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Recent questions tagged q20
Questions
Show that each of the given three vectors is a unit vector : $\large \frac{1}{7}$$ (2\hat i + 3\hat j + 6\hat k),\large\frac{1}{7} $$(3\hat i - 6\hat j + 2\hat k),\large\frac{1}{7} $$(6\hat i + 2\hat j - 3\hat k)$ (Also show that they are mutually perpendicular to each other).
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
A die is thrown 5 times.Find the probability that an odd number will come up exactly three times.
cbse
class12
ch13
q20
p273
short-answer
exemplar
sec-a
easy
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
A man rides his motorcycle at the speed of 50km/hour.He has to speed Rs 2 per km on petrol.If he rides it at at a faster speed of 80km/hour,the petrol cost increases to Rs 3 per km.He has at most Rs120 to spend on petrol and one hour's time.He wishes to find the maximum distance that he can travel.Determine the maximum distance that the man can travel.
cbse
class12
ch12
q20
p253
exemplar
sec-c
medium
math
asked
Jan 7, 2013
by
sreemathi.v
1
answer
Find the shortest distance between the following two lines : $ \overrightarrow r = (1+\lambda)\hat i + (2-\lambda)\hat j + (\lambda + 1)\hat k ; \overrightarrow r = (2\hat i -\hat j -\hat k) + \mu (2\hat i + \hat j +\hat k).$
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Find the value of \( \lambda \), so that lines $\large \frac{1-x}{3}=\frac{7y-14}{2\lambda}=\frac{5z-10}{11} $ and $ \large \frac{7-7x}{3\lambda}=\large\frac{y-5}{1}=\frac{6-z}{5} $ are perpendicular to each other.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
Find the position vector of a point R which divided the line joining the points whose positive vectors are \( P(\hat i +2\hat j - \hat k ) and Q ( -\hat i + \hat j + \hat k )\) in the ratio 2 : 1. (i) internally (ii) externally.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Find the direction cosines of the vector joining the points A(1, 2, -3 ) and B ( -1, -2, 1 ), directed from A to B.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Find the equation of the plane through the points $(2,1,-1)$ and $(-1,3,4)$ and perpendicular to the plane $x-2y+4z=10.$
cbse
class12
ch11
sec-c
q20
p236
exemplar
difficult
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
If $ \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k, $ Find a vector \( \overrightarrow c \) such that \( \overrightarrow a \) x \( \overrightarrow c = \overrightarrow b \) and \( \overrightarrow a . \overrightarrow c = 3\).
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
If $ \overrightarrow a + \overrightarrow b + \overrightarrow c = 0\: and\: | \overrightarrow a | = 3, |\overrightarrow b | = 5\: and \: |\overrightarrow c | = 7 .$Show that the angle between \( \overrightarrow a \: and \overrightarrow b\) is \( 60^{\circ} \)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 3, 2013
by
thanvigandhi_1
0
answers
For any three vectors : $ \overrightarrow a, \overrightarrow b \: and \: \overrightarrow c $ prove that $ \bigg[ \overrightarrow a + \overrightarrow b \: \: \overrightarrow b + \overrightarrow c \: \overrightarrow c + \overrightarrow a \bigg] = 2 \bigg[ \overrightarrow a \: \overrightarrow b \: \overrightarrow c \bigg]. $
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 2, 2013
by
thanvigandhi_1
0
answers
Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}x[x], & if\;0\leq x<2\\(x-1)x, & if\;2\leq x<3\end{array}\right.$at $x=2$
cbse
class12
ch5
q20
p109
short-answer
exemplar
easy
sec-a
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Show that four points with position vectors \( 6\hat i - 7\hat j, 19 \hat j - 4\hat k, 3\hat j - 6\hat k \: and \: 2\hat i + 5\hat j + 10\hat k\) are not co-planar.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 31, 2012
by
thanvigandhi_1
0
answers
If \( \overrightarrow a + \overrightarrow b + \overrightarrow c = 0\) and \( | \overrightarrow a | = 3, | \overrightarrow b | = 5\) and \( |\overrightarrow c | = 7\), show that the angle between \( \overrightarrow a\: and \: \overrightarrow b \) is equal to \( 60^{\circ}\)
cbse
class12
modelpaper
2008-1
sec-b
q20
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
If a, b, c are the lengths of the sides respectively to the angles A, B and C of a \( \Delta\)ABC, using vectors, prove that \( \cos C = \large\frac{a^2 + b^2 - c^2}{2ab} \)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
If \( \overrightarrow a, \overrightarrow b \) and \( \overrightarrow c \) are three unit vectors such that \( \overrightarrow a.\overrightarrow b = \overrightarrow a. \overrightarrow c = 0\) and angle between \( \overrightarrow b \: and \: \overrightarrow c \) is \( \large\frac{\pi}{6}, \) prove that \( \overrightarrow a = \pm\: 2 ( \overrightarrow b\) x \( \overrightarrow c ) \).
