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Recent questions in CBSE XII
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CBSE XII
CBSE XII
Math
Physics
Chemistry
Biology
For each of the differential equations given below,indicate its order and degree(if defined) $(i)\;\large\frac{d^2y}{dx^2}+5x\bigg(\frac{dy}{dx}\bigg)^2-6y=\log x$
cbse
class12
bookproblem
ch9
misc
q1
q1-1
p419
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
The order of the differential equation $2x^2\large\frac{d^2y}{dx^2}$$-3\frac{dy}{dx}$$+y=0\;is$
cbse
class12
bookproblem
ch9
sec1
q12
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Write Minors and Cofactors of the elements of following determinants: $ (i) \quad \begin{vmatrix} 2&-4 \\ 0&3 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec4
q1
q1-1
p126
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
If area of triangle is $35\; sq\; units$ with vertices $(2, -6), (5, 4)$ and $(k, 4)$. Then $k$ is
cbse
class12
bookproblem
ch4
sec3
q5
p123
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Find equation of line joining (1, 2) and (3, 6) using determinants
cbse
class12
bookproblem
ch4
sec3
q4
p123
qp1
medium
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Find the value of $k$ if area of triangle is $4\; sq. units$ and vertices are: $(k, 0), (4, 0), (0, 2)$
cbse
class12
bookproblem
ch4
sec3
q3
p123
qp1
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Show that the points A (a, b + c), B (b, c + a), C (c, a + b) are collinear.
cbse
class12
bookproblem
ch4
sec3
q2
p123
medium
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Find area of the triangle with vertices at the point given in (1, 0), (6, 0), (4, 3)
cbse
class12
bookproblem
ch4
sec3
q1
p122
qp1
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Which of the following is correct:
cbse
class12
bookproblem
ch4
sec2
q16
p121
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Let $A$ be a square matrix of order $3 \times 3$, then $ |kA|$ is equal to:
cbse
class12
bookproblem
ch4
sec2
q15
p121
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} a^2+1&ab&ac \\ ab&b^2+1&bc \\ ca&cb&c^2+1 \end{vmatrix} = 1+a^2+b^2+c^2 \end{array} \]
cbse
class12
bookproblem
ch4
sec2
q14
p121
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1+a^2-b^2&2ab&-2b \\ 2ab&1-a^2+b^2&2a \\ 2b&-2a&1-a^2-b^2 \end{vmatrix} = (1+a^2+b^2)^3 \end{array} \]
cbse
class12
bookproblem
ch4
sec2
q13
p121
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that \[ \begin{array}{l} \begin{vmatrix} 1&x&x^2 \\ x^2&1&x \\ x&x^2&1 \end{vmatrix} = (1-x^3)^2 \end{array} \]
cbse
class12
bookproblem
ch4
sec2
q12
p121
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Solve the following $\tan^{-1} \sqrt{3} -sec^{-1} (-2)$:
cbse
class12
bookproblem
ch2
sec1
q14
p42
medium
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
By using the properties of determinants show that $ (i) \begin{vmatrix} a-b-c&2a&2a \\ 2b&b-c-a&2b \\ 2c&2c&c-a-b \end{vmatrix} = (a+b+c)^3 $
cbse
class12
bookproblem
ch4
sec2
q11
q11-1
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
The degree of the differential equation $\bigg(\large\frac{d^2y}{dx^2}\bigg)^3+\bigg(\frac{dy}{dx}\bigg)^2$$+\sin\bigg(\large\frac{dy}{dx}\bigg)$$+1=0\; is$
cbse
class12
bookproblem
ch9
sec1
q11
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
By using the properties of determinants show that $ (i) \begin{vmatrix} x+4&2x&2x \\ 2x&x+4&2x \\ 2x&2x&x+4 \end{vmatrix} = (5x+4)(4-x)^2 $
cbse
class12
bookproblem
ch4
sec2
q10
q10-1
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
By using the properties of determinants show that \[\begin{vmatrix} x&x^2&yz \\ y&y^2&zx \\ z&z^2&xy \end{vmatrix} = (x-y)(y-z)(z-x)(xy+yz+zx) \]
cbse
class12
bookproblem
ch4
sec2
q9
p120
difficult
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Determine order and degree (if defined) of differential equation $y''+2y'+\sin y=0$
cbse
class12
bookproblem
ch9
sec1
q10
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Determine order and degree (if defined) of differential equation $y''+(y')^2+2y=0$
cbse
class12
bookproblem
ch9
sec1
q9
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
Determine order and degree (if defined) of differential equation $y'+y=e^x$
cbse
class12
bookproblem
ch9
sec1
q8
p383
easy
math
sec-a
asked
Nov 28, 2012
by
sreemathi.v
1
answer
By using the properties of determinants show that $ (i) \quad \begin{vmatrix} 1&a&a^2 \\ 1&b&b^2 \\ 1&c&c^2 \end{vmatrix} = (a-b)(b-c)(c-a) $
cbse
class12
bookproblem
ch4
sec2
q8
q8-1
p120
easy
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} -a^2&ab&ac \\ ba&-b^2&bc \\ ca&cb&-c^2 \end{vmatrix} = 4a^2b^2c^2\]
cbse
class12
bookproblem
ch4
sec2
q7
p120
medium
sec-b
