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Recent questions tagged q21
Questions
Find the shortest distance between the lines given by $\overrightarrow{r}=(8+3\lambda)\hat i-(9+16\lambda)\hat j+(10+7\lambda)\hat k\; and\; \overrightarrow{r}=15\hat i+29\hat j+5\hat k+\mu(3\hat i+8\hat j-5\hat k)$
cbse
class12
ch11
q21
p237
exemplar
difficult
sec-c
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 red balls. One ball is drawn at random from one of the bags and is found to be red. Find the probability that it was drawn from bag II.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 3, 2013
by
thanvigandhi_1
1
answer
Find the vector and cartesian equation of the sphere described on the join of the points (2, -3, 4 ) and (-5, 6, -7 ) as the extremities of a diameter.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Find the root of the perpendicular drawn from the point P(1, 6, 3) on the line $\large \frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}. $ Also, find its distance from P.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Examine the differentiability of $f$,where $f$ is defined by $f(x)=\left \{\begin{array}{1 1}x^2\sin\large\frac{1}{x}, & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at $x=0$
cbse
class12
ch5
q21
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the equation of the plane passing through the points ( 1, 2, 3 ) and (0, -1, 0 ) and parrallel to the line, \( \large\frac{x-1}{2} = \frac{y+2}{3} = \frac{z}{-3} \).
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 31, 2012
by
thanvigandhi_1
1
answer
Find the image of the point ( 1, 2, 3 ) in the plane \( x + 2y + 4z = 38\).
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 31, 2012
by
thanvigandhi_1
0
answers
Find the point on the line \( \large\frac{x+2}{3} = \frac{y+1}{2} = \frac{z-3}{2} \) at a distance \( 3 \sqrt 2 \) from the point (1, 2, 3)
cbse
class12
modelpaper
2008-1
sec-b
q21
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Solve for x : $ 2\tan^{-1} ( \cos x ) = \tan^{-1} (2 cosec x) $
cbse
class12
modelpaper
2009
sec-b
q21
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Show that the four points ( 0, -1, -1 ), ( 4, 5, 1 ) and (-4, 4, 4 ) are coplanar. Also find the equation of the plane containing them.
cbse
class12
modelpaper
2011
sec-b
q21
math
asked
Dec 28, 2012
by
thanvigandhi_1
1
answer
If $a+b+c\neq 0\;and\;\begin{vmatrix}a & b & c\\b & c & a\\c & a & b\end{vmatrix}=0,then\;prove\;that\;a=b=c.$
cbse
class12
ch4
sec-b
q21
p79
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find whether the lines \( \overrightarrow r = ( \hat i - \hat j - \hat k ) + \lambda (2\hat i + \hat j ) \: and \: \overrightarrow r = ( 2\hat i - \hat j ) + \mu ( \hat i + \hat j - \hat k )\) intersect or not. If intersecting find their point of intersection.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
Show that points ( -6, 3, 2 ) ( 3, -2, 4 ) (5, 7, 3 ) and ( -13, 17, -1 ) are coplaner.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
Let R be the set of real numbers, f : R\( \rightarrow \)R be the function defined by f (x) = 4x + 3, x ∈ R. Show that f is invertible. Find the inverse of f.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
Which of the following is an example of matrices A,B and C such that AB=AC,where A is non-zero matrix,but $B\neq C.$
cbse
class12
ch3
q21
p55
short-answer
exemplar
easy
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
prove the following : $ \cot^{-1} \bigg(\large \frac{\sqrt {1+\sin x} + \sqrt {1-\sin x}}{\sqrt {1+\sin x} - \sqrt {1-\sin x}} \bigg) = \large\frac{x}{2},$$ x \in \: \bigg(0,\large \frac{\pi}{4} \bigg) $
cbse
class12
modelpaper
2009
sec-b
q21
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
Which of the following is the principal value branch of $\text{cosec}^{-1}x$?
cbse
class12
ch2
q21
p37
objective
exemplar
easy
sec-a
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Find the shortest distance between the following lines : \[ \frac{x-3}{1} = \frac{y-5}{-2} = \frac{z-7}{1} \: and \: \frac{x+1}{7} = \frac{y+1}{-6} = \frac{z+1}{1} \]
cbse
class12
modelpaper
2008-1
sec-b
q21
math
asked
Dec 19, 2012
by
thanvigandhi_1
0
answers
Find the equation of the plane passing through the line of intersection of the planes \(\overrightarrow r. (\hat i + \hat j + \hat k)=1\) and \( \overrightarrow r. (2\hat i + 3\hat j - \hat k) + 4 = 0\) and parallel to \(x\) - axis.
