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CBSE XII
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Math
Math
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Relations and Functions
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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
Two schools $P$ and $Q$ want to award their selected students on the values of Tolerance,Kindness and Leadership. The school $P$ wants to award $Rs.x,\:Rs.y\:and\:\:Rs.z$ each for the three respective values to $3,2\:and\:1$ students respectively with a total award money of $ Rs.2,200.$ School $Q$ wants to spend $Rs.3,100$ to award its 4,1 and 3 students on the respective values (by giving the same award money to the three values as school $P$). If the total amount of award for one prize on each value is $Rs.1,200,$ using matrices, find the award money for each value.
cbse
class12
modelpaper-2014
65-2-3
sec-c
q25
math
asked
Mar 23, 2014
by
rvidyagovindarajan_1
1
answer
If $x=a\:cos\theta+b\:sin\theta$ and $y=a\:sin\theta-b\:cos\theta$, then show that $y^2.\large\frac{d^2y}{dx^2}$$-x\large\frac{dy}{dx}$$+y=0$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q17
math
asked
Mar 23, 2014
by
rvidyagovindarajan_1
1
answer
Three cards are drawn at random (without replacement) from a well shuffled pack of 52 playing cards. Find the probability distribution of number of red cards. Hence find the mean of the distribution.
cbse
class12
modelpaper-2014
65-2-3
sec-b
q16
math
asked
Mar 23, 2014
by
rvidyagovindarajan_1
1
answer
Show that $cot^{-1}7+cos^{-1}8+cot^{-1}18=cot^{-1}3$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q14-b
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Solve: $cos(tan^{-1}x)=sin(cot^{-1}(\large\frac{3}{4}))$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q14-a
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Integrate the function $(3x-2)\sqrt{x^2+x+1}$
cbse
class12
modelpaper-2014
65-2-3
q18-b
math
sec-b
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Solve the differential equation $(x^2-yx^2)dy+(y^2+x^2y^2)dx=0$ Given $y=1$ when $x=1$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q13
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find a unit vector perpendicular to each of the vector \( \overrightarrow a + \overrightarrow b\) and \( \overrightarrow a - \overrightarrow b\), where \( \overrightarrow a = \hat i + \hat j + \hat k\) and \( \overrightarrow b = \hat i + 2\hat j +3\hat k\)
cbse
class12
modelpaper-2014
65-2-3
sec-b
q11-b
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the distance of the point $P(-1,-5,-10)$ from the point of intersection of the line joining the points $A(2,-1,2)$ and $B(5,3,4)$with the plane $x-y+z=5$
cbse
class12
modelpaper-2014
65-2-3
sec-c
q24-b
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the equation of the plane that contains the point $(1,-1,2)$ and is $\perp$ to the planes $2x+3y-2z=5$ and $x+2y-3z=8$. Hence find the distance of the point $(-2,5,5)$ from the plane obtained above.
cbse
class12
modelpaper-2014
65-2-3
sec-c
q24-a
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate: $\large \int \limits_0^1$$ x\;e^{x^2}\; dx$
cbse
class12
ch7
modelpaper-2014
easy
q10
sec-b
math
asked
Mar 21, 2014
by
balaji
1
answer
Find the distance between the two lines $l_1$ and $l_2$ where $l_1: \overrightarrow r=(\hat i+2\hat j-4\hat k)+\lambda(2\hat i+3\hat j+6\hat k)$ and $l_2: \overrightarrow r=(3\hat i+3\hat j-5\hat k)+\mu(4\hat i+6\hat j+12\hat k)$
cbse
class12
modelpaper-2014
65-2-3
sec-b
q19
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Write the value of the following: $\hat i \times (\hat j + \hat k)+ $$\hat j \times (\hat k + \hat i)+ $$\hat k \times (\hat i + \hat j)$
cbse
class12
ch10
modelpaper-2014
sec-a
q9
easy
math
asked
Mar 21, 2014
by
balaji
1
answer
If $\begin{pmatrix} a+4 &3b \\ 8 & -6 \end{pmatrix} = \begin{pmatrix} 2a+2 &b+2 \\ 8 & a-8b \end{pmatrix}$, write the value of $a-2b$.
