STUPIDSID
Answer the following questions with most appropriate answer
1 (a) 1
The maximum value of y = 3cos2x is ____
(a) 1
(b)2
(c)-1
(d)3.
(a) 1
(b)2
(c)-1
(d)3.
1 M
1 (a) 2
If √x+√y=√a then dy/dx_____
a) √(y/a)
(b) √(x/a)
(c) -√(y/x)
(d) -√(y/a).
a) √(y/a)
(b) √(x/a)
(c) -√(y/x)
(d) -√(y/a).
1 M
1 (a) 3
The ( a ? x ) y2 = x2 ( a + x ) is symmetric about
(a) X-axis
(b)Y-axis
(c)both X and Y axis (d) line Y = X
(a) X-axis
(b)Y-axis
(c)both X and Y axis (d) line Y = X
1 M
1 (a) 4
Tangents at origin to the curve y2( a + x ) = x2( 3 a ? x ) is ____
a) ±√x
(b)1
(c) ±√2x
(d) none of these.
a) ±√x
(b)1
(c) ±√2x
(d) none of these.
1 M
1 (a) 5
The parametric equations of x2/3 + y2/3 = a2/3 ( a ≠ 0 ) are
(a) x = a cos θ, y = a sin θ
(b)x = a 3 cos θ , y = a 3 sin θ
(c)x = a cos 3 θ , y = a sin 3 θ
(d)x=1, y=0
(a) x = a cos θ, y = a sin θ
(b)x = a 3 cos θ , y = a 3 sin θ
(c)x = a cos 3 θ , y = a sin 3 θ
(d)x=1, y=0
1 M
1 (a) 6
The area bounded by the curve y = x3 , x-axis and two ordinates x = 1 to x = 2 equal to
(a) 15/2
(b)15/3
(c)15/5
(d)15/4
(a) 15/2
(b)15/3
(c)15/5
(d)15/4
1 M
1 (a) 7
\[ \lim_{x\to 2}\dfrac{x^{2}-x-2}{x^{2}-4}= \ \_\_\_\_\_\_\]
(a) 7/4
(b)3/4
(c)2
(d)-3/4
(a) 7/4
(b)3/4
(c)2
(d)-3/4
1 M
Answer the following questions with most appropriate answer
1 (b) 1
The slope of the tangent to the curve y = xex at ( 0 , 0 ) is___
(a) 0
(b)1
(c)-1
(d)4
(b)1
(c)-1
(d)4
1 M
1 (b) 2
The point of inflection of\[\dfrac{x^{3}}{3}-\dfrac{x^{2}}{2}-2x+14\] is______
(a) 1/2
(b)-1/2
(c)-1
(d)-2
(a) 1/2
(b)-1/2
(c)-1
(d)-2
1 M
1 (b) 3
Using the matrix method, the solution of x + y = 2 , 4 x + y = 6
\[ (a)\left ( \dfrac{-4}{3},\dfrac{2}{3} \right ) (b)\left ( \dfrac{4}{3},\dfrac{-2}{2} \right ) (c)\left ( \dfrac{4}{3},\dfrac{2}{3} \right )(d)(1,2)\]
\[ (a)\left ( \dfrac{-4}{3},\dfrac{2}{3} \right ) (b)\left ( \dfrac{4}{3},\dfrac{-2}{2} \right ) (c)\left ( \dfrac{4}{3},\dfrac{2}{3} \right )(d)(1,2)\]
1 M
1 (b) 4
\[\int e^{2x} \cos 3xdx=\_\_\_\_+c \]
\[(a)\dfrac{e^{2x}}{13}(2 \cos3x+ 3\sin 3x)(b)\dfrac{e^{2x}}{13}(3 \cos3x+ 2\sin3x) (c)\dfrac{e^{2x}}{13}(2 \cos3x+ 3\sin 3x)\] (d) none of these.
\[(a)\dfrac{e^{2x}}{13}(2 \cos3x+ 3\sin 3x)(b)\dfrac{e^{2x}}{13}(3 \cos3x+ 2\sin3x) (c)\dfrac{e^{2x}}{13}(2 \cos3x+ 3\sin 3x)\] (d) none of these.