cbse
class12
modelpaper
2011
sec-b
q20
math
asked
Dec 28, 2012
by
thanvigandhi_1
0
answers
Given $A=\begin{bmatrix}2 & 2 & 4\\4 & 2 & 4\\2 & 1 & 5\end{bmatrix},B=\begin{bmatrix}1 & 1 & 0\\2 & 3 & 4\\0 & 1 & 2\end{bmatrix}$,find BA and use this to solve the system of equations y+2z=7,x-y=3,2x+3y+4z=17
cbse
class12
ch4
sec-c
q20
p79
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If the sum of two unit vectors is a unit vector, show that the magnitude of their difference is \( \sqrt 3\)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
If a,b,c are the lengths of the sides BC, CA and AB of a triangle ABC respectively, prove that \( \large\frac{a}{sinA} = \frac{b}{sin B} = \frac{c}{sinC} \)
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
If R is the set of real numbers and f : R\( \rightarrow\)R be the function defined by \(f (x) = 1 (3 – x^3 )^{\frac{1}{3}}\) , then (fof) (x) is equal to \[ \begin{array} (A) \: x^{\frac{1}{3}} \quad & (B)\: x^3 \\ (C) \: x \quad & (D)\: (3 – x^3) \end{array} \]
cbse
class12
modelpaper
2012
sec-a
q20
math
asked
Dec 23, 2012
by
thanvigandhi_1
0
answers
If A=[3 , 5],B=[7, 3],then find a non-zero matrix C such that AC=BC.
cbse
class12
ch3
q20
p55
short-answer
exemplar
sec-b
easy
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Find the shortest distance between the following two lines : $ \overrightarrow r = (1+\lambda)\hat i + (2-\lambda)\hat j + (\lambda+1)\hat k ; \overrightarrow r = ( 2\hat i - \hat j - \hat k ) + \mu \: ( 2\hat i + \hat j + 2\hat k ). $
cbse
class12
modelpaper
2009
sec-b
q20
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
Which of the following is the principal value branch of $\cos^{-1}x$?
cbse
class12
ch2
q20
p37
objective
exemplar
easy
sec-a
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
If \( \overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k \) find a vector \( \overrightarrow c \) such that \( \overrightarrow a\) x \( \overrightarrow c = \overrightarrow b \) and \( \overrightarrow a . \overrightarrow c = 3\)
cbse
class12
modelpaper
2008-1
sec-b
q20
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
Let A=R-{3},B=R-{1}.Let $f \;:\;A \rightarrow B$ be defined by $f(x)=\Large{\frac{x-2}{x-3}}\normalsize \forall x \in A$.Then show that f is bijective.