cbse
class12
ch3
modelpaper-2014
sec-a
easy
math
asked
Mar 21, 2014
by
balaji
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a^2&bc&ac+c^2 \\ a^2+ab&b^2&ac \\ ab&b^2+bc&c^2 \end{vmatrix} = 4a^2b^2c^2\]
cbse
class12
modelpaper-2014
65-2-3
sec-b
q22
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of $\hat i\times (\hat j+\hat k)+\hat j\times (\hat k+\hat i)+\hat k\times (\hat i+\hat j)$
cbse
class12
modelpaper-2014
65-2-3
sec-a
q9
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of $a-2b$ if $\begin{bmatrix}a+4 & 3b\\8 & -6\end{bmatrix}=\begin{bmatrix}2a+2 & b+2\\8 & a-8b\end{bmatrix}\qquad$
cbse
class12
modelpaper-2014
65-2-3
sec-a
q8
math
asked
Mar 21, 2014
by
rvidyagovindarajan_1
1
answer
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are diamodns? (ii) only 3 cards are diamonds? (iii) none is a diamonds?
cbse
class12
modelpaper-2014
65-2-3
sec-c
q26-1
math
asked
Mar 20, 2014
by
balaji.thirumalai
1
answer
Five cards are drawn successively with replacement from a well-shuffled deck of 52 cards. What is the probability that (i) all the five cards are spades? (ii) only 3 cards are spades? (iii) none is a spade?
cl593
cbse
class12
bookproblem
ch13
sec5
p577
q4
sec-b
easy
math
asked
Mar 20, 2014
by
balaji.thirumalai
1
answer
Evlauate$ \Large \int_0^{\pi/4}$$ \large \frac{\sin x+\cos x}{9+16\sin 2x}$$dx$
cbse
class12
ch7
modelpaper-2014
65-2-3
sec-c
q29
math
asked
Mar 20, 2014
by
balaji.thirumalai
1
answer
Find the projection of the vector \( \hat i + \hat j + \hat k\) on the vector $\hat j$.
cbse
class12
modelpaper-2014
65-2-3
sec-a
q7
math
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Find the value of the following:\[cos^{-1} \big(- \frac {1} {2} \big)+2 sin^{-1}\frac {1} {2} \]
cbse
modelpaper-2014
65-2-3
sec-a
q6
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Let $R=\{(a,a^3):\:a\: is\: a\: prime\:number\: less\: than\: 5\}$ be a relation. Find the Range of $R$.
cbse
modelpaper-2014
65-2-3
sec-a
q5
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
If $A$ is a $3\times 3$ matrix, and $ |A|\neq0$ and $|3A|=k.|A|,$ then write the value of $k$
cbse
modelpaper-2014
65-2-3
sec-a
q4
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Find the angle between the pairs of lines: $ \overrightarrow r = 2\hat i -5 \hat j +\hat k + \lambda (3\hat i +2 \hat j +6\hat k)\: and \: \overrightarrow r = 7\hat i - 6\hat k + \mu (\hat i +2\hat j +2\hat k) $
cbse
modelpaper-2014
65-2-3
sec-a
q3
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Use elementary column operation $C_2\rightarrow C_2-2C_1$ in the matrix equation $\begin{bmatrix}4 & 2\\3 & 3\end{bmatrix}=\begin{bmatrix}1 & 2\\0 & 3\end{bmatrix}\:\begin{bmatrix}2 & 0\\1 & 1\end{bmatrix}$
cbse
modelpaper-2014
65-2-3
sec-a
q2
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate $\int\large\frac{dx}{sin^2x\:cos^2x}$
cbse
modelpaper-2014
65-2-3
sec-a
q1
easy
asked
Mar 20, 2014
by
rvidyagovindarajan_1
1
answer
Solve $ \bigg( 1 + e^{\Large\frac{x}{y}} \bigg) dx + e^{\Large\frac{x}{y}} \bigg( 1 -\large \frac{x}{y} \bigg) $$dy= 0 $
jeemain
math
differential-equations
difficult
asked
Mar 13, 2014
by
balaji.thirumalai
1
answer
The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is?