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 0&a&-b \\ -a&0&-c \\ b&c&0 \end{vmatrix} = 0 \]
cbse
class12
bookproblem
ch4
sec2
q6
p120
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} b+c&q+r&y+z \\ c+a&r+p&z+x \\ a+b&p+q&x+y \end{vmatrix} = 2 \begin{vmatrix} a&p&x \\ b&q&y \\ c&r&z \end{vmatrix} \]
cbse
class12
bookproblem
ch4
sec2
q5
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 1&bc&a(b+c) \\ 1&ca&b(c+a) \\ 1&ab&c(a+b) \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q4
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} 2&7&65 \\ 3&8&75 \\ 5&9&86 \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q3
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} a-b&b-c&c-a \\b-c&c-a&a-b \\c-a&a-b&b-c \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q2
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Using the property of determinants and without expanding, prove that \[ \begin{vmatrix} x&a&x+a \\y&b&y+b \\ z&c&z+c \end{vmatrix} = 0\]
cbse
class12
bookproblem
ch4
sec2
q1
p119
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
$ \text{If } \begin{vmatrix} x&2 \\ 18&x \end{vmatrix} = \begin{vmatrix} 6&2 \\ 18&6 \end{vmatrix}$, then $x$ is equal to:
cbse
class12
bookproblem
ch4
sec1
q8
p109
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Find the value of $x$, if $ \begin{vmatrix} 2&4 \\ 5&1 \end{vmatrix} = \begin{vmatrix} 2x&4 \\ 6&x \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q7
q7-1
p109
easy
shortanswer
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
If $A = \begin{bmatrix} 1&1&-2\\ 2&1&-3 \\5&4&-9 \end{bmatrix}$, then find $|A|$
cbse
class12
bookproblem
ch4
sec1
q6
p109
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Evaluate the determinant: $\begin{vmatrix} 3&-1&-2 \\ 0&0&-1 \\3&-5&0 \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q5
q5-1
p108
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
\[ \text{If A = } \begin{bmatrix} 1&0&1 \\ 0&1&2 \\ 0&0&4 \end{bmatrix}, \text{then show that } |\;3A\;| = 27|\;A\;|\]
cbse
class12
bookproblem
ch4
sec1
q4
p108
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
\[ \text{If A = } \begin{bmatrix} 1&2 \\ 4&2 \end{bmatrix}, \text{then show that } |\;2A\;| = 4|\;A;|\]
cbse
class12
bookproblem
ch4
sec1
q3
p108
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Evaluate the determinant: $\begin{vmatrix} cos\theta &-sin\theta \\ sin\theta & cos\theta \end{vmatrix}$
cbse
class12
bookproblem
ch4
sec1
q2
q2-1
p108
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
Evaluate the determinant:$ \begin{vmatrix} 2&4 \\ -5&-1 \end{vmatrix} $
cbse
class12
bookproblem
ch4
sec1
q1
p108
easy
sec-a
math
asked
Nov 28, 2012
by
balaji.thirumalai
1
answer
If $ \sin^{-1} x=y$ then:
cbse
class12
bookproblem
ch2
sec1
q13
p42
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
1
answer
Find the value of the following:\[cos^{-1} \frac {1} {2} +2 sin^{-1}\frac {1} {2} \]
cbse
class12
bookproblem
ch2
sec1
q12
p42
medium
sec-b
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the value of the following: \[ tan^{-1} (1) \;+ \; cos^{-1} \frac {-1} {2} + sin^{-1} \frac {-1} {2} \]
cbse
class12
bookproblem
ch2
sec1
q11
p42
easy
sec-b
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: <br> $ \mathrm{cosec}^{-1} (-\sqrt 2) $
cbse
class12
bookproblem
ch2
sec1
q10
p42
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal value of the following: $cos^{-1} \bigg( -\frac {1} {\sqrt 2} \bigg) $
cbse
class12
bookproblem
ch2
sec1
q9
p42
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following : $\cot^{-1} (\sqrt 3) $
cbse
class12
bookproblem
ch2
sec1
q8
p42
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: $sec^{-1} \bigg( \frac {2} {\sqrt 3} \bigg) $
cbse
class12
bookproblem
ch2
sec1
q7
p42
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: $tan^{-1} (-1)$
cbse
class12
bookproblem
ch2
sec1
q6
p41
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: $cos^{-1} \bigg(-\frac {1} {2} \bigg ) $
cbse
class12
bookproblem
ch2
sec1
q5
p41
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: <br>$ tan^{-1} (-\sqrt3)$
cbse
class12
bookproblem
ch2
sec1
q4
p41
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: $cosec^{-1} (2) $
cbse
class12
bookproblem
ch2
sec1
q3
p41
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
1
answer
Find the principal values of the following: <br> $cos^{-1} \bigg(\large\frac { \sqrt 3} {2}\bigg)$
cbse
class12
bookproblem
ch2
sec1
q2
p41
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
Find the principal values of the following: <br> $ sin^{-1} \bigg( -\frac {1} {2}\bigg) $
cbse
class12
bookproblem
ch2
sec1
q1
p41
easy
sec-a
math
asked
Nov 28, 2012
by
vaishali.a
2
answers
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