of the following statements is correct? {ZåZ{bpIV H$WZm| ‘| go H$m¡Z ghr h¡?
(A) R1 and R2 are equivalence relations, R3 (A) R1 and R2 are equivalence relations, R3
and R4 are not and R4 are not
(B) R1 and R3 are equivalence relations, R2 (B) R1 and R3 are equivalence relations, R2
and R4 are not and R4 are not
(C) R1 and R4 are equivalence relations, R2 (C) R1 and R4 are equivalence relations, R2
and R3 are not and R3 are not
(D) R1, R2, R3 and R4 are all equivalence (D) R1, R2, R3 and R4 are all equivalence
relations relations

098. If two fair coins are flipped and at least one of 098. `{X Xmo {g¸o$ CN>mbo OmVo h¢ Am¡a H$‘ go H$‘ EH$
the outcomes is known to be a head, what is n[aUm‘ H$mo EH$ head Ho$ ê$n ‘| OmZm OmVm h¡, Vmo
the probability that both outcomes are heads? Š`m g§^mdZm h¡ {H$ XmoZm| n[aUm‘ head h¢?
(A) 1 / 3 (B) 1 / 4 (A) 1 / 3 (B) 1 / 4
(C) 1 / 2 (D) 2 / 3 (C) 1 / 2 (D) 2 / 3

099. ICMP is primarily used for 099. ICMP ‘w»` ê$n go {H$gHo$ {bE à`moJ {H$`m OmVm h¡
(A) Error and diagnostic function (A) Error and diagnostic function
(B) Addressing (B) Addressing
(C) Forwarding (C) Forwarding
(D) None of the above (D) BZ‘| go H$moB© Zht

100. What is the minimum number of two input 100. Xmo BZnwQ> OR JoQ> Ho$ H$m¶© H$mo H$aZo Ho$ {bE Cn¶moJ
NAND gates used to perform the function of {H$¶o OmZodmbo Xmo BZnwQ> NAND JoQ> H$s ݶyZV‘
two input OR gate? g§»¶m ³¶m h¡&
(A) One (B) Two (A) EH$ (B) Xmo
(C) Three (D) Four (C) VrZ (D) Mma

5-AA ] [ 23 ] [ P.T.O.

SPACE FOR ROUGH WORK / H$ÀMo H$m‘ Ho$ {b¶o OJh

5-AA ] [ 24 ]