Jawaharlal Nehru University MCA entrance exam last year question papers

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1. Fora, b e R, define A=[ o 2J and B = Ln b].
Statement I : For any a, A is a diagonalizable matrix.
Statement II : For any a and b m 1, B is a diagonalizable matrix.
(a) Statement I is true , statement II is false
(b) Statement I is false, statement II is true
(c) Both the statements are false
(d) Both the statements are true
2. If @ means triple of, # means double of and A means half of, then the value of
@#A@A5 + @#@A2 is
(a) 39.5
(b) 40.5
(c) 39.74
(d) None of the above
3. A ray of light incident at the point (-2, -1) gets reflected from the tangent at (0, -1) to the
circle x2 + y2 = L The refracted ray touches the circle. The equation of the line along
which the incident ray moved is
(a) 4x-3y+11=0
(b) 4x+3y+11=0
(c) 3x+4y+11=0
(d) None of the above
4. The approximate value of tof (x) dx, where f(x) =
l+x
1
+x
3 , using Taylor's linear
approximation of f(x) at x = 0 is
(a) 0095
(b) 0.105
(c) 0.09
(d) 0.11
5. What is the next term in the sequence 49, 121, 225, 361, ...?
(a) 400
(b) 441
(c) 481
(d) 529
6. The number of pairs (a, b), for which a(x + 1) 2 = b(x 2 - 3x + 2) + x + 1= 0 Vx E R, is
(a) 0
(b) 1
(c) 2
(d) infinite
7. A function y = f (x) is defined parametrically as y = t2 + tltl, x = 2t - I tl, t c- R. Then at
x=0, f(x) is
(a) continuous but non-differentiable
(b) differentiable
(c) discontinuous
(d) None of the above
/22-A 4
I I 1 I I 111 1 p u l l M l , i , I I I 1 I I I !, II I+. li I Ni N I„ +, i1
S. The value of tan- '(1) +tan i(2)+tan-1(3) is equal to
(d) None of the above
9. The number of positive integral solutions of tan-1(x)+cot-1(y)=tan-1(3) is
(a) one
(b) two
(c) three
(d) four
10. The interval, in which cos-1 (x) > sin-'(x), is
(a) (- -% 1)
(b) (-1, 1)
(c) [-1, 1/'h)
(d) [-1, 1[
11. If (1, - 1, -1)T is an eigenvector of the matrix
4 1 1
-5 0 -3
-1 -1 2
then the corresponding eigenvalue is
(a) 2
(b) -2
(c) -1
(d) 3
12. A father's age is 4 times the age of his elder son and 5 times the age of his younger son.
When the elder son lived to three times his present age, then the father 's age will exceed
his younger son's age by 3 years. What is the age of the father?
(a) 40 years
(b) 32 years
(c) 30 years
(d) None of the above
13. The perimeter of a triangle ABC is 6 times the arithmetic mean of the sines of its angles.
If the side a is 1, then angle A is
14. Out of the 18 points in a plane, no three points are in the straight line except 5 points
which are collinear. The number of straight lines that can be formed joining them is
15. The orthocentre of the triangle formed by the lines x + y = 1, 2x + 3y = 6 and
4x-y+4=0 lies in
(a) I quadrant
(b) II quadrant
(c) III quadrant
(d) IV quadrant
16. Given the system of straight lines
a(2x+ y- 3)+b(3x+ 2y- 5) = 0
the line of the system situated farthest from the point (4, -3) has the equation
(a) 4x+lly-15=0
(b) 7x+y-8=0
(c) 4x+3y-7=0
(d) 3x-4y+1=0
17. If A + B = 3, where A, B > 0, then the minimum value of secA + sec B is equal to
(a) 4 /a
(b) 8/a
(c) 6
(d) None of the above
18. If a, b, c and d are distinct real numbers such that
(a2 +b2 +c2)x2 -2x(ab+bc+cd)+b2 +c2 +d2 5 0
then they satisfy
(a) AP
(b) GP
(c) HP
(d) ab=cd
19. The equation y2 - x 2 + 2x -1= 0 represents
(a) a pair of straight lines
(b) a circle
(c) a parabola
(d) an ellipse
/22-A 7 [. P.T.O.
20. The dimension of a subspace of R4 spanned by the vectors {(2, -1, 0, 1), (1, 2, -3, 2),
(1, -3, 2, 0), (0, 0, 1, -1)} is
21. In what ratio should wheat at ? 4-5 per kg be mixed with another variety at is 525 per
kg so that the mixture is worth of F 5 per kg?
(a) 1 : 2
(b) 2 : 1
(c) 1 : 3
(d) 3 : 1
22. The values of p, for which the roots of the equation (p - 3)x 2 - 2px + 5p = 0 are real and
positive, are
(a) pE(3^ 15/41
(b) p E (3, 15 /4)
(c) p E ]3, 15/4)
(d) p E [3, 15 /4]
(1+x+x2)
23. lim is equal to
X- - x(lnx)3
(a) 2
(b) e2
(c) a-2
(d) None of the above
24. The value of 2sin29+4cos(9+aJsinasin9 + cos(2a+29) is
(a) cos9+cosa
(b) independent of 9
(c) independent of a
(d) None of the above
29. Which of the following is rational number?
(a) sinl5°
(b) cos 151
(c) sinl5° cosl5°
(d) sin 15° cos75°