1 M
1 (b) 5
If y = ln√(2x) the derivative of the function y with respect to x is ____
(a) 0
(b)-1/2x (
(c) 1/2x
(d)1/x
(a) 0
(b)-1/2x (
(c) 1/2x
(d)1/x
1 M
1 (b) 6
f ( x ) = x2+ 4 x + 5 has the minimum value ____
(a) 0
(b)1
(c)-1
(d)2
(a) 0
(b)1
(c)-1
(d)2
1 M
1 (b) 7
A curve which passes through the origin and has the slope -1/3 is given by
(a) x + 3 y ? 1 = 0 (b) x + 3 y = 0
(c)x ? 3 y = 0
(d)none of these
(a) x + 3 y ? 1 = 0 (b) x + 3 y = 0
(c)x ? 3 y = 0
(d)none of these
1 M
Answer the given MCQ.
1 (c) 1
F(x) is strictly increasing function on R then______
A) f(x) = 0 for all x
B) f(x) > 0 for all x
C) f(x) < 0 for all x
D) none of these.
A) f(x) = 0 for all x
B) f(x) > 0 for all x
C) f(x) < 0 for all x
D) none of these.
1 M
1 (c) 2
F(x) is strictly decreasing function on R then______
A) f(x) = 0 for all x
B) f(x) > 0 for all x
C) f(x) < 0 for all x
D) none of these.
A) f(x) = 0 for all x
B) f(x) > 0 for all x
C) f(x) < 0 for all x
D) none of these.
1 M
1 (c) 3
dy/dx = ky, k > 0 is the deferential equation for_______
A) Population Model
C) Cooling Model
B) Mixing problem model
D) none of these.
A) Population Model
C) Cooling Model
B) Mixing problem model
D) none of these.
1 M
1 (c) 4
dy/dx = x then y = _______
(a) y=x2 \[(b)y=\dfrac{\infty^{2} }{0}+c\] (c) y=x (d) none of these.
(a) y=x2 \[(b)y=\dfrac{\infty^{2} }{0}+c\] (c) y=x (d) none of these.
1 M
1 (c) 5
Curve of y = x2 +3 is______
A) Symmetric with respect to x axis.
B) Symmetric with respect to y axis.
C) Symmetric with respect to origin.
D) none of these.
A) Symmetric with respect to x axis.
B) Symmetric with respect to y axis.
C) Symmetric with respect to origin.
D) none of these.
1 M
1 (c) 6
r = a cosθ is_____
(a) Line (b) laminiscate (c) circle (d) None of these.
(a) Line (b) laminiscate (c) circle (d) None of these.
1 M
1 (c) 7
\[\int_{0}^{1}x^{2}dx\]is_____
(a) area under a line (b) area under circle (c) area under parabola (d) none of these.
(a) area under a line (b) area under circle (c) area under parabola (d) none of these.
1 M
Answer the given MCQ.
1 (d) 1
\[\int_{a}^{-a} f(x)dx=0\]if_________
(a) f is an odd function (b) f is neither odd nor even function (c) f is an even function (d) none of these.
(a) f is an odd function (b) f is neither odd nor even function (c) f is an even function (d) none of these.
1 M
1 (d) 2
z = x2 + y2 is ________
A) Cone
B) Paraboloid
C) Sphere
D) None of there.
A) Cone
B) Paraboloid
C) Sphere
D) None of there.
1 M
1 (d) 3
\[ \lim_{(x,y)\to(0,0)}\dfrac{x^{2}-yx}{x+y}=\]_____
A)2
B) 1
C) 0
D) -1
A)2
B) 1
C) 0
D) -1
1 M
1 (d) 4
\[If z=x^{2}-y^{2}then \dfrac{\partial z }{\partial x}=\]_______
A)2y
B) 0
C) 2z
D) none of these.
A)2y
B) 0
C) 2z
D) none of these.
