OJEE 2017 Question Paper M.Tech Common Engineering Maths

FOR OJEE EXAM PREPARATION

OJEE 2017
Question Paper ·
M.Tech Common
Engineering Maths
EXAM YEAR TYPE SUBJECT

OJEE 2017 Question Paper M.Tech Common Engineering Maths

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co m .
. s e
em l a

as a g

d y d y 3
dy 2
1. If y = c1 e2x + c2 ex + c3 e−x satisfies the differential equation dx 3 + a dx2 + b dx + cy = 0,
3 3 3
then a +babc
+c
is equal to

m
(A) 12

om . co
.c e m
s
(B) − 41

em l a
l a s ag
ag
(C) 12

(D) 0

2. The solution of the differential equation (x cos x − sin x)dx = xy sin xdy is
(A) sin x = ln |xy| + c

m
(B) ln | sinx x | = y + c

. co
s em
x
(C) | sin
a
|=c

l
xy

(D) none of the above. a g
where c is any arbitrary constant.

3. If y = f (x) passing through (1, 2) satisfies the differential equation y(1 + xy)dx −
xdy = 0, then
2x
(A) f (x) = 2−x 2

m
m c. o
c. o m
(B) f (x) = xx+1

e
2 +1

em la s
las ag
x−1
(C) f (x) = 4−x2

ag (D) f (x) = 4x
1−2x2

4. The real value of n for which the substitution y = z n will transform the differential
dy
equation 2x4 y dx + y 4 = 4x6 into a homogeneous equation is
(A) 12

m . c
c. o m
(B) 1

m s e
se
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Page 1 of 6

(C) 32

(D) 2
dy
5. The integrating factor of the differential equation dx (x ln x) + y = 2 ln x is given by
(A) x

(B) ex

(C) ln x

(D) ln(ln x).

6. The total number of linearly independent solutions of a homogeneous nth order first
degree differential equation with constant coefficients is
(A) n2

(B) n

(C) n − 1

(D) n + 1

7. The general solution of the differential equation (2x cos y + y 2 cos x)dx + (2y sin x −
x2 sin y)dy is
(A) x2 cos y + y 2 sin x = C

(B) x cos y − y sin x = C

(C) x2 cos2 y + y 2 sin2 x = C

(D) none of the above.

8. The number of distinct values of a 2 × 2 determinant whose entries are from the set
{−1, 0, 1} is
(A) 3

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co m .
. s e
em l a

as a g

(B) 4

m
(C) 5

om . co
.c e m
s
(D) 6

e m l a
a s
9. If 0 ≤ [x] < 2, −1 ≤ [y] < 1 and 1 ≤ [z] < 3 where [.] denotes the greatest integer
l ag
ag
function, then the maximum value of the det(A) where
 
[x]+1 [y] [z]
A =  [x] [y]+1 [z]  is
[x] [y] [z]+1
(A) 2

(B) 4

m
. co
em
(C) 6

l a s
a g
(D) 8

10. If all the elements of a third order determinant are equal to 1 or −1, then the
determinant itself is
(A) an odd number

(B) an even number

m
m c. o
c. o
(C) an imaginary number

e m
em l a s
las g
(D) a real number

11. For the system of equation x + 2y + 3z = 1, 2x + y + 3za= 2, 5x + 5y + 9z = 4
ag
(A) There is only one solution

(B) There exist infinitely many solutions

(C) There dose not exist any solution

m . c
c. o s e m
m
(D) None of the above

se
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12. If ~a + ~b + ~c = 0, |~a| = 3, |~b| = 5, and |~c| = 7 then the angle between ~a and ~b is
(A) π/6

(B) π/3

(C) 2π/3

(D) 5π/3

13. Vectors |~a| and |~b| are inclined at an angle θ = 1200 , if |~a| = 1, |~b| = 2, then
{(~a + 3~b) × (3~a − ~b)}2 is equal to
(A) 310

(B) 290

(C) 301

(D) 300

14. The characteristic of an orthogonal matrix A is
(A) A−1 A = I

(B) A.A−1 = I

(C) A′ .A−1 = I

(D) A.A′ = I

15. The Laplace transform of the function f (t) = 3 sin 4t − 2 cos 5t is
(A) s212
+16
− s22s
+25

(B) s212
−16
− s22s
+25

(C) s212
+16
− s22s
−25

(D) s212
+16
+ s22s
+25

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co m .
. s e
em l a

as a g

16. The inverse Laplace transform of 2s+1
s2 −4
is
(A) 2 cos h3t + 21 sin h3t

m
om
(B) 2 cos h2t − 12 sin h2t
. co
.c e m
e m l a s
s g
(C) 2 cos h2t + 21 sin h2t

g a
l2 cos ht + sin ht a
a
(D) 1
2

17. The function f (x) = cos 3x has period
(A) 2π/3

(B) 2π

m
. co
em
(C) 3π/2

l a s
a g
(D) π

18. Let f (x) = f (−x), ∀ x ∈ (−π, π) and f is periodic with period 2π, then the Fourier
series of f (x)
(A) contains only cosine terms

(B) contains only sine terms

m
m c. o
c. o
(C) contains both sine and cosine terms

e m
em l a s
las g
(D) Fourier series of the above function does not exist.

19. If A is a skew symmetric matrix, then the trace of A is a
ag
(A) −5

(B) −1

(C) 0

m . c
c. o s e m
m
(D) 1

se
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20. The equations λx − y = 2, 2x − 3y = −λ, 3x − 2y = −1 are consistent for
(A) λ = −4

(B) λ = −1

(C) λ = −1, 4

(D) λ = 1, −4

∗ ∗ ∗ ∗ ∗ ∗ ∗ END ∗ ∗ ∗ ∗ ∗ ∗ ∗

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