Mathematics
Previous year question paper with solutions for Mathematics Mar-2018
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Question paper 1
1.(i)
and g(x) = 
, then gof (x) is : (A)
(B) 
(C)
(D) None of theseAnswer:
(A)
(ii) The value of
is : (A)
(B) 
(C)
(D) 5
Answer:
(A)
(iii) If A=2142 and B=43-21,
then 2A + B is : (A)
(B) 
(C)
(D) None of theseAnswer:
(A)
(iv)If 0, 41 32 = − 0,then value of x is :
(A) 3 (B) −3
(C) 5 (D) −5
Answer:
(D) −5
(v) The derivative of
w. r. t. x is : (A)
(B)
(C)
(D) None of theseAnswer:
(B)
(vi) The function f(x) = 2 cosx +
x has maxima or minima at x = ……. . (A)
(B) 
(C)
(D) 
Answer:
(A)
(vii) The slope of normal to the curve x =
(A) 1 (B) −1
(C) 0 (D) 2
Answer:
(A) 1
(viii) The value of
is : (A)
(B) 
(C)
(D) None of these Answer:
(C)
(ix) The value of
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(C)
(x) The order of the differential equation
is : (A) 1 (B) 0
(C) 2 (D) None of these
Answer:
(C) 2
(xi) Solution of the differential equation
is : (A) y = cos x + c (B)
(C) y = − cos x + c (D) None of these
Answer:
(A) y = cos x + c
(xii) If P(A) = 0.5, P(B) = 0.6 and P(A ∪ B) = 0.8, then P(B/A) is :
(A)
(B) (C)
(D) None of theseAnswer:
(A)
(xiii) A card is drawn from a well-shuffled deck of 52 cards and then a second card is drawn. The probability that the first card is a spade and the second card is a club if the first card is not replaced is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(D) None of these
(xvi) If A and B are two independent events such that P(A ∪ B) = 0.5 and P(A) = 0.2, then P(B) is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(D) None of these
(xv) The value of λ for which the vectors
are perpendicular is : (A) 2 (B) 3
(C) 5 (D) 4
Answer:
(D) 4
(xvi) The direction ratios of a line 3x + 1 = 6y − 2 = 1 − z are :
(A) 2, 1, −6 (B) 1, 2, −3
(C) 6, 1, −2 (D) None of these
Answer:
(D) None of these
SECTION-B
2. Show that f(x) = 3x + 5, for all x ∈ Q is one-one.
Answer:
3. Prove that :
Answer:
4. If ,
then find 
Answer:
5. Find the area of the triangle whose vertices are (1, −1), (2, 4) and (−3, 5).
Answer:
6. Find the derivative of
w. r.t .x,Answer:
7. Find
, if x = a(1 + cos θ), y = a(θ + sin θ).Answer:
8. Evaluate :
Answer:
9. Evaluate :
Answer:
10. Solve the differential equation :
Answer:
11. A problem in Mathematics is given to three students whose chances of
solving it are
respectively. What is the probability that the problem will be solved ?Answer:
12. Prove that
Answer:
13. Show that the function :
is continuous but not derivable at x = 0.Answer:
14. Prove that the curve
Answer:
15. A bag contains 3 white and 4 red balls. Three balls are drawn one by one with replacement. Find the probability distribution of the number of red balls.
Answer:
White balls =3
Red balls=4
Total=7
Probability for red
16. Find the area of triangle whose vertices are (1, 2, 4), (3, 1, −2), (4, 3, 1).
Answer:
17. Solve the following equations by matrix method :
x + y + z = 6,
y + 3z = 11,
x − 2y + z = 0
Answer:
18. Show that the curves x
divide the area of the square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts. Answer:
OR
Evaluate :
Answer:
19. Find the foot of the perpendicular from the point (2, −1, 5) on the line
.Answer:
OR
Find the equation of the plane passing through the points (−2, 6, −6), (−3, 10, −9) and (−5, 0, −6).
Answer:
20. Solve graphically the following L. P. P. :
Minimize : Z = 5x + 3y
subject to constraints :
2x + y ≥ 10,
x + 3y ≥ 15, x ≤ 10,
y ≤ 8, x, y ≥ 0.