27. Two taps can fill a tank in 18 minutes and 24 minutes respectively. When both the taps
are opened , find when the first tap is turned off so that the tank may be filled in
12 minutes.
(a) After 6 minutes
(b) After 10 minutes
(c) After 9 minutes
(d) After 12 minutes
/22-A 9 1 P.T.O.
28. If (cosx)/a=(sin x)/b, then I acos2x+bsin2x I is
(a) a3b
29. The area of the triangle formed by the lines y = ax, x + y - a = 0 and the y-axis is equal
to
(a) 1/211+al
(b) a2 /11+a1
(c) (1/2)11/(1+a)1
(d) a2 /211+a1
30. A variable point (1+(a /-h), 2+(a /f)) lies in between two parallel lines x+2y= 1 and
2x + 4 y = 15. Then the range of a is given by
(a) O<a<5h/6
(b) -4'/3<a<5f/6
(c) -4f/3<a<0
(d) None of the above
31. A and B are two fixed points . The vertex C of a triangle ABC moves such that
cot A + cot B = constant . The locus of C is a straight line
(a) perpendicular to AB
(b) parallel to AB
(c) inclined at an angle (A - B) to AB
(d) None of the above
32. A straight line L with negative slope passes through the point (8, 2) and cuts the positive
coordinate axes at points P and Q. As L varies the absolute minimum value of OP + OQ
(0 is the origin) is
33. If a circle passes through the points of intersection of the lines 2x - y+ 1 = 0 and
x + ay - 3 = 0 with the axes of the reference, then the value of a is
34. A foot of the normal from the point (4, 3) to a circle is (2, 1) and the diameter of the
circle has the equation 2x - y = 2. Then the equation of the circle is
(a) x2+y2+2x-1=0
(b) x2+y2-2x-1=0
(c) x2+y2+2y-1=0
(d) None of the above
32. A straight line L with negative slope passes through the point (8, 2) and cuts the positive
coordinate axes at points P and Q. As L varies the absolute minimum value of OP + OQ
(0 is the origin) is
(a) 10
(b) 18
(c) 16
(d) 12
33. If a circle passes through the points of intersection of the lines 2x - y+ 1 = 0 and
x + ay - 3 = 0 with the axes of the reference, then the value of a is
(a) 0.5
(b) 2
(c) 1
(d) -2
34. A foot of the normal from the point (4, 3) to a circle is (2, 1) and the diameter of the
circle has the equation 2x - y = 2. Then the equation of the circle is
(a) x2+y2+2x-1=0
(b) x2 + y2 - 2x - 1 = 0
(c) x2+y2+2y-1=0
(d) None of the above
35. The radius of convergence of the power series
L=0 3n!
is
(a) 1/27
(b) 27
(c) 1/3
(d) 3
36. The average minimum temperature for Monday, Tuesday and Wednesday was 4 degree
and that for Tuesday, Wednesday and Thursday was 5.5 degree. If the temperature on
Monday was 2.6 degree, what was the temperature on Thursday?
(a) 4.1 degree
(b) 12.1 degree
(c) 7.1 degree
(d) 11.1 degree
37. The equation of the circle touching the line ( y( = x at a distance V units from the origin
is
(a) x2+y2-4x+2=0
(b) x2+y2+4x-2=0
(c) x2+y2+4x+2=0
(d) None of the above
38. Circles with radii 3, 4 and 5 touch each other externally. Pis the point of intersection of
tangents to these circles at their points of contact. The distance of P from the point of
contact is
39. The angle between the circles
Cl:x2+y2-4x+6y+11=0
C2: x2+y2-2x+8y+13=0
is
(a) 15-
(b) 30-
(c) 45-
(d) 60-
40. For 1 < 4 < 4, the coefficient of z2 in the Laurent series expansion of 1 is equal
z2 -5z+4
to
(a) 1/192
(b) 1/48
(c) -1/48
(d) -1/192
41. A sum of r 3,310 is to be paid back in 3 equal annual installments. What is the total
interest charged if the interest is compounded annually at 10%?
(a) F 1,331
(b) f 683
(c) r 331
(d) r 993
42. The greatest integer which divides the number 101100 - 1 is
(a) 100
(b) 1000
(c) 10000
(d) None of the above
43. The sum of the coefficients of all the integral powers of x in the expansion of (1+2,x)40
is
(a) 340+1
(b) 3 40 -1
(c) (1/2)(3 40 _ 1)
(d) (1/2)(340
+1)
44. If (1+x)n =Co +Clx+...+ Cnxn, then the value of
n n
0E's= 0(Cr +Cs)
is equal to
(a) (n+1)2n+1
(b) (n-1)2n+1
(c) (n+ 1)2n
(d) None of the above
45. Which of the following is not the property of nCr?
(a)
(b)
(C)
nCl=nC
n-1
n Cr = C,_r
r nCr = n n-i Cr-1
(d) (r-1)nCr =(n-1)n-1Cr-1
46. In triangle ABC, the value of r^=OnCrarbn-r cos(rB-(n- r)A) is equal to
(a) Cn
(b) bn
(c) an
(d) 0
/22-A 14
I 1 0 . 1 11 1 . wu 41 11 11, 1 xM.Wqui 11P . i
47. A city has 12 gates. In how many ways can a person enter the city through one gate and
come out through a different gate?
(a) 144
(b) 132
(c) 12
(d) None of the above
48. Let z be a complex variable and P(z) be a monic polynomial with real coefficients such
that P (0) = - 1. If P(z) = 0 has no real roots in the open disc (z : 4 < 1), then
(a) P(1) > 1
(b) 0<P(1)<1
(c) P(1) = 1
(d) P(1) = 0
49. A bag contains 5 paisa coins, 10 paisa coins and 20 paisa coins in the ratio of 3: 2: 1.
If their total value is P 11 , what is the number of 5 paisa coins?
50. In how many ways can 5 letters be posted in 4 letter boxes?
(a) 20
(b) 32
(c) 45
(d) 54


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Contact Details:
Jawaharlal Nehru University
JNU New Campus,
JNU Ring Road,
Jawaharlal Nehru University,
New Delhi,
Delhi 110067 ‎
011 2670 4090
India

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