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Recent questions tagged difficult
Questions
Using vectors,prove that the parallelogram on the same base and between the same parallels are equal in area.
cbse
class12
ch10
q14
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
The area of the region in the first quadrant enclosed by the x-axis,the line y=x and the circle $x^2+y^2=32$ is \begin{array}{1 1}(A)\;16\pi\; sq.units & (B)\;4\pi \;sq.units\\(C)\;32\pi\; sq.units & (D)\;24\pi\;sq.units \end{array}
cbse
class12
ch8
q27
p178
objective
exemplar
sec-b
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
2
answers
The area of the region bounded by the y-axis ,$y=\cos x$ and $y=\sin x,0\leq x\leq \large\frac{\pi}{2}$ is\begin{array}{1 1}(A)\;1\sqrt 2sq.units & (B)\;(\sqrt 2+1)sq.units\\(C)\;(\sqrt 2-1)sq.units & (D)\;(2\sqrt 2-1)sq.units \end{array}
cbse
class12
ch8
q24
p177
objective
exemplar
sec-b
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area bounded by the lines $y=4x+5,y=5-x$ and $4y=x+5.$
cbse
class12
ch8
q21
p177
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Compute the area of the bounded by the line $x+2y=2,y-x=1$ and $2x+y=7.$
cbse
class12
ch8
q20
p177
exemplar
sec-c
difficult
modelpaper
2012
q25
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area of region bounded by the triangle whose vertices are $(-1,1),(0,5)$ and $(3,2)$ using integration.
cbse
class12
ch8
q18
p177
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area of the region bounded by the curve $y^2=2x$ and $x^2+y^2=4x.$
cbse
class12
ch8
q16
p177
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area bounded by the curve $y=\sqrt x,x=2y+3$ in the first quadrant and $x$-axis.
cbse
class12
ch8
q15
p177
short-answer
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area of the enclosed by the curve $y=-x^2$ and the straight line $x+y+2=0.$
cbse
class12
ch8
q14
p177
short-answer
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area of the region bounded by the curve $y^2=4x,x^2=4y$.
cbse
class12
ch8
q4
p176
short-answer
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
Find the area of the region bounded by the curve $y=x^3$ and $y=x+6$ and $x=0$.
cbse
class12
ch8
q3
p176
short-answer
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
$\Large\int\frac{\sin x}{3+4\cos^2x}$$dx$=___________.
cbse
class12
ch7
q62
p169
fitb
exemplar
sec-b
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
If $\Large \int\frac{dx}{(x+2)(x^2+1)}=\normalsize a\log\mid 1+x^2\mid+b\tan^{-1}x+\frac{1}{5}\log\mid x+2\mid+C$,then\begin{array}{1 1}(A)\;a=\frac{-1}{10},b=\frac{-2}{5} & (B)\;a=\frac{1}{10},b=\frac{-2}{5}\\(C)\;a=\frac{-1}{10},b=\frac{2}{5} & (D)\;a=\frac{1}{10},b=\frac{2}{5}\end{array}
cbse
class12
ch7
q53
p168
objective
exemplar
sec-c
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
$\Large \int\frac{dx}{\sin(x-a)\sin(x-b)}$ is equal to\begin{array}{1 1}(A)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C & (B)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \\(C)\;cosec(b-a)\log\begin{vmatrix}\frac{\sin(x-b)}{\sin(x-a)}\end{vmatrix}+C &(D)\;\sin(b-a)\log\begin{vmatrix}\frac{\sin(x-a)}{\sin(x-b)}\end{vmatrix}+C \end{array}
cbse
class12
ch7
q49
p167
objective
exemplar
sec-b
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_ {\Large\frac{-\pi}{4}}^{\Large\frac{\pi}{4}} \log(\sin x+\cos x)dx$
cbse
class12
ch7
q47
p166
exemplar
sec-c
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_0^{\Large \pi} x \log \sin xdx$
cbse
class12
ch7
q46
p166
exemplar
sec-b
difficult
math
asked
Jan 15, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_0^{\Large\frac{\pi}{2}}\large\frac{dx}{(a^2\cos^2x+b^2\sin^2x)^2}\quad\normalsize \text{(Hint:Divide Numerator and Denominator by $\cos^4x)$}$
cbse
class12
ch7
q44
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate :$\int \sqrt \tan x \;dx\;$
cbse
class12
ch7
q43
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int e^{-3x}\cos^3xdx$
cbse
class12
ch7
q42
p166