Answer:
X
0
5
y
10
0
X
0
15
y
5
0
Question paper 2
1. (i)If f(x) = log (1 + x) and g(x) = , xe then value of (fog )(x) is :
(A) log x (B) ( ) 1log +xe
(C) log (1 + x) (D) None of these
Answer:
(B) ( ) 1log +xe
(ii) The value of
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(iii) If A=
and B= 
the matrix X such that A + B − X = 0, then value of X is : (A)
(B) 
(C)
(D) None of thesAnswer:
(A)
(iv) If ,
then value of x is : (A) ± 4 (B) ± 6
(C) ± 8 (D) None of these
Answer:
(B) ± 6
(v) The derivative of x 3 tan w. r. t. x is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(A)
(vi) The value of x for which sin 2x attains its maximum, is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(B)
(vii)The slope of normal to the curve
is : (A) 1 (B) −1
(C) 3 (D) −2
Answer:
(A) 1
(viii) The value of
is : (A)
(B) 2 sin x + c (C)
(D) None of these Answer:
(A)
(xi) The value of
is : (A)
(B)
(C)
(D) None of these
Answer:
(x) The degree of the differential equation
is : (A) 1 (B) 2
(C) 3 (D) 0
Answer:
(A) 1
(xi) Solution of the differential equation
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(C)
(xii) If PA=713,PB=913and
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(B)
(xiii) A bag contains 10 white and 15 black balls. Two balls are drawn in succession without replacement. The probability that first is white and second is black, is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(C)
(xiv) If P(A) = 0.6, P(A ∪ B) = 0.7 and A and B are independent events, then P(B) is :
(A)
(B) (C)
(D) None of theseAnswer:
(D) None of these
(xv) If angle between two vectors
is 0 then the value of 
is : (A) 0 (B) 1
(C) ab (D) −ab
Answer:
(C) ab
(xvi)The direction cosines of a line equally inclined to the coordinate axis are :
(A) 1, 1, 1 (B)
(C)
(D) 
Answer:
(B)
SECTION-B
2.
for all n ∈ N, show that f is not one-one.Answer:
3. Prove that :
Answer:
4. If A=
and 
then find f(A).Answer:
5. Find the area of the triangle whose vertices are (4, 2), (4, 5) and (−2, 2).
Answer:
6. Find the derivative of
Answer:
7. Find
when x = cos 2θ + 2 cos θ, y = sin 2θ − 2 sin θ.Answer:
8. Evaluate :
Answer:
9. Evaluate :
Answer:
10. Solve the differential equation :
Answer:
11. A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that both are black.
Answer:
First bag, Red balls=3
Black balls=5
2nd bag, Red balls=6
Black balls=4
SECTION-C
12. Prove that :
Answer:
13.Show that the function f(x) = |x − 1|+ |x + 1|, for all x ∈ R, is not differentiable at x = −1.
Answer:
LHD
RHD
14. Find the equation of tangent to the curve x = 1 − cos θ, y = θ − sin θ at
Answer:
15. Find the probability distribution of the number of times a total of 9 appears in two throws of two dice.
Answer:
Sample space
LET X BE Radom varealde x for which takes value 0,1,2,3,4
x
0
1
2
3
4
P(x)
Vertices are (1,2,3) (2,5,-1),(-1,1,2)
16. If
=3.Answer:
Area of
SECTION-C
17. Solve the following equations by matrix method :
8x + 4y + 3z = 19,
2x + y + z = 5,
x + 2y + 2z = 7.
Answer:
put in (1)
18. Draw a sketch of the region bounded by the curve y x 4 2 = and the line x = 4y − 2 and determine its area.
Answer:
Shaded area = Ao A
Area A O D B C A ------(1)
For point solve –
OR
Evaluate :
Answer:
19. Find the image of the point (1, 6, 3) in the line
Answer:
OR
Find the equation of the plane passing through the points (0, 1, 1), (1, 1, 2) and (−1, 2, −2).
Answer:
20. Solve graphically the following L. P. P. :
Minimize : Z = −3x + 4y
subject to constraints :
x + 2y ≤ 8,
3x + 2y ≤ 12,
x, y ≥ 0.
