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Recent questions tagged medium
Questions
Let $f(t)=\begin{vmatrix}\cos t & t & 1\\2\sin t & t & 2t\\\sin t & t & t\end{vmatrix}$, then $\displaystyle \lim_{t \to 0}\Large \frac{f(t)}{t^2}$ is equal to
cbse
class12
ch4
sec-a
q30
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If A,B and C are angles of a triangle ,then the determinant$\begin{vmatrix}1 & \cos C & \cos B\\\cos C & 1 & \cos A\\\cos B & \cos A & 1\end{vmatrix}$ is equal to
cbse
class12
ch4
sec-a
q29
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
The number of distinct real roots of $\begin{vmatrix}\sin x & \cos x & \cos x\\\cos x & \sin x & \cos x\\\cos x & \cos x &\sin x\end{vmatrix}=0\;$ in the interval $\large \frac{-\pi}{4}$$ \leq x \leq\large \frac {\pi}{4}$ is
cbse
class12
ch4
sec-a
q28
p81
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
The determinant $\begin{vmatrix}b^2 - ab & b - c & bc - ac\\ab - a^2 & a - b & b^2 - ab\\bc - ac & c - a & ab -a^2\end{vmatrix}$ equals
cbse
class12
ch4
sec-a
q27
p80
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find the value of the determinant $\begin{vmatrix}a-b & b+c & a\\b-c & c+a & b\\c-a & a+b & c\end{vmatrix}$
cbse
class12
ch4
sec-a
q25
p80
objective
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If x+y+z=0,prove that $\begin{vmatrix}xa & yb & zc\\yc & za & xb\\zb & xc & ya\end{vmatrix}=xyz\begin{vmatrix}a & b & c\\c & a & b\\b & c & a\end{vmatrix}$.
cbse
class12
ch4
sec-b
q23
p80
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Prove that $\begin{vmatrix}bc - a^2 & ca - b^2 & ab - c^2\\ca - b^2 & ab - c^2 & bc - a^2\\ab -c^2 & bc - a^2 & ca - b^2\end{vmatrix}$ is divisible by a+b+c and find the quotient.
cbse
class12
ch4
sec-b
q22
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Using matrix method ,solve the system of equations 3x+2y-2z=3,x+2y+3z=6,2x-y+z=2.
cbse
class12
ch4
sec-c
q19
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 2 & 0\\-2 & -1 & -2\\0 & -1 & 1\end{bmatrix},find\;A^{-1}.$\[Using\;A^{-1}, solve\; the\; system\; of\; linear\; equations\; x-2y=10,2x-y-z=8,-2y+Z=7.\]
cbse
class12
ch4
sec-c
q18
p79
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find $A^{-1}$ if $A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}$ and show that $ A^{-1}=\Large \frac{A^2-3I}{2}$
cbse
class12
ch4
sec-c
q17
p79
short-answer
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Prove that \( tan^{-1} \bigg(\frac{\large 1}{\large 4} \bigg) + tan^{-1} \bigg( \frac{\large 2}{\large 9} \bigg ) = \frac{\large 1}{\large 2} cos^{-1} \bigg( \frac{3}{5} \bigg). \)
cbse
modelpaper
2012
sec-b
q12
ch2
medium
asked
Dec 26, 2012
by
thanvigandhi_1
1
answer
Simplify\( 2\tan^{-1} \bigg(\large \frac{1}{5} \bigg) + \sec^{-1} \bigg( \large\frac{5\sqrt 2}{7} \bigg) + 2\: tan^{-1} \bigg( \frac{1}{8} \bigg) \)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
medium
math
asked
Dec 25, 2012
by
thanvigandhi_1
1
answer
Using the properties of determinants, prove that: $\begin{vmatrix} y^2z^2 & yz &y+ z \\ z^2x^2 & zx & z+x \\ x^2y^2 & xy & x+y \end{vmatrix}\;=\;0$
cbse
class12
ch4
sec-b
q7
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix}$
cbse
class12
ch4
sec-b
q6
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} 3x & -x+y & -x+z \\ x-y & 3y & z-y \\ x-z & y-z & 3z \end{vmatrix}$
cbse
class12
ch4
sec-b
q4
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} 0 & xy^2 & xz^2 \\ x^2y & 0 & yz^2 \\ x^2z & zy^2 & 0 \end{vmatrix}$
cbse
class12
ch4
sec-b
q3
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Find x,y,z if $A=\begin{bmatrix}0 & 2y & z\\x & y & -z\\x & -y & z\end{bmatrix}\;satisfies\;A'=A^{-1}$.