1 M
1 (d) 5
Equation of tangent plane of z = x at (2,0,2) is
A)z=x
B) x+y+z=2
C) x+z=0
D) none of these.
A)z=x
B) x+y+z=2
C) x+z=0
D) none of these.
1 M
1 (d) 6
If z = x2 +y2 + 3 minimum value z is ______
A) 3
B) ∞
C) 0
D) none of these.
A) 3
B) ∞
C) 0
D) none of these.
1 M
1 (d) 7
Y = sin2x is increasing in interval _________
A) (0,π) \[
B) (0,\dfrac{\pi}{4})\
(c)\ (0,\dfrac{\pi}{2})\]
D) none of these.
A) (0,π) \[
B) (0,\dfrac{\pi}{4})\
(c)\ (0,\dfrac{\pi}{2})\]
D) none of these.
1 M
2 (a)
Test the convergence of\[\dfrac{1}{1.2.3}+\dfrac{3}{2.3.4}+\dfrac{5}{3.4.5}+.........\].
3 M
2 (b)
Prove that\[1+\dfrac{2}{3}+\dfrac{4}{9}+\dfrac{8}{27}+\dfrac{16}{81}+......\]converges and find its sum.
4 M
2 (c)
State Taylor's series for one variable and hence find √(36.12).
7 M
3 (a)
Find \[\dfrac{\partial w }{\partial r},\dfrac{\partial w }{\partial s}\] in terns of r and s if w =2y+z2 where \[x=\dfrac{r}{s},y=r^{2}+ln s, z=2r\].
3 M
3 (c)
\[If u=\cos ec^{-1}\left [ \dfrac{x^{1/2}+y^{1/2}}{x^{1/3}+y^{1/3}} \right ]^{1/2} show that x^{2}\dfrac{\partial^2 u}{\partial x^2}+2xy\dfrac{\partial^2 u}{\partial x \partial y}+y^{2}\dfrac{\partial^2 u}{\partial y^2}=\dfrac{\tan u}{144}(13+\tan ^{2} u)\]. Also state Euler's modified theorem.
7 M
4 (a)
Evaluate \[ \lim_{x\to 0}\left [ \dfrac{1}{x^{2}}-\dfrac{1}{\sin^{2}x} \right ]\].
3 M
4 (b)
Expand ex sin y in powers of x and y upto third degree.
4 M
4 (c)
A rectangular box, open at the top, is to have a volume 32 c.c. Find the
dimensions of the box requiring least material for its construction.
7 M
5 (a)
Find the volume of the tetrahedron bounded by the plane x + y + z = 2 and the
planes x = 0 , y = 0 and z = 0 .
3 M
5 (b)
Trace the curve r = a ( 1 + cos θ ).
4 M
5 (c)
Evaluate \[\int_{0}^{4a}\int_{x^{2}/4a}^{2\sqrt{ax}} \limits dydx\] by changing the order of integration.
7 M
6 (a)
Evaluate \[\int_{0}^{\infty }\dfrac{dx}{x^{2}+1}\].
3 M
6 (b)
Evaluate the integral \[\int_{0}^{1}\int_{0}^{1-x}\limits e^{\dfrac{y}{e^{x+y}}}\] dydx by changing the variables x + y = u , y = uv.
4 M
6 (c)
Evaluate \[\iint_{R}\limits x^{2}\] dA where R is the region in the first quadrant bounded by the hyperbola xy = 16 and the lines y = x , y = 0 and x = 8 .
7 M
7 (a)
Test the convergence of \[\sum_{n=1}^{\infty }\dfrac{2tan^{-1}n}{1+n^{2}}\].
3 M
7 (b)
Find the equation of tangent plane and normal line to the surface xyz = 6 at
( 1 , 2 , 3 )
4 M
7 (c)
Evaluate \[\int_{0}^{1}\limits \int_{0}^{\sqrt{1-x^{2}}}\limits\int_{0}^{\sqrt{1-x^{2}-y^{2}}}\limits\] xyz dzdydx.
7 M
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