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Recent questions in CBSE XII
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CBSE XII
CBSE XII
Math
Physics
Chemistry
Biology
In a bank, principal increases continuously at the rate of $5\%$ per year. An amount of $Rs.1000$ is deposited with this bank, how much will it work after $10$ years $(e^{0.5}=1.648)$.
cbse
class12
bookproblem
ch9
sec4
q21
p397
sec-c
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
In a culture, the bacteria count is $1,00,000.$ The number is increased by $10\%$ in $2$hours.In how many hours will the count reach $2,00,000$ if the rate of growth of bacteria is proportional to the number present?
cbse
class12
bookproblem
ch9
sec4
q22
p397
sec-c
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
The general solution of the differential equation\(\frac{\large dy}{\large dx}=e^{x+y}\)is
cbse
class12
bookproblem
ch9
sec4
q23
p397
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $(x^2+xy)\;dy=(x^2+y^2)\;dx$
cbse
class12
bookproblem
ch9
sec5
q1
p406
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve\[y'=\frac{x+y}{x}\]
cbse
class12
bookproblem
ch9
sec5
q2
p406
easy
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve\[(x-y)\;dy-(x+y)\;dx=0\]
cbse
class12
bookproblem
ch9
sec5
q3
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $(x^2-y^2)dx+2xy\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q4
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x^2\large\frac{dy}{dx}$$=x^2-2y^2+xy$
cbse
class12
bookproblem
ch9
sec5
q5
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x\;dy-y\;dx=\sqrt{x^2+y^2}dx$
cbse
class12
bookproblem
ch9
sec5
q6
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $\left\{x\cos\bigg(\large\frac{y}{x}\bigg)\normalsize+y\sin\bigg(\large\frac{y}{x}\bigg)\right\}ydx=\left\{y\sin\bigg(\large\frac{y}{x}\bigg)-\normalsize x\cos\bigg(\large\frac{y}{x}\bigg)\right\}\normalsize xdy$
cbse
class12
bookproblem
ch9
sec5
q7
p406
difficult
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $x\large\frac{dy}{dx}$$-y+x\sin\bigg(\large\frac{y}{x}\bigg)=$$0$
cbse
class12
bookproblem
ch9
sec5
q8
p406
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Show that the differential equation is homogeneous and solve $y\: dx+x\log\bigg(\large\frac{y}{x}\bigg)$$dy-2x\;dy=0$
cbse
class12
bookproblem
ch9
sec5
q9
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q11
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $x^2dy+(xy+y^2)\;dx=0;y=\;1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q12
p406
difficult
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $\large\frac{dy}{dx}-\large\frac{y}{x}$$+cosec\bigg(\large\frac{y}{x}\bigg)$$=0;\;y=\;0\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q14
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $2xy+y^2-2x^2\large\frac{dy}{dx}$$=0;\;y=\;2\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q15
p406
medium
modelpaper
2012
q19
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
A homogeneous differential equation of the form $\frac{\large dx}{\large dy}=h\bigg(\frac{\large x}{\large y}\bigg)$ can be solved by making the substitution
cbse
class12
bookproblem
ch9
sec5
q16
p406
easy
sec-a
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Which of the following is a homogeneous differential equation?
cbse
class12
bookproblem
ch9
sec5
q17
p407
sec-a
easy
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $\large\frac{dy}{dx}$$+2y=\sin x$
cbse
class12
bookproblem
ch9
sec6
q1
p413
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}$$+3y=e^{-2x}$
cbse
class12
bookproblem
ch9
sec6
q2
p413
easy
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}+\frac{y}{x}$$=x^2$
cbse
class12
bookproblem
ch9
sec6
q3
p413
easy
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation$\large\frac{dy}{dx}$$+(\sec x)y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$
cbse
class12
bookproblem
ch9
sec6
q4
p413
easy
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $\cos^2x\large\frac{dy}{dx}$$+y=\tan x\bigg(0\leq x<\large\frac{\pi}{2}\bigg)$
cbse
class12
bookproblem
ch9
sec6
q5
p413
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+2y=x^2\log x$
cbse
class12
bookproblem
ch9
sec6
q6
p413
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $x \log x\large\frac{dy}{dx}$$+y=\large\frac{2}{x}$$\log x$
cbse
class12
bookproblem
ch9
sec6
q7
p413
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $(1+x^2)dy+2xy\;dx=\cot x\;dx\;(x\neq0)$
cbse
class12
bookproblem
ch9
sec6
q8
p413
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $x\large\frac{dy}{dx}$$+y-x+xy\cot x=0\;(x\neq0)$
cbse
class12
bookproblem
ch9
sec6
q9
p414
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $(x+y)\large\frac{dy}{dx}$$=1$
cbse
class12
bookproblem
ch9
sec6
q10
p414
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$
cbse
class12
bookproblem
ch9
sec6
q11
p414
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $(x+3y^2)\large\frac{dy}{dx}=y$$\;(y>0)$
cbse
class12
bookproblem
ch9
sec6
q12
p414
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition$\large\frac{dy}{dx}$$+2y\tan x=\sin x;\;y=o\;when\;x=\large\frac{\pi}{3}$
cbse
class12
bookproblem
ch9
sec6
q13
p414
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $(1+x^2)\large\frac{dy}{dx}$$+2xy=\large\frac{1}{1+x^2}$$;y=0\;when\;x=1$
cbse
class12
bookproblem
ch9
sec6
q14
p414
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $\large\frac{dy}{dx}-$$3y\cot x=\sin 2x;\;y=2\;when\;x=\large\frac{\pi}{2}$
cbse
class12
bookproblem
ch9
sec6
q15
p414
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the equation of curve passing through the origin given that the slope of the tangent to the curve at any point \((x,y)\) is equal to the sum of the coordinates of the point .