cbse
class12
ch3
q50
exemplar
sec-c
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If AB=BA for any two square matrices,prove by mathematical induction that $(AB)^n=A^nB^n$.
cbse
class12
ch3
q49
p58
exemplar
sec-c
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If the matrix $\begin{bmatrix}0 & a & 3\\2 & b & -1\\c & 1 & 0\end{bmatrix}\;$is a skew symmetric matrix,find the values of a,b and c.
cbse
class12
ch3
q45
p58
short-answer
exemplar
sec-b
medium
qod
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Find inverse,by elementary row operations(if possible),of the following matrices$\quad\begin{bmatrix}1 & 3\\-5 & 7\end{bmatrix}$
cbse
class12
ch3
q37
q37-1
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Prove by Mathematical Induction that $(A')^n=(A^n)'$,where $n\in N$ for any square matrix A.
cbse
class12
ch3
q36
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
Let $A=\begin{bmatrix}1 & 2\\1 & 3\end{bmatrix},B=\begin{bmatrix}4 & 0\\1 & 5\end{bmatrix},C=\begin{bmatrix}2 & 0\\1 & 2\end{bmatrix}\;$and$\;a=4,b=-2$.Show that$\;(g)\;(AB)^T=B^TA^T.$
cbse
class12
ch3
q32g
p57
short-answer
exemplar
sec-b
medium
math
asked
Dec 23, 2012
by
sreemathi.v
1
answer
If $A=\begin{bmatrix}1 & 0 & -1\\2 & 1 & 3\\0 & 1 & 1\end{bmatrix},then\;verify\;that\;A^2+A=A(A+I),where\;I\;is\;3\times 3\;unit\;matrix.$
cbse
class12
ch3
q26
p56
short-answer
exemplar
medium
sec-b
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
Does $A=\begin{bmatrix}5 & 3\\1 & 2\end{bmatrix}$ satisfy the equation $\;A^2-3A-7I=0$ and hence find $\;A^{-1}$
class12
cbse
ch3
q11
p54
short-answer
exemplar
sec-c
medium
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
True or False: The principal value of $\sin^{-1}\begin{bmatrix}\cos\bigg(\sin^{-1}\frac{1}{2}\bigg)\end{bmatrix}\;is\;\Large {\frac{\pi}{3}}$
cbse
class12
ch2
q55
p41
true-or-false
exemplar
medium
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
True or False: The minimum value of n for which $\tan^{-1}\Large {\frac{n}{\pi}}\;>\Large {\frac{\pi}{4}},\normalsize\;n\in N,$ is valid is 5
cbse
class12
ch2
q54
p41
true-or-false
exemplar
medium
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
If $\cos^{-1}x\;>\;\sin^{-1}x,$ then \begin{array}{1 1}(A)\quad\frac{1}{\sqrt 2}<x\leq 1& (B)\quad 0\leq x<\frac{1}{\sqrt 2}\\(C)\quad -1\leq x<\frac{1}{\sqrt 2} & (D)\quad x>0\end{array}
cbse
class12
ch2
q37
p39
objective
exemplar
medium
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
If $\cos^{-1}\alpha+\cos^{-1}\beta+\cos^{-1}\gamma=3\pi$,then $\alpha(\beta+\gamma)+\beta(\gamma+\alpha)+\gamma(\alpha+\beta)$ equals\[(A)\;0\quad(B)\quad 1\quad(C)\quad 6\quad(D)\quad 12\]
cbse
class12
ch2
q35
p39
objective
exemplar
medium
sec-b
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
The value of the expression $\tan\bigg(\frac{1}{2}\cos^{-1}{\frac{2}{\sqrt 5}}\bigg)$ is:
cbse
class12
ch2
q33
p39
objective
exemplar
medium
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
If $\sin^{-1}\frac{2a}{1+a^2} +\cos^{-1}\frac{1-a^2}{1+a^2}=\tan^{-1}\frac{2x}{1-x^2},where\; a,x,\in\;[0,1],$then the value of x is
cbse
class12
ch2
q31
p38
objective
exemplar
medium
sec-b
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
If $\tan^{-1}x+\tan^{-1}y=\frac{4\pi}{5},then\;\cot^{-1}x+\cot^{-1}y$ equals:
cbse
class12
ch2
q30
p38
objective
exemplar
medium
sec-a
math
asked
Dec 21, 2012
by
sreemathi.v
1
answer
The value of $\sin(\tan^{-1}(.75))$ is equal to
cbse
class12
ch2
q27
p38
objective
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
If $\cos\bigg(\sin^{-1}\frac{2}{5}+\cos^{-1}x\bigg)=0$,then x is equal to
cbse
class12
ch2
q26
p38
objective
exemplar
medium
sec-a
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
What is the value of $\tan({\frac{1}{2}}\sin^{-1}{\frac{3}{4}})$?