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\int\limits_{\Large \frac{\pi}{3}}^{\Large \frac{\pi}{2}}\large\frac{\sqrt{1+\cos x}}{(1-\cos x)^{\large\frac{5}{2}}}$
cbse
class12
ch7
q41
p166
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int e^{\tan^{-1}x}\bigg(\frac{1+x+x^2}{1+x^2}\bigg)dx$
cbse
class12
ch7
q39
p166
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\displaystyle\int\frac{2x-1}{(x-1)(x+2)(x-3)}dx$
cbse
class12
ch7
q38
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following:$\displaystyle\int\frac{x^2dx}{(x^2+a^2)(x^2+b^2)}$
cbse
class12
ch7
q36
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\displaystyle\int\frac{x^2dx}{x^4-x^2-12}$
cbse
class12
ch7
q35
p165
exemplar
sec-c
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following: $\int\limits_0^{\Large \frac{1}{2}}\frac{dx}{(1+x^2)\sqrt {1-x^2}}$$(Hint:let\;x=\sin\theta)$
cbse
class12
ch7
q34
p165
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following as limits of sums: $ \int\limits_0^2e^xdx$
cbse
class12
ch7
q28
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following as limits of sums: $\int\limits_0^2(x^2+3)dx$
cbse
class12
ch7
q27
p165
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following : $\begin{align*} \int \frac{\sin^6x+\cos^6x}{\sin^2x \cos^2x}dx \end{align*}$
cbse
class12
ch7
q23
p164
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\frac{\sin^{-1}x}{(1-x^2)^{\frac{3}{2}}}dx$
cbse
class12
ch7
q21
p164
short-answer
exemplar
sec-b
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\int\sqrt {2ax-x^2}dx$
cbse
class12
ch7
q20
p164
exemplar
short-answer
sec-a
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate the following $\displaystyle\int \large \frac{( x)}{\sqrt x+1}$$dx \quad(Hint:Put\;\sqrt x=z)$
cbse
class12
ch7
q10
p164
short-answer
exemplar
sec-a
difficult
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
The maximum value of $\Large\frac{1}{x}$ is:
cbse
class12
ch6
q59
p141
objective
exemplar
sec-a
difficult
math
asked
Jan 12, 2013
by
sreemathi.v
1
answer
$f(x)=x^x$ has a stationary point at
cbse
class12
ch6
q58
p141
objective
exemplar
sec-a
difficult
math
asked
Jan 12, 2013
by
sreemathi.v
1
answer
The smallest value of the polynomial $x^3-18x^2+96x$ in [0,9] is
cbse
class12
ch6
q53
p141
objective
exemplar
difficult
sec-c
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
AB is a diameter of a circle and C is any point on the circle.Show that the area of $\bigtriangleup ABC$ is maximum,when it is isosceles.
cbse
class12
ch6
q32
p138
exemplar
difficult
sec-c
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
If the sum of the surface areas of cube and a sphere is constant.What is the ratio of an edge of the cube to the diameter of the sphere,when the sum of their volumes is minimum?
cbse
class12
ch6
q31
p138
exemplar
difficult
sec-c
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Show that $f(x)=2x+\cot^{-1}x+log\bigg(\sqrt {(1+x^2)}-x\bigg)$ is increasing in R.
cbse
class12
ch6
q20
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the equation of the normal lines to the curve $3x^2-y^2=8$ which are parallel to the line x+3y=4.
cbse
class12
ch6
q17
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).
cbse
class12
ch6
q16
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Find the condition that the curves $2x=y^2$ and $2xy=k$ intersect orthogonally.
cbse
class12
ch6
q12
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
A man, 2m tall, walks at the rate of $1\frac{2}{3}m/s$ towards a street light which is $5\frac{1}{3}m$ above the ground.At what rate is the tip of his shadow moving?At what rate is the length of the shadow changing when he is $3\frac{1}{3}m$ from the base of the light?
cbse
class12
ch6
q8
p135
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
Two men A and B start with velocities v at the same time from the junction of two roads inclined at $45^\circ$ to each other.If they travel by different roads,find the rate at which they are being separated.
