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Math
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Math
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Recent questions tagged modelpaper-2014-chennai
Questions
Evaluate : \[\] $ \int \large\frac{1}{\sin^4x+\sin^2x \cos^2x + \cos^4x}$$dx$
modelpaper-2014-chennai
cbse
class12
math
sec-c
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If the sum of the lengths of the hypotenuse and a side of a right triangle is given, show that the area of the triangle is maximum, when the angle between them is $60^{\circ}$.
modelpaper-2014-chennai
cbse
class12
math
sec-c
q28
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. The school A wants to award Rs.x each, Rs.y each and Rs.z each for the three respective values to 3,2 and 1 students respectively with a total award money of Rs. 1,600. School B wants to spend Rs. 2,300 to award its 4, 1 and 3 students on the respective values ( by giving the same award money to the three values as before ). If the total amount of award for one prize on each value is Rs. 900 using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for award.
modelpaper-2014-chennai
cbse
class12
math
sec-c
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Two numbers are selected at random ( without replacement ) from the first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of the random variable X, and hence find the mean of the distribution.
modelpaper-2014-chennai
cbse
class12
math
sec-c
q26b
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
There are three coins. One is a two-headed coin ( having head on both faces ), another is a biased coin that comes up heads 75% of the times and third is also a biased coin that comes up tails 40% of the times. One of the three coins is chosen at random and tossed, and it shows heads. What is the probability that it was the two-headed coin?
modelpaper-2014-chennai
cbse
class12
math
sec-c
26a
asked
Mar 25, 2014
by
thanvigandhi_1
2
answers
A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours of fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs. 80 on each piece of type A and Rs. 120 on each piece of type B. How many pieces of type A and B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?
modelpaper-2014-chennai
cbse
class12
math
sec-c
q25
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Using integration, find the area of the region bounded by the triangle whose vertices are (-1, 2) ( 1, 5) and ( 3, 4)
modelpaper-2014-chennai
cbse
class12
math
sec-c
q24
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Find the distance of the point (2, 12, 5) from the point of intersection of the line $ \overrightarrow r = 2\hat i - 4\hat j + 2 \hat k + \lambda ( 3\hat i + 4 \hat j + 2 \hat k ) $ and the plane $ \overrightarrow r. ( \hat i - 2 \hat j + \hat k ) =0.$
modelpaper-2014-chennai
cbse
class12
math
sec-c
23b
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Find the equation of the plane through the line of intersection of the planes $ x+y+z=1$ and $2x+3y+4z=5$ which is perpendicular to the plane $x-y+z=0$. Also find the distance of the plane obtained above, from the origin.
modelpaper-2014-chennai
cbse
class12
math
sec-c
q23a
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Find the value of p, so that the lines $ l_1 : \large\frac{1-x}{3} $$= \large\frac{7y-14}{p} $$= \large\frac{z-3}{2}$ and $l_2 : \large\frac{7-7x}{3p} $$= \large\frac{y-5}{1} $$ = \large\frac{6-z}{5}$ are perpendicular to each other. Also find the equations of a line passing through a point ( 3, 2, -4 ) and parallel to line $l_1$.
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Find the particular solution of the differential equation $ log \bigg( \large\frac{dy}{dx} \bigg) =3x+4y,$ given that $ y=0$ when $x=0$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
If $ x = \cos\: t ( 3-2 \: \cos^2 t)\: and \: y = \sin \: t ( 3-2 \sin^2\: t)$ find the value of $ \large\frac{dy}{dx} $ at $ t = \large\frac{\pi}{4}$
modelpaper-2014-chennai
cbse
class12
math
sec-b
q20
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Using properties of determinants, prove that, \[\] $\begin{vmatrix} 1+a & 1 & 1 \\[0.3em] 1 & 1+b & 1 \\[0.3em] 1 & 1 & 1+c \end{vmatrix} = abc +bc+ca+ab$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ y = Pe^{ax}+Qe^{bx}$, show that \[\] $\large\frac{d^2y}{dx^2}$$-(a+b) \large\frac{dy}{dx}$$+aby=0$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least three successes
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
If $ \tan^{-1} \bigg( \large\frac{x-2}{x-4} \bigg) $$+ \tan^{-1} \bigg( \large\frac{x+2}{x+4} \bigg) $$ = \large\frac{\pi}{4}$ find the value of x.