cbse
class12
bookproblem
ch9
sec6
q16
p414
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the equation of curve passing through the point(0,2) given that the sum of the coordinates of any point on the curve exceeds the magnitude of the slope of the tangent to the curve at that point by 5
cbse
class12
bookproblem
ch9
sec6
q17
p414
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
The integrating factor of the differential equation $x\large\frac{dy}{dx}$$-y=2x^2 $ is
cbse
class12
bookproblem
ch9
sec6
q18
p414
easy
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
The integrating factor of the differential equation $(1-y^2)\large\frac{dx}{dy}$$+yx=ay\: \;is$
cbse
class12
bookproblem
ch9
sec6
q19
p414
easy
math
sec-a
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the vector and the cartesian equations of the line that passes through the points $(3, -2, -5), (3, -2, 6).$
cbse
class12
bookproblem
ch11
sec2
p478
q9
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the vector and the cartesian equations of the lines that passes through the origin and $(5, -2, 3).$
cbse
class12
bookproblem
ch11
sec2
p477
q8
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
The cartesian equation of a line is $\frac{\large x-5}{\large 3} = \frac{\large y+4}{\large 7} = \frac{\large z-6}{\large 2}$. Write its vector form.
cbse
class12
bookproblem
ch11
sec2
p477
q7
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the cartesian equation of the line which passes through the point (-2, 4, -5) and parallel to the line given by $\frac{\large x+3}{\large 3} = \frac{\large y-4}{\large 5} = \frac{\large z+8}{\large 6}$.
cbse
class12
bookproblem
ch11
sec2
p477
q6
medium
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the equation of the line in vector and in cartesian form that passes through the point with position vector $2\hat{ i}- \hat{j} + 4\hat{k}$ and is in the direction$\hat{i} + 2\hat{j} - \hat{k}$.
cbse
class12
bookproblem
ch11
sec2
p477
q5
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the equation of the line which passes through the point $(1, 2, 3)$ and is parallel to the vector $3\hat{i} + 2\hat{j} -2\hat{k}$. .
cbse
class12
bookproblem
ch11
sec2
p477
q4
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Show that the line through the points $(4, 7, 8), (2, 3, 4)$ is parallel to the line through the points $(-1, -2, 1), (1, 2, 5)$
cbse
class12
bookproblem
ch11
sec2
p477
q3
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Show that the line through the points (1, -1, 2), (3, 4, -2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).
cbse
class12
bookproblem
ch11
sec2
p477
q2
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Show that the three lines with direction cosines $\large \frac{12}{13}, \frac{-3}{13}, \frac{-4}{13}; \;\; \frac{4}{13}, \frac{12}{13}, \frac{3}{13}; \;\; \frac{3}{13}, \frac{-4}{13}, \frac{12}{13}$ are mutually perpendicular.
cbse
class12
bookproblem
ch11
sec2
p477
q1
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, -4), (-1, 1, 2) and ( -5, -5, -2).
cbse
class12
bookproblem
ch11
sec1
p467
q5
difficult
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Show that the points (2, 3, 4), (-1, -2, 1), (5, 8, 7) are collinear.
cbse
class12
bookproblem
ch11
sec1
p467
q4
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
If a line has the direction ratios $-18, 12, -4,$ then what are its direction cosines?
cbse
class12
bookproblem
ch11
sec1
p467
q3
easy
sec-a
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find the direction cosines of a line which makes equal angles with the coordinate axes.
cbse
class12
bookproblem
ch11
sec1
p467
q2
easy
sec-a
modelpaper
2012
q10
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
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