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Recent questions in CBSE XII
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CBSE XII
CBSE XII
Math
Physics
Chemistry
Biology
Choose the correct answers in the value of $\int\limits_0^1\tan^{-1}\bigg(\frac{\large 2x-1}{\large 1+x-x^2}\bigg)dx\;is$\[(A)\;1\qquad(B)\;0\qquad(C)\;-1\qquad(D)\;\frac{\pi}{4}\]
cbse
class12
bookproblem
ch7
misc
q44
p354
sec-a
medium
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Integrate the function\[\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}\qquad[Hint:\frac{1}{x^\frac{1}{2}+x^\frac{1}{3}}=\frac{1}{x^\frac{1}{3}\bigg(1+x^\frac{1}{6}\bigg)},put\;x=t^6]\]
cbse
class12
bookproblem
ch7
misc
q5
p352
sec-b
difficult
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Integrate the function\[\int\frac{1}{x^2(x^4+1)^\frac{3}{4}}\]
cbse
class12
bookproblem
ch7
misc
q4
p352
sec-b
medium
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Integrate the function\[\frac{1}{x\sqrt{ax-x^2}}[Hint:Put\;x=\frac{a}{t}]\]
cbse
class12
bookproblem
ch7
misc
q3
p352
sec-b
medium
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Integrate the function\[\frac{1}{\sqrt{x+a}+\sqrt{x+b}}\]
cbse
class12
bookproblem
ch7
misc
q2
p352
sec-b
medium
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Integrate the function\[\int\frac{1}{x-x^3}\]
cbse
class12
bookproblem
ch7
misc
q1
p352
sec-b
difficult
math
asked
Dec 2, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=e^x+1\qquad:\;y''-y'=0$
cbse
class12
bookproblem
ch9
sec2
q1
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x^2+2x+C\qquad:\;y'-2x-2=0$
cbse
class12
bookproblem
ch9
sec2
q2
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\cos x+C\qquad:y'+\sin x=0$
cbse
class12
bookproblem
ch9
sec2
q3
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation\[y=\sqrt{1+x^2}\qquad:\;y'\;=\frac{xy}{1+x^2}\]
cbse
class12
bookproblem
ch9
sec2
q4
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=Ax\qquad:\;xy'\;=\;y\;(x\neq0)$
cbse
class12
bookproblem
ch9
sec2
q5
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=x\sin x\qquad:xy'=y+x\sqrt{x^2-y^2} (x\neq0\;and\;x>y\;or\;x<-y)$
cbse
class12
bookproblem
ch9
sec2
q6
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $xy=\log\: y+C\qquad:y'=\large\frac{y^2}{1-xy}$$\;(xy\neq1)$
cbse
class12
bookproblem
ch9
sec2
q7
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y-\cos y=x\qquad:\;(y\sin y+\cos y+x)y'=y$
cbse
class12
bookproblem
ch9
sec2
q8
385
medium
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation
cbse
class12
bookproblem
ch9
sec2
q9
p385
medium
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Verify that the given function(explicit or implicit)is a solution of the corresponding differential equation $y=\sqrt{a^2-x^2}\;x\in\;(-a,a):\;x+y\;\large\frac{dy}{dx}$$=0(y\neq0)$
cbse
class12
bookproblem
ch9
sec2
q10
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
The number of arbitrary constants in the general solution of a differential equation of fourth order are
cbse
class12
bookproblem
ch9
sec2
q11
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
The number of arbitrary constants in the particular solution of a differential equation of third order are
cbse
class12
bookproblem
ch9
sec2
q12
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $\large\frac{x}{a}+\frac{y}{b}=1$
cbse
class12
bookproblem
ch9
sec3
q1
p391
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.$y^2=a(b^2-x^2)$
cbse
class12
bookproblem
ch9
sec3
q2
p391
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. $y=a\: e^{3x}+b\: e^{-2x}$
cbse
class12
bookproblem
ch9
sec3
q3
p391
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^{2x}(a+bx)$
cbse
class12
bookproblem
ch9
sec3
q4
p391
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b $y=e^x(a\;\cos x+b\;\sin x)$
cbse
class12
bookproblem
ch9
sec3
q5
p391
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form the differential equation of the family of circles touching the \(y\) - axis at origin.