cbse
class12
ch6
q4
p135
short-answer
exemplar
difficult
sec-b
math
asked
Jan 10, 2013
by
sreemathi.v
1
answer
The probability distribution of a random variable x is given as under:\[P(X=x)=\left \{\begin{array}{1 1}kx^2 & for\;x=1,2,3\\2kx & for\;x=4,5,6\\0 & otherwise\end{array}\right.\]Where k is a constant.Calculate\[(i)\;E(X)\quad(ii)\;E(3X^2)\quad(iii)\;P(X\geq 4)\]
cbse
class12
ch13
q51
p278
exemplar
sec-c
difficult
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
Let X be a discrete random variable whose probability distribution is defined as follows:\[P(X=x)=\left \{\begin{array}{1 1}k(x+1) & for\;x=1,2,3,4\\2kx & for\;x=5,6,7\\0 & otherwise\end{array} \right.\]where k is a constant. Calculate\[(i)\;the\;value\;of\;k\quad(ii)\;E(X)\quad(iii)\;standard\;deviation\;of\;X\]
cbse
class12
ch13
q49
p277
exemplar
sec-c
difficult
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
A shop keeper sells three types of flower seeds $A_1,A_2 and\;A_3$.They are sold as a mixture where the proportions arev4:4:2 respectively.The germination rates of the three types of seeds are 45%,60% and 35%.Calculate the probability\[\begin{array}{1 1}(i)\;of\;a\;randomly\;chosen\;seed\;to\;germinate\\(ii)\;that\;it\;will\;not\;germinate\;given\;that\;seed\;is\;of\;type\;A_3\\(iii)\;that\;it\;is\;of\;the\;type\;A_2\;given\;that\;a\;randomly\;chosen\;seed\;does\;not\;germinate\end{array}\]
cbse
class12
ch13
q43
p276
exemplar
sec-c
difficult
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
Three bags contain a number of red and white balls as follows:
cbse
class12
ch13
q41
p276
exemplar
sec-c
difficult
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
Maximise and minimise Z=3x-4y, subject to $\qquad$ \begin{array}{1 1}x-2y\leq 0\\-3x+y\leq 4\\x-y\leq 6\\x,y\geq 0\end{array}
cbse
class12
ch12
q25
p254
exemplar
sec-c
difficult
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
A company makes 3 model of calculators:A,B and c at factory I and factory II.The company has orders for at least 6400 calculators of model A;4000 calculator of model B and 4800 calculator of model C.At factory I ,50 calculators of model A,50 of model B and 30 of model C are made every day;at factory II,40 calculators of model A,20 of model B and 40 of model C are made every day.It costs Rs 12000 and Rs 15000 each day to operate factory I and II respectively.Find the number of days each factory should operate to minimize the operating costs and still meet the demand.
cbse
class12
ch12
q24
p254
exemplar
sec-c
difficult
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
In order to supplement daily diet,a person wishes to take some X and some wishes Y tablets. The person needs atleast 18 milligrams of iron ,21 milligrams of calcium and 16 milligram of vitamins.The price of each tablet of X and Y is Rs.2 and Rs.1 respectively.How many tablets of each should the person take in order to satisfy the above requirement at the minimum cost? The contents of iron ,calcium and vitamins in X and Y(in milligrams per tablet) are given as below: \[\] $\begin{matrix} \underline{\text{Tablets} }& \underline{\text{Iron}}&& \underline{\text{Calcium}} && \underline{\text{Vitamin}} \\ \text{X}& 6 &&3 && 2 \\ \text{Y}& 2 &&3 && 4 \\ \end{matrix}$
cbse
class12
ch12
q23
p254
exemplar
sec-c
difficult
math
asked
Jan 8, 2013
by
sreemathi.v
1
answer
A manufacturer produces two Models of bikes-Model X and Model Y.Model X takes a 6 man-hours to make per unit,while Model Y takes 10 man-hours per unit.There is a total of 450 man-hour available per week.Handling and marketing costs are Rs 2000 and Rs 1000 per unit for models X and Y respectively.The total funds available for these purposes are Rs 80,000 per week.Profits per unit for models X and Y are Rs 1000 and Rs 500,respectively.How many bikes of each model should the manufacturer produce so as to yield a maximum profit.Find the maximum profit.
cbse
class12
ch12
q22
p253
exemplar
sec-c
difficult
math
asked
Jan 7, 2013
by
sreemathi.v
1
answer
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