cbse
class12
ch2
q18
p37
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
What does $\tan^{-1}{\frac{1}{4}}+\tan^{-1}{\frac{2}{9}}$ reduce to?
cbse
class12
ch2
q16
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Show that $\sin^{-1}{\frac{5}{13}}+\cos^{-1}{\frac{3}{5}}=\tan^{-1}{\frac{63}{16}}$
cbse
class12
ch2
q15
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Solve the following equation $\cos\big(\tan^{-1}x\big)=\sin\bigg(\cot^{-1}{\frac{3}{4}}\bigg)$
cbse
class12
ch2
q11
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Show that $\cos\bigg(2\tan^{-1}{\frac{1}{7}}\bigg)=\sin\bigg(4\tan^{-1}{\frac{1}{3}}\bigg)$
cbse
class12
ch2
q10
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
If $2\tan^{-1}(\cos x)=\tan^{-1}(2cosecx)$,then what is the value of $x$?
cbse
class12
ch2
q9
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Find the value of the expression $\sin \bigg(2\tan^{-1}{\frac{1}{3}}\bigg)+\cos \big(\tan^{-1}2\sqrt 2\big)$
cbse
class12
ch2
q8
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Find the value of $\; \tan^{-1}\bigg(\tan{\frac{5\pi}{6}}\bigg)+\cos^{-1}\bigg(\cos{\frac{13\pi}{6}}\bigg)$
cbse
class12
ch2
q1
p35
short-answer
exemplar
medium
sec-a
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Find the vector equation of a plane which is at a distance of 7 units from the origin and normal to the vector \(3\hat i + 5\hat j - 6 \hat k.\)
cbse
class12
bookproblem
ch11
sec3
q2
p493
medium
sec-b
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the equation of the plane through the intersection of the planes $3x -y + 2z -4 = 0$ and $x + y + z -2 = 0$ and the point $(2, 2, 1).$
cbse
class12
bookproblem
ch11
sec3
q9
p493
medium
sec-b
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the vector equation of the plane passing through the intersection of the planes $ \overrightarrow r .(2\hat i + 2 \hat j - 3\hat k) = 7, \overrightarrow r .(2\hat i + 5\hat j + 3\hat k ) = 9$ and through the point $(2, 1, 3).$
cbse
class12
bookproblem
ch11
sec3
q10
p493
sec-b
medium
math
asked
Dec 15, 2012
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$x -y + z = 0.$
cbse
class12
bookproblem
ch11
sec3
q11
p493
sec-b
medium
math
asked
Dec 15, 2012
by
thanvigandhi_1
1
answer
Find the shortest distance between the lines whose vector equations are $ \overrightarrow r = ( \hat i + 2\hat j + 3\hat k) + \lambda ( \hat i - 3\hat j + 2\hat k )$ and $ \overrightarrow r = 4 \hat i + 5\hat j + 6\hat k + \mu (2\hat i + 3\hat j + \hat k )$
cbse
class12
bookproblem
ch11
sec2
q16
p478
medium
sec-c
modelpaper
2012
q22
math
asked
Dec 14, 2012
by
thanvigandhi_1
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 shortest distance between the lines $ \overrightarrow r = ( \hat i + 2\hat j + \hat k) + \lambda ( \hat i - \hat j + \hat k )$ and $ \overrightarrow r = 2 \hat i - \hat j - \hat k + \mu (2\hat i + \hat j + 2\hat k )$
cbse
class12
bookproblem
ch11
sec2
q14
p478
medium
sec-b
modelpaper
2012
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
Find the values of p so that the lines $ \frac{ \large 1 - x }{ \large 3} = \frac{ \large 7y - 14}{ \large 2p} = \frac{ \large z - 3}{ \large 2}\: and \: \frac{ \large 7 - 7x }{ \large 3 \: p} = \frac{ \large y - 5}{ \large 1} = \frac{ \large 6 - z}{ \large 5}$ are at right angles.
cbse
class12
bookproblem
ch11
sec2
q12
p478
medium
sec-b
math
asked
Dec 14, 2012
by
thanvigandhi_1
1
answer
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