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
prove that : \[\] $ \tan^{-1} \bigg[ \large\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}} \bigg]$$ = \large\frac{\pi}{4}$$- \large\frac{1}{2}$$ \cos^{-1}x , \large\frac{-1}{\sqrt 2}$$ \leq x \leq 1$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If the function $ f : R \rightarrow R $ be given by $ f(x) = x^2+2$ and $ g : R \rightarrow R $ be given by $ g(x) = \large\frac{x}{x-1} , x \neq 1$, find fog and gof and hence find fog (2) and gof (-3)
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Find the equations of the tangent and normal to the curve $ \large\frac{x^2}{a^2}$$ - \large\frac{y^2}{b^2} = 1$ at the point $ ( \sqrt 2a, b)$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Find the value(s) of $x$ for which $y = [x(x-2)]^2$ is an increasing function.
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Evaluate : \[\] $\int \large\frac{x+2}{\sqrt{x^2+5x+6}} dx$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Evaluate : \[\] $ \int_0^{\pi} \large\frac{4x \sin x}{1+ \cos^2x} dx$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
The scalar product of the vector $ \overrightarrow a = \hat i + \hat j + \hat k$ with a unit vector along the sums of vectors $ \overrightarrow b = 2 \hat i + 4\hat j - 5 \hat k$ and $ \overrightarrow c = \lambda \hat i + 2 \hat j + 3 \hat k\;$ is equal to one. Find the value of $ \lambda $ and hence find the unit vector along $ \overrightarrow b + \overrightarrow c$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Show that the four points A, B, C and D with position vectors $ 4\hat i + 5 \hat j + \hat k, \: \: -\hat j - \hat k, \: \: 3\hat i + 9 \hat j + 4\hat k,$ and $ 4(-\hat i + \hat j + \hat k) $ respectively are coplanar.
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
Solve the differential equation $(1+x^2) \large\frac{dy}{dx}$$ +y = e^{ tan^{-1}}x$
modelpaper-2014-chennai
cbse
class12
math
sec-b
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ \overrightarrow a$ and $ \overrightarrow b$ are perpendicular vectors $ | \overrightarrow a + \overrightarrow b | = 13$ and $ | \overrightarrow a |=5$, find the value of $ | \overrightarrow b|.$
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ \int_0^a \large\frac{1}{4+x^2}$$ dx = \large\frac{\pi}{8}$, find the value of $a$
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If the cartesian equation of the lines are $ \large\frac{3-x}{5} $$= \large\frac{y+4}{7}$$=\large\frac{2z-6}{4}$, write the vector equation of the line.
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ R = \{ (x, y) : x + 2y =8\}$ is a relation on N. write the range of R
modelpaper-2014-chennai
cbse
class12
math
sec-a
q7
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
Find the value of 'P' for which the vectors $ 3 \hat i + 2 \hat j + 2 \hat k$ and $ \hat i - 2P \hat j + 3 \hat k $ are parallel.
modelpaper-2014-chennai
cbse
class12
math
sec-a
q6
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
If $ f(x) =\int_0^x t\: \sin\: t\: dt$, then write the value of $f'(x)$
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ \begin{bmatrix} 3x & 7 \\[0.3em] -2 & 4 \end{bmatrix} = \begin{bmatrix} 8 & 7 \\[0.3em] 6 & 4 \end{bmatrix}$, find the value of $x$.
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $\tan^{-1}x+ \tan^{-1}y = \large\frac{\pi}{4},$$ xy < 1$, then the write the value of $x+y+xy$
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $ \begin{bmatrix} x-y & z \\[0.3em] 2x-y & w \end{bmatrix} =\begin{bmatrix} -1 & 4 \\[0.3em] 0 & 5 \end{bmatrix} $, find the value of $X$ and $Y$
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
0
answers
If $A$ is a square matrix such that $A^2=A$, then write the value of $7A -(I+A)^3$ where $I$ is an identity matrix.
modelpaper-2014-chennai
cbse
class12
math
sec-a
asked
Mar 25, 2014
by
thanvigandhi_1
1
answer
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