MATHEMATICS
Previous year question paper with solutions for MATHEMATICS Mar-2018
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Question paper 1
1. (a) if
then value of -
(i)
0
(ii)
2
(iii)
6
(iv)
8
Answer:
(b) The principal value of
is :(i)
(ii)
(iii)
(iv)
Answer:
(iv)
(c) If
then value of 
will be.(i)
0
(ii)
1
(iii)
-1
(iv)
Answer:
(ii)
1
(d) The slope of the tangent to the curve
at 
is :(i)
6
(ii)
10
(iii)
1
(iv)
12
Answer:
(iii)
1
(e) The order of differential equation
(i)
0
(ii)
1
(iii)
2
(iv)
3
Answer:
(iii)
2
(f) Direction ratios of the line joining points A (2,3,-4) and (1,-5,3)is:
(i)
1,5,7
(ii)
-1,-5,-7
(iii)
1,-5-7
(iv)
-1,-5,7
Answer:
(iv)
-1,-5,7
2. If
and 
are given by 
and 
then find g of.Answer:
3. Integrate the given function with respect to x:
Answer:
4. Find the value of
if the vectors 
and 
Answer:
5. Determine the direction-cosines of a line making equal angles with the co-ordinate axes.
Answer:
Dir.-cosines of a line making
with x-axis, 
with y-axis & 
with z-axis are l,m,n
Dir.-cosines are:
We know:
6. Find the values of x for which
Answer:
7. Find
, if x=at2 , y=2atAnswer:
8. Differentiate a w.e.t.x where ‘a’ is positive constant.
Answer:
9. Find the interval in which the function f given by
is strictly increasing Answer:
For str. Inc.;
In
; 
is st. inc.10.Evaluate : \
Answer:
11.Find the general solution of the differential equation
Answer:
Integrating
Or
Find the particular solution of the differential equation
given that y= 1, when x=0.Answer:
Integrating
Putting x=0 & y=1 in
Soln. is
12. Find the unit vector perpendicular to each of the vectors
and 
Answer:
The
vector to both 
=
Now, unit vector in the direc.
Or
Find the area of a parallelogram whose adjacent sides are given by the vectors
and 
Answer:
&
Area of parallelogram
Area of parallelogram
13. Find the vector equation for the line passing through the point (-1,0,2)and (3,4,6).
Answer:
A(-1,0,2)and B(3,4,6).
vector equation for the line passing through the point with position vectors
is:
14. Consider the function
given by 
. Prave that f is one onto. Find also function of f.Answer:
15. Prove that
Answer:
16. Find the inverse of matrix
by using elementary operation. Answer:
Or
Evaluate the determinant:
Answer:
17.Examine the function
for its continuity at point x=2 Answer:
is not cont. at ‘2’18. Integrate the function
with respect to xAnswer:
19. Prove that
Answer:
L.S.H=I=0π4log1+tanx dx â‘
Property: 0afxdx=0afa-xdx
Or
Find
Answer:
20. If two vectors
are such that 
the find 
Answer:
21.From a pack of 52 playing cards , two cards are draw at random without replacement. Find the Probability of being both cards black.
Answer:
Let
: 1st card drawn is black .
: 2nd card drawn is black.
Or
Prove that if E and F are two independent events, then E and F are also independent
Answer:
E and F are two indep.
E and F’ are two independent
22. If
, then verify that 
Also find 
Answer:
23. Find the area laying above x-axis and included between the circle
and inside of the parabola 
Answer:
intersection pt.
intersection pt. of
Or
Find the area enclosed by the ellipse
Answer:
Since ellipse
is symmetrical both x-axis & y-axis Area enclosed by
Put in
;
24. Prove that the rectangle of maximum area , inscribed in a circle, is a square.
Answer:
Let the length and breadth of the rectangle inscribed in a circle of radius
a be x & y resp.
Diff. w.r.t.x;
Diff. w.r.t.x;
For
to be minimum;
:.
is max. at x=2a
Thus
:. The rectangle is a
square if side
Or
Prove that the radius of the right circular cylinder of greatest surface area which can be inscribed in a given cone is half of that of the cone
Answer:
let OC=r be radius of cone
& OA=h, height of cone
&
Let OE =x be radius of cylinder =OO’
From
Now curved surface area of cylinder
Diff. w.r.t.x;
Now
Hence, radius of cylinder with greatest curved surface area which can be inscribed in a given cone is half of that cone
25. Solve the differential equation
Answer:
Integration,
Ans.
26. Find the vector and Cartesian equation of a line passing through the point (1,2,3) and parallel to the vector
Answer:
27. A bag contains 3 black and 4 red balls. Two balls are drawn at random one at a time. Without replacement. Find the probability that the first ball is black if the second ball is known to be red.
Answer:
Black
3Red
4Let event
B: drawn ball is black
R: drawn ball is red
To find : P(B
R) Since
Now to find
Put in
Or
From a pack of 52 well-shuffled playing cards. Two cards are drawn at a time find the probability distribution of the kings
Answer:
Let X be the number of king obtained
Hence x={x can be 0,1or 2
28. solve the following linear programming problem graphically:
Maximize
Subject to the given constraints:
Answer:
s/t
Plotting
x
0
10
y
5
0
Plotting
x
0
5
y
-15
0
(0,0) satisfies (B)
: Shade the region left to
: OABC is the reqd. region
Intersection point of
:
Point
O(0,0)
A(0,5)
B
C(5,0) Z=15
: B
is optimal pt.& optimal soln. is :