cbse
class12
bookproblem
ch9
sec3
q6
p391
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form the differential equation of the family of parabolas having vertex at origin at axis along positive y-axis.
cbse
class12
bookproblem
ch9
sec3
q7
p391
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form the differential equation of the family of ellipses having foci on $y$-axis and centre at origin.
cbse
class12
bookproblem
ch9
sec3
q8
p391
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form the differential equation of the family of hyperbolas having foci on $x$-axis and centre at origin.
cbse
class12
bookproblem
ch9
sec3
q9
p391
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Form the differential equation of the family of circles having centre on $y$-axis and radius $3$ units.
cbse
class12
bookproblem
ch9
sec3
q10
p391
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
2
answers
Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?
cbse
class12
bookproblem
ch9
sec3
q11
p391
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Which of the following differential equations has $y = x$ as one of its particular solution?
cbse
class12
bookproblem
ch9
sec3
q12
p391
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\large\frac{dy}{dx}=\frac{1-\cos x}{1+\cos x}$
cbse
class12
bookproblem
ch9
sec4
q1
p395
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\large\frac{dy}{dx} $$=\sqrt {4-y^2} \; (-2\lt y \lt 2) $
cbse
class12
bookproblem
ch9
sec4
q2
p395
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\large\frac{dy}{dx}$$+y=1(y\neq1)$
cbse
class12
bookproblem
ch9
sec4
q3
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\sec^2x\;\tan y\;dx+\sec^2y\;\tan x\;dy=0$
cbse
class12
bookproblem
ch9
sec4
q4
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $(e^x+e^{-x})\;dy-(e^x-e^{-x})\;dx=0$
cbse
class12
bookproblem
ch9
sec4
q5
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\large\frac{dy}{dx}$$=(1+x^2)(1+y^2)$
cbse
class12
bookproblem
ch9
sec4
q6
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $y\;\log\: y\;dx-x\;dy=0$
cbse
class12
bookproblem
ch9
sec4
q7
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $x^5\large\frac{dy}{dx}$$=-y^5$
cbse
class12
bookproblem
ch9
sec4
q8
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $\large\frac{dy}{dx}=$$\sin^{-1}x$
cbse
class12
bookproblem
ch9
sec4
q9
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the general solution $e^x\tan y\;dx+(1-e^x)\sec ^2y\;dy=0$
cbse
class12
bookproblem
ch9
sec4
q10
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $(x^3+x^2+x+1)\large\frac{dy}{dx}$$=2x^2+x;y=1\;when\;x=0$
cbse
class12
bookproblem
ch9
sec4
q11
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $x(x^2-1)\large\frac{dy}{dx}$$=1;y=0\;when\;x=2$
cbse
class12
bookproblem
ch9
sec4
q12
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $\cos\bigg(\large\frac{dy}{dx}\bigg)$$=a\;(a\;\in\;R);y=2\;when\;x=0$
cbse
class12
bookproblem
ch9
sec4
q13
p396
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition$\large\frac{dy}{dx}=$$y\tan x;\;y=1\;when\;x=0$
cbse
class12
bookproblem
ch9
sec4
q14
p396
easy
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the equation of a curve passing through the point $(0,0)$ and whose differential equation is $y'=e^x\;\sin x.$
cbse
class12
bookproblem
ch9
sec4
q15
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
For the differential equation $xy\large\frac{dy}{dx}=$$(x+2)(y+2),$ find the solution curve passing through the point $(1,-1)$.
cbse
class12
bookproblem
ch9
sec4
q16
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the equation of a curve passing through the point (0,-2) given that at any point (x,y) on the curve,the product of the slope of its tangent and y coordinate of the point is equal to the x coordinate of the point.
cbse
class12
bookproblem
ch9
sec4
q17
p396
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
At any point (x,y) of a curve,the slope of the tangent is twice the slope of the line segment joining the point of contact to the point (-4,-3).Find the equation of the curve given that it passes through (-2,1).
cbse
class12
bookproblem
ch9
sec4
q18
p396
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$
cbse
class12
bookproblem
ch9
sec4
q20
p397
sec-c
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
The volume of spherical balloon being inflated changes at a constant rate.If initially its radius is 3units and after 3seconds it is 6units.Find the radius of balloon after t seconds.
cbse
class12
bookproblem
ch9
sec4
q19
p396
sec-c
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
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