MATHEMATICS
Previous year question paper with solutions for MATHEMATICS Mar-2017
Our website provides solved previous year question paper for MATHEMATICS Mar-2017. Doing preparation from the previous year question paper helps you to get good marks in exams. From our Mathematics question paper bank, students can download solved previous year question paper. The solutions to these previous year question paper are very easy to understand.
These Questions are downloaded from www.brpaper.com You can also download previous years question papers of 10th and 12th (PSEB & CBSE), B-Tech, Diploma, BBA, BCA, MBA, MCA, M-Tech, PGDCA, B-Com, BSc-IT, MSC-IT.
Print this page
Question paper 1
(SECTION -"A")
1. Find the identity element for the binary operation defined in the set of positive rational numbers by
Answer:
Let e be the identity element & let a be any elt of
Then
[applying
]
[: e is identity elemennt ] 2. If
then write down the value of 
Answer:
3. If then find A=
B
then find ABAnswer:
4. Find the cofactor of the element 6 in the matrix
Answer:
Minor of ‘6’=
‘6’ is (2,3)th element
:Co-factor of ‘6’=-
5. if
find the value of 
Answer:
6. Integrate the function
with rapect to x.Answer:
7. Evaluate:
Answer:
8. If
then evaluate 
Answer:
9. If
and 
then find 
Answer:
&
10. Find the length of intercepes made by the plane
on co-ordinate axisAnswer:
6, 3, 2, are intecests
(SECTION -"B")
11. Prove that the function
defined by 
is neither one-ane nar onla,Answer:
Also
any 
such that
:
is not onto OR
Let
be a function defined as 
where 
. Show that fis invertible. Find the inverseAnswer:
Prove
is 
Let
& let
=
:
is one-one . is onto :- let 
Such that f
Since
for some 
:
:
is onto12. Prove that
Answer:
L.H.S
Dividing numerator & denominator by
13. Evaluate the determinants
Answer:
Taking common 2 from
;=2
expanding by
14. Examine the function
for continuity at x= 0 .Answer:
R.H.S =
L.H.S = lt fx lt -x
= 0
L.H.S= R.H.S =
is cont . at x=0OR
If
then find 
Answer:
Diff . x w.r.t
;
From
15. Verity mean value theorem if
in the interval [a,b], where a = 2 and b = 4.Answer:
in 
Condition- I
is cont. in Since
is polynomial : it is cont. in
Condition- II
is differentiable in Since
is polyIt is diff in
Now ,
Now
Value of c is 3 which lies b/w 2 and 4
Hence , c=
Hence mean value the is satisfied
16. Find the equation of tumpent to the curve
at the point (3,0) Answer:
The eq. of tangent to
:
become 
17. Evaluate
Answer:
18. Find the general solution of the differential equation
Answer:
Integrating ;
19. Find the particular solution of the differential equation
given that 
Answer:
Soln. is
: soln. is
20. Find the angle between the vectors
and 
Answer:
21. Find the canesian equation of the line passing through the point (1.2.3) and (2.3.5)
Answer:
Let A(1,2,3) &
B(2,3,5) be two points
Vectors eqn. of a line
Passing thru two points with position vectors
is 
Given 2 points are
A(1,2,3) & B(2,3,5)
& 
so
There, the vector eq. is
Cartesian eq. n :
Cartesian eq. n : of a line passing thru’
Two points A(x1,y1,z1) & B (x2,y2,z2) is
Since line passes thru
A(1,2,3)
x1=1,y1=2,z1=3
Also passes through B (2,3,5)
x2=2,y2=3,z2=5
: Eq. of line is :
(OR)
Find the angle between the plans whose vector equations are
and 
Answer:
Angle is given by:
22. A dice is tossed twice and the sum of them numbers appeared is found to be 6. Find the conditional probability of the number * appearing at least once.
Answer:
we need to find the prof. that 4 has appeared at least once, given the sum of no.’s is observed to be 6 let A: sum of of no,’ 595 6
E: 4has appeared at least once
(SECTION - "C")
23. Find the inverse of the following matrix by using elementary operations
Answer:
24. Show that for a right circular cylinder of given total surface and maximum volume, the height is equal to the diameter of the base
Answer:
Let S be the given surface area of the closed cylinder whose radius is r and height h let. V be its be its volume .
Foe max. min.
From
:
: V is maximum
Thus volume is max
When
; volume is max. when
Height = diameter of base
25. Prove that ;
Answer:
26. The area between curve x=y2 and the line x=4 is divided in two equal parts by the line x=a. Using he method of integration, find the value of a.
Answer:
Let AB represent the line segment of x=a
CD represent the line segment of x=4 diagram
Since the line x=a divides the region into equal parts
: Area (OBA)= Area (ABCD)
Since weve is sym about x-axis, we can take either +ve or negative value of y
From
OR
Find the area bounded by the parabola 4ay=a2 and its latus rectum.
Answer:
Comparing
with standard from of a parabola 
Eq. of latus rectum
Intersection points
The reqd. area =
27. Find the Cartesian equation of the line passing through (1, 2, -4) and perpendicular to each of the
Answer:
Let A(1, 2, -4) be the points
The vectors eqn. of a line passing thro. A point with position vector
&to a vector 
is 
The line passes thro. (1,2,4)
Given line is
r to
is r to We known that
is r to 
so, is cross product of Required normal =
Now putting value of
in formula 
28. If E and F are two independent events, then the probability of the occurrence of at least one of E and F is 1-P (E’) P(F’).
Answer:
Two events E&F are independent if
Prob. of occurrence of at least one of A&B
Prob. of occurrence of only A
Prob. of occurrence of only B
Prob. of occurrence of A or B
(OR)
It is known about a man that he speaks truth 3 out of 4 times. He tosses a dice and tells that the number appearing on the dice is 6. Find the probability that the number appearing on the dice is actually 6.
Answer:
Let
: man speaks truth 
: man liesE: 6 on dice
To find
Putting all value in
29. Solve the following linear programming problem graphically-
Minimize
Subject to the constraints-
Answer:
Minimize
Diagram The system is .
Plotting
Plotting
:Z=7 is optimum soln.