1
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Let $$y(x)$$ be a solution of the differential equation
$$\left( {1 + {e^x}} \right)y' + y{e^x} = 1.$$
If $$y(0)=2$$, then which of the following statement is (are) true?
A
$$y(-4)=0$$
B
$$y(-2)=0$$
C
$$y(x)$$ has a critical point in the interval $$(-1, 0)$$
D
$$y(x)$$ has no critical point in the interval $$(-1,0)$$
2
JEE Advanced 2015 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-2
Consider the family of all circles whose centres lie on the straight line $$y=x,$$ If this family of circle is represented by the differential equation $$Py'' + Qy' + 1 = 0,$$ where $$P, Q$$ are functions of $$x,y$$ and $$y'$$ $$\left( {here\,\,\,y' = {{dy} \over {dx}},y'' = {{{d^2}y} \over {d{x^2}}}} \right)$$ then which of the following statements is (are) true?
A
$$P = y + x$$
B
$$\,P = y - x$$
C
$$\,P + Q = 1 - x + y + y' + {\left( {y'} \right)^2}$$
D
$$\,P - Q = 1 - x + y - y' - {\left( {y'} \right)^2}$$
3
IIT-JEE 2012 Paper 1 Offline
MCQ (More than One Correct Answer)
+4
-1
If $$y(x)$$ satisfies the differential equation $$y' - y\,tan\,x = 2x\,secx$$ and $$y(0)=0,$$ then
A
$$y\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {8\sqrt 2 }}$$
B
$$y'\left( {{\pi \over 4}} \right) = {{{\pi ^2}} \over {18}}$$
C
$$y\left( {{\pi \over 3}} \right) = {{{\pi ^2}} \over 9}$$
D
$$y'\left( {{\pi \over 3}} \right) = {{4\pi } \over 3} + {{2{\pi ^2}} \over {3\sqrt 3 }}$$
4
IIT-JEE 2006
MCQ (More than One Correct Answer)
+5
-1.25
A curve $$y=f(x)$$ passes through $$(1,1)$$ and at $$P(x,y),$$ tangent cuts the $$x$$-axis and $$y$$-axis at $$A$$ and $$B$$ respectively such that $$BP:AP=3:1,$$ then
A
equation of curve is $$xy'-3y=0$$
B
normal at $$(1,1)$$ is $$x+3y=4$$
C
curve passes through $$(2, 1/8)$$
D
equation of curve is $$xy'+3y=0$$
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