cbse
class12
ch1
q20
p12
exemplar
sec-b
math
asked
Dec 18, 2012
by
sreemathi.v
1
answer
Find the shortest distance between the lines: $ \frac{ \large x + 1 }{ \large 7} = \frac{ \large y + 1}{ \large -6} = \frac{ \large z + 1}{ \large 1}$ and $ \frac{ \large x - 3 }{ \large 1} = \frac{ \large y - 5}{ \large -2} = \frac{ \large z - 7}{ \large 1}$
cbse
class12
bookproblem
ch11
sec2
q15
p478
medium
sec-b
modelpaper
2012
q20
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the values of each of the expressions in $ \sin \bigg(\frac{\pi}{3} - \sin^{-1} ( -\frac{1}{2} ) \bigg) $ is equal to
cbse
class12
bookproblem
ch2
sec2
q20
p48
easy
sec-a
math
asked
Dec 10, 2012
by
thanvigandhi_1
1
answer
Find the integral $\displaystyle\int\frac{\large 2-3\sin x}{\large \cos^2x}dx$
cbse
class12
bookproblem
ch7
sec1
q20
p299
sec-a
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Integrate the function $\frac{\large e^{2x}-e^{-2x}}{\large e^{2x}+e^{-2x}}$
cbse
class12
bookproblem
ch7
sec2
q20
p305
sec-a
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Find the integrals of the functions $\frac{\cos2x}{(\cos x+\sin x)^2}$
cbse
class12
bookproblem
ch7
sec3
q20
p307
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the functions\[\frac{x+2}{\sqrt{4x-x^2}}\]
cbse
class12
bookproblem
ch7
sec4
q20
p316
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the rational functions\[\frac{1}{x(x^4-1)}\]
cbse
class12
bookproblem
ch7
sec5
q20
p323
sec-c
difficult
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Using the fact that \(\sin (A + B) = \sin A \cos B + \cos A \sin B\) and the differentiation, obtain the sum formula for cosines.
cbse
class12
bookproblem
ch5
misc
q20
p192
sec-b
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\frac{(x-3)e^x}{(x-1)^3}$
cbse
class12
bookproblem
ch7
sec6
q20
p328
sec-a
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Evaluate the definite integral $\displaystyle\int\limits_0^1(xe^x+\sin\frac{\pi\;x}{4})dx$
cbse
class12
bookproblem
ch7
sec9
q20
p338
sec-b
medium
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Choose the correct answer in the value of $\displaystyle\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}(x^3+x\cos x+\tan^5x+1)dx$ is
cbse
class12
bookproblem
ch7
sec11
q20
p347
sec-a
medium
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
Integrate the function\[\int\sqrt{\frac{1-\sqrt x}{1+\sqrt x}}\]
cbse
class12
bookproblem
ch7
misc
q20
p352
sec-b
difficult
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
In a bank,principal increases continuously at the rate of r% per year.Find the value of r if Rs100 doubles itself in 10years. $\quad (log_e2=0.6931)$
cbse
class12
bookproblem
ch9
sec4
q20
p397
sec-c
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Choose the correct answer in the slope of the tangent to the curve \(x = t^2 + 3t – 8, y = 2t^2 – 2t – 5\) at the point \((2,– 1)\) is
cbse
class12
bookproblem
ch6
misc
q20
p243
sec-b
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the right circular cylinder of given surface and maximum volume is such that its height is equal to the diameter of the base.
cbse
class12
bookproblem
ch6
sec5
q20
p233
sec-c
medium
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics books. Their selling prices are Rs 80, Rs 60 and Rs 40 each respectively. Find the total amount the bookshop will receive from selling all the books using matrix algebra.
cbse
class12
bookproblem
ch3
sec2
q20
p83
medium
long-answer
sec-b
math
asked
Nov 25, 2012
by
pady_1
1
answer
Find the equation of the normal at the point \((am^2,am^3)\) for the curve \(ay^2 = x^3.\)
cbse
class12
bookproblem
ch6
sec3
q20
p212
sec-b
easy
math
asked
Nov 24, 2012
by
thanvigandhi_1
1
answer
Is the function defined by $ f (x) = x^2 - \sin\; x + 5 $ continuous at $ x =\pi $ ?
cbse
class12
bookproblem
ch5
sec1
q20
p160
sec-b
easy
math
asked
Nov 5, 2012
by
thanvigandhi_1
1
answer
Find the vector equation of the line passing through (1, 2, -4) and perpendicular to the two lines $\frac{\large x-8}{\large 3} = \frac{\large y+19}{\large -16} = \frac{\large z-10}{\large 7}$ and $\frac{\large x-15}{\large 3} = \frac{\large y-29}{\large 8} = \frac{\large z-5}{\large -5}$
cbse
class12
bookproblem
ch11
misc
p499
q20
sec-c
medium
math
asked
Nov 2, 2012
by
balaji.thirumalai
1
answer
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