cl1434
cbse
class12
ch3
sec-a
easy
additionalproblem
math
asked
Feb 18, 2014
by
balaji.thirumalai
1
answer
integrate 1/1+x3
class12
math
asked
Feb 14, 2014
by
sriku270_1
1
answer
What is the difference between Bayes theorem and Total Probability theorem?
cbse
class12
math
ch13
probability
asked
Feb 12, 2014
by
sindhusankar30_1
1
answer
$ \text{If } \Delta = \begin{vmatrix} a_{11}&a_{12}&a_{13} \\ a_{21}&a_{22}&a_{23} \\ a_{31}&a_{32}&a_{33} \end{vmatrix} \text{ and } A_y \text{ is Cofactor of } a_y \text{, then the value of } a_{11}A_{21}+a_{12}A_{22}+a_{13}A_{23}=? $
cl786
cbse
class12
bookproblem
ch4
sec4
q5
p126
easy
sec-a
math
asked
Feb 11, 2014
by
rvidyagovindarajan_1
1
answer
A tow truck drags a stationary car along the road. The chain makes an angle of 30 degrees with the road and the tension in the chain is 1500 N. How much work is done (in Joules) by the truck in pulling the car 1 km (approximate answer, rounded off)?
cbse
class12
ch10
additionalproblem
medium
sec-a
math
asked
Feb 11, 2014
by
balaji.thirumalai
1
answer
Sketch the region and find the area bounded between $y=\sqrt {5-x^2}$ and $y=|x-1|$ using integration.
cl3079
cbse
class12
ch8
q8
p176
short-answer
exemplar
sec-c
difficult
math
asked
Feb 10, 2014
by
rvidyagovindarajan_1
1
answer
Evaluate: $\large \int \limits_{-1}^1 $$x$ $ \left | x \right |$ $ dx$.
cl1124
cbse
class12
bookproblem
ch8
misc
q17
p376
sec-a
medium
math
asked
Feb 10, 2014
by
rvidyagovindarajan_1
1
answer
If $ \sqrt{1-y^2}-\sqrt{1-x^2}=a(x-y),\normalsize$ then find $\large\frac{dy}{dx}$
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q45
p14
sec-b
difficult
math
jeemain
limits-continuity-and-differentiability
asked
Feb 5, 2014
by
rvidyagovindarajan_1
1
answer
An open box with square base is to be made of a given quantity of card board of area $ 36 sq.metre.$ Find the maximum volume of the box.
cbse
class12
ch6
q29
p137
exemplar
medium
sec-c
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
Find the area bounded by curves $x^2 + (y-1)^2 = 1$ and $x^2 + y^2 = 1$.
class12
cbse
additionalproblem
ch8
sec-c
medium
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
Find the area bounded by curves \((x - 1)^2 + y^2 = 1\) and \(x^2 + y^2 = 1.\)
cbse
class12
bookproblem
ch8
sec2
q2
p371
sec-b
medium
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
Solve the differential equation $\large\frac{dy}{dx}$$=cos(x+y)+sin(x+y)$ and find the particular solution if $y(0)=0$
class12
cbse
medium
sec-c
ch9
additionalproblem
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
If the lines $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\lambda(3\hat i+2k\hat j-2\hat k)$ and $\overrightarrow r=(\hat i+2\hat j+3\hat k)+\mu(k\hat i+\hat j+5\hat k)$ are $\perp$ to one another then find the equation of the plane containing them.
class12
cbse
medium
sec-c
ch11
additionalproblem
math
asked
Feb 4, 2014
by
rvidyagovindarajan_1
1
answer
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