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Signature of Supdt:
Roll No:
……………………………………………….
……………………………………………….
MRD-XII-14(S)
Serial No. of Answer Book:
Mathematics
Fic No. (For Office Use Only)
……………………………………………….
(Part-II)
……………………………………………….
Fic No. (For Office Use Only)
……………………………………………….
Total Time: 3:00 Hrs
Mathematic (Part-II)
Total Marks: 100
Note: There are THREE sections in this paper i.e. Section A, B and C.
“Section-A”
Time: 20 Minutes
Marks: 20
Note. Use this sheet for this section. No mark will be awarded for cutting, erasing or over writing.
Q.1. Write the correct option i.e. A, B, C and D in the empty box provided opposite to each part.
i.
Any subset of Cartesian product is called _____________
(A)
Function
(B)
Domain
(C)
Range
(D)
Relation
ii.
Range R = { ________∈A/(a,b) ∈R}
(A)
a
(B)
b
(C)
(a, b)
(D)
None of these
iii.
The function f(x) = x2 + x is ___________.
(A)
Odd
(B)
Even
(C)
Constant
(D)
None of these
1/X
iv.
(1 + x) = ____________.
→0
(A)
a
(B)
x
(C)
e
(D)
1/e
2
v.
(3x + 6) = ______________
(A)
3x2 + 6
(B)
6x +6
(C)
6x2
(D)
6x
x
(a ) = _____________.
vi.
vii.
viii.
ix.
x.
xi.
xii.
xiii.
xiv.
(A)
exlna
(B)
axlna
(C)
ax
(D)
lna
kx
dx
=
____________
+
C
(A)
ekxlna
(B)
aKX/lna
(C)
eKX/k
(D)
eKX
If P1 (2, 3) and P2 (6, 3) be two prints of a line segment, then mid point is ___________.
(A)
(4 , 3)
(B)
(3 , 4)
(C)
(2 , 3)
(D)
(6 , 3)
F
= ____________
(A)
1/2
(B)
2
(C)
2/3
(D)
3/2
If m1 and m2 are the slopes of perpendicular lines l1 and l2 then ___________
(A)
m1 , m2 = 1
(B)
m1 , m2 = -1 (C)
m1 = m2 (D)
m1 = -m
An equation x/a + y/b = 1 is _________ form.
(A)
Slope
(B)
Normal
(C)
Two-Point
(D)
None of these
If three points A, B, C lie on the same line is called…………………….
(A)
Collinear
(B)
Non-Collinear (C)
Normal
(D)
None of these
Length of the latus rectum of ellipse x2/9 + y2/16 = 1 is ____________.
(A)
18
(B)
9/2
(C)
9/4
(D)
9/16
Unit vector of → = 2i + 6k is ____________.
(A)
√
(C)
xv.
xvi.
xvii.
xviii.
xix.
xx.
√
(2i + 6K)
(B)
(2i + 6K)
(D)
√
√
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(vii)
(viii)
(ix)
(x)
(xi)
(xii)
(xiii)
(2i + 6K)
(2i + 6K)
(xiv)
a.b=||||___________
(A)
Sinθ
(B)
-Sinθ
(C)
Cosθ
(D)
-Cosθ
The centre of the circle (x – h)2 + (x – K)2 = r2 is ___________
(A)
(-h, -k)
(B)
(-k, -h)
(C)
(h, k)
(D)
(k, h)
If a plane is titled slightly in any direction, the section is an oval curve called ___________
(A)
Circle
(B)
ellipse
(C)
hyperbola
(D)
parabola
2i→.(3→ x 2→) =____________
(i)
(xiv)
(xv)
(xvi)
(xvii)
(A)
12
(B)
12i
(C)
-12
The vertex of the parabola (y – 2)2 = 8(x -4) is ___________
(A)
(-2 , -4)
(B)
(2 , 4)
(C)
(-4 , -2)
If the degree of P(x) is less than that of Q(x), then P(x) / Q(x) is
called ___________ rational function.
(A)
Proper
(B)
improper
(C)
Both A and B
(D)
0
(xviii)
(D)
(4 , 2)
(xix)
(D)
None of these
(xx)
MRD-XII-14(S)
Mathematics (Part-II)
Total Time: 2:40 Hrs.
Total Marks: 80
“Section-B”
Marks: 50
Q.2. Answer any TEN parts. Each part carries equal marks.
i.
ii.
iii.
iv.
v.
vi.
vii.
viii.
ix.
x.
xi.
xii.
xiii.
√X+7 → 2 X−2
Find the derivative ab – initio of the function y = (2x + 1)2
If f: x X2 – 2 and g: x x + 3 find fog.
Evaluate the limit
If y = Tanx + % Tanx + √Tanx + ⋯ … … . .
Prove that (2y – 1) dy/dx = Sec2x
)
*
Evaluate +)
*
Sin2x
Cosx
dx
Find value of K, so that the point (K, 4) lies on the line joining the prints (1, 5) and 2, 3).
Transform 4x – 3y + 14 = 0 into normal form.
Graph the linear inequality – 3x + 2y < 7
Find the equation of the circle whose centre is (3 , 4) and which contains the point (8, 9).
Show that I + 7j + 3k is perpendicular to both i– j + 2k and 2i + j – 3k.
Find the equation of the hyperbola whose Foci are (+5, 0) and vertices are (+1, 0).
Find lnx dx
Find derivative of (23)56 .
“Section-C”
Marks: 30
Note: Attempt any three questions. Each question carries equal marks.
Q.3. (a)
(b)
Prove that lim X0 Sinx / x = 1
Discus the continuity of the function.
f:x x–4 ,
-1 < x < 2
2
x –6 ,
2<x<5
Q.4. Using chain rule differentiate x2 + 1 / x2 – 1
(a)
(b)
Q.5. (a)
(b)
Q.6. (a)
(b)
W.r.t X3
Evaluate (7) (7)
Show that the point A(4, -2, 1), B(5, 1, 6), C(2,2,5) and D(3,5,0) are coplanar.
Find the equation of the tangent and normal at the point (3, 12/5) to the ellipse x2/25 + y2/ 9 = 1
Find the equation of the circle which contains the points (4,1), (6,5) and has its centre on the
line 4x + y – 16 = 0
Let ABC be a triangle whose vertices are A(O, O), B(8, 6), C(12, 0), Verify that median of a triangle
ABC are concurrent.
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