cbse
class12
bookproblem
ch11
misc
q15
p498
difficult
sec-b
modelpaper
2012
q21
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the value of $ \tan^{-1} \sqrt 3 - \cot^{-1} (-\sqrt 3)$
cbse
class12
bookproblem
ch2
sec2
q21
p48
easy
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
The anti derivative of $\bigg(\sqrt x+\frac{1}{\sqrt x}\bigg)$ equals
cbse
class12
bookproblem
ch7
sec1
q21
p299
sec-a
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Integrate the function $\tan^2(2x-3)$
cbse
class12
bookproblem
ch7
sec2
q21
p305
sec-b
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Find the integrals of the functions $\sin^{-1}(\cos x)$
cbse
class12
bookproblem
ch7
sec3
q21
p307
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the functions\[\frac{x+2}{\sqrt{x^2+2x+3}}\]
cbse
class12
bookproblem
ch7
sec4
q21
p316
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the rational functions $\frac{1}{(e^x-1)} [Hint:Put\;e^x=\;t]$
cbse
class12
bookproblem
ch7
sec5
q21
p323
sec-b
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Does there exist a function which is continuous everywhere but not differentiable at exactly two points? Justify your answer.
cbse
class12
bookproblem
ch5
misc
q21
p192
sec-a
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
If \(cos\: y = x \cos (a + y)\), with $\cos$ \(a \neq \pm 1\), prove that \( \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}\)
cbse
class12
bookproblem
ch5
misc
q16
p192
sec-b
medium
modelpaper-2014
q21
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\;\int\;e^{2x}\sin\; x$
cbse
class12
bookproblem
ch7
sec6
q21
p328
sec-b
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Choose the correct answer in $\int\limits_1^\sqrt 3\frac{dx}{1+x^2}\;equals$\[(A)\;\frac{\pi}{3}\qquad(B)\;\frac{2\pi}{3}\qquad(C)\;\frac{\pi}{6}\qquad(D)\;\frac{\pi}{12}\]
cbse
class12
bookproblem
ch7
sec9
q21
p338
sec-a
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Choose the correct answer in the value of $\int\limits_0^\frac{\pi}{2}log\bigg(\frac{\large 4+3\sin x}{\large 4+3\cos x}\bigg)dx$ is
cbse
class12
bookproblem
ch7
sec11
q21
p347
sec-a
easy
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
Integrate the function $\int\large\frac{2+\sin2x}{1+\cos2x}$$e^x$
cbse
class12
bookproblem
ch7
misc
q21
p352
sec-b
medium
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
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
Prove that if a plane has the intercepts $a, b, c$ and is at a distance of $p$ units from the origin, then $\large\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2} = \frac{1}{p^2}$.
cbse
class12
bookproblem
ch11
misc
p499
q21
difficult
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Choose the correct answer in the line \(y = mx + 1\) is a tangent to the curve \(y^2 = 4x\) if the value of \(m\) is
cbse
class12
bookproblem
ch6
misc
q21
p244
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Form the conjunction and the disjunction of (i) p : Anand reads newspaper, q : Anand plays cricket. (ii) p : I like tea. q : I like ice-cream.
tnstate
class12
bookproblem
ch9
sec1
exercise9-1
p161
q21
asked
Nov 27, 2012
by
balaji.thirumalai
0
answers
In a hurdle race, a player has to cross 10 hurdles. The probability that he will clear each hurdle is 5/6 . What is the probability that he will knock down fewer than 2 hurdles?
cbse
class12
bookproblem
ch13
misc
p583
q6
sec-b
easy
modelpaper
2012
q21
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Of all the closed cylindrical cans (right circular), of a given volume of 100 cubic centimetres, find the dimensions of the can which has the minimum surface area?
cbse
class12
bookproblem
ch6
sec5
q21
p233
sec-b
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
Assume $X, Y, Z, W$ and $P$ are matrices of order $2\times n, 3\times k, 2\times p, n\times 3$ and $p\times k$, respectively. The restriction on $n, p, k$ so that $PY + WY$ will be defined are:
cbse
class12
bookproblem
ch3
sec2
q21
p83
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find the equation of the normals to the curve $y = x^3 + 2x + 6$ which are parallel to the line $x + 14y + 4 = 0$.
cbse
class12
bookproblem
ch6
sec3
q21
p213
sec-b
medium
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
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