Answer:
For first lines
n
0
8
y
4
0
For 2nd line
N
0
4
y
6
0
For point B, solve
Question paper 3
SECTION – A
1. (i) If f(x) = log (1 + x) and g(x) = x e ,then value of (gof )(x) is :
(A) x e + 1 (B) 1 + x
(C) log x (D) None of these
Answer:
(B) 1 + x
(ii)The value of
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(A)
(iii) If A=
and 
then 2A + B is : (A)
(B) 
(C)
(D) None of theseAnswer:
(C)
(iv) If
then value of m is : (A) 3 (B) 4
(C) – 3 (D) None of these
Answer:
(C) – 3
(v) Derivative of 3 sin x3
is :(A)
(B) 
(C)
(D) None of theseAnswer:
(B)
(vi) The maximum and minimum value of function f(x) = sin3x + 4 are respectively :
(A) 5 and 3 (B) 6 and 4
(C) 4 and 3 (D) None of these
Answer:
(A) 5 and 3
(vii) The slope of tangent to the curve
is : (A) 1 (B) 2
(C) −1 (D) None of these
Answer:
(C) −1
(viii) The value of
is : (A) tan x − x + c (B) cot x − x + c
(C) sec x − x + c (D) None of these
Answer:
(A) tan x − x + c
(ix) The value of
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(B)
(x) The degree of the differential equation
=0 is : (A) 2 (B) 3
(C) 1 (D) None of these
Answer:
(C) 1
(xi) Solution of the differential equation
is : (A) y = tan x − x + c (B) y = cot x − x + c
(C) y = sec x − x + c (D) None of these
Answer:
(A) y = tan x − x + c
(xii) If
then P(A/B) is : (A)
(B) 
(C)
(D) None of theseAnswer:
(C)
(xiii) A card is drawn from a pack of 52 cards and then a second card is drawn without replacement. The probability that both cards drawn are queens is :
(A)
(B) 
(C)
(D) None of theseAnswer:
(B)
(xiv) If A and B are two independent events such that P(A ∪ B) = 0.60 and P(A) = 0.2, then P(B) is :
(A) 0.5 (B) 0.6
(C) 0.7 (D) None of these
Answer:
(D) None of these
(xv) The angle between the vector
is : (A)
(B) 
(C)
(D) None of theseAnswer:
(D) None of these
(xvi) If direction cosines of two lines are proportional to 4, 3, 2 and 1, −2, 1, then the angle between the lines is :
(A) 90° (B) 60°
(C) 45° (D) None of these
Answer:
(C) 45°
SECTION-B
2. Show that fx=
is not one-one.Answer:
3. Prove that :
Answer:
4. If ,
Answer:
5. Find the area of the triangle whose vertices are (0, 0), (−2, 3) and (10, 7).
Answer:
Vertices of A.are
Area
.
6. Find the derivative of
Answer:
Taking Log both sdes
Taking derivative w.rt x
7. Finddydx, when
Answer:
8. Evaluate :
Answer:
By product Rule
9. Evaluate : .
Answer:
10. Solve the differential equation :
Answer:
11. A bag contains 3 red and 5 black balls and a second bag contains 6 red and 4 black balls. A ball is drawn from each bag. Find the probability that both are red.
Answer:
In bag 2,
SECTION – C
12. Prove that :
Answer:
13. Show that the function f(x) = |x − 2|, x ∈ R is continuous but not differentiable at x = 2.
Answer:
since every modular function is continvees for all values of Real no.
is not Differenle able at x=214. Find the equation of tangent at the point t to the curve
Answer:
15. Find the probability distribution of the number of tails in four tosses of a coin
Answer:
Sample space = (1,1) (1,2) (1.3) (1,4) (1,5) (1,6)
Let x be the pasdom vanble that sum is 9
16. Find the area of triangle whose vertices are (1, 2, 3), (2, 5, −1), (−1, 1, 2).
Answer:
SECTION-D
17.Solve the following equations by matrix method :
x + 2y − 3z = − 4,
2x + 3y + 2z = 2,
3x − 3y − 4z = 11.
Answer:
Here
18. Find the area enclosed between the straight line y = x + 2 and the curve
Answer:
OR
Evaluate :
Answer:
19. Find the equation of the perpendicular from the point (3, −1, 11) to the line
Also find the foot of perpendicular.Answer:
Carlerion eq. of line is
Given let in (1,6,3)
To find Inage of P(1,6,3) draw a line PR to given line
Let R be mage of P and Q be the mid point of PR P(1,6,3)
Let (a,b,c) be direction
Apply condition of perpendicular
Any point on line (2) is
Let Q also lies on (1)
Qis mid point of RR
OR
Find the equation of the plane passing through the points (2, 1, 0), (3, −2, −2) and (3, 1, 7).
Answer:
three Points (2,1,0) , (3,-2,-2) (3,1,7)
Eq.of plane is 7
20. Solve graphically the following L. P. P. :
Minimize : Z = 18x + 10y
subject to constraints :
4x + y ≥ 20,
2x + 3y ≥ 30,
x, y ≥ 0.
Answer:
For(1)
X
0
5
y
20
0
For eq -2
X
0
15
y
10
0
Draw the graph
