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Recent questions tagged q11
Questions
Show that $| \overrightarrow a | \overrightarrow b + | \overrightarrow b | \overrightarrow a$ is perpendicular to $| \overrightarrow a | \overrightarrow b - | \overrightarrow b | \overrightarrow a$, for any two nonzero vectors $\overrightarrow a$ and $\overrightarrow b$.
cbse
class12
bookproblem
ch10
sec3
q11
p448
easy
sec-b
math
asked
Dec 6, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\frac{\large x}{\large \sqrt{x+4}},x\;>\;0$
cbse
class12
bookproblem
ch7
sec2
q11
p304
sec-b
easy
math
asked
Dec 6, 2012
by
sreemathi.v
1
answer
Find the integrals of the functions\[\cos^42x\]
cbse
class12
bookproblem
ch7
sec3
q11
p307
sec-b
medium
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the functions\[\frac{1}{9x^2+6x+5}\]
cbse
class12
bookproblem
ch7
sec4
q11
p316
sec-a
easy
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Integrate the rational functions\[\frac{5x}{(x+1)(x^2-4)}\]
cbse
class12
bookproblem
ch7
sec5
q11
p322
sec-c
difficult
math
asked
Dec 5, 2012
by
sreemathi.v
1
answer
Let the vectors $ \overrightarrow a$ and $ \overrightarrow b$ be such that $| \overrightarrow a | = 3$ and $ |\overrightarrow b | = \frac{\large \sqrt 2}{\large 3}$ , then $\overrightarrow a \times \overrightarrow b$ is a unit vector, if the angle between $ \overrightarrow a$ and $ \overrightarrow b$ is
cbse
class12
bookproblem
ch10
sec4
q11
p455
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are $ \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3}, \: \frac{\large 1}{\large \sqrt 3} $
cbse
class12
bookproblem
ch10
misc
q11
p458
easy
sec-a
math
asked
Dec 5, 2012
by
thanvigandhi_1
1
answer
Integrate the function $\frac{x\cos^{-1}x}{\sqrt{1-x^2}}$
cbse
class12
bookproblem
ch7
sec6
q11
p327
sec-b
medium
math
modelpaper-2014
p18-a
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Using the method of integration find the area bounded by the curve I x I + I y I =1 . [Hint: The required region is bounded by lines \(x + y = 1, x - y = 1, -x + y = 1\) and \( -x -y = 1\)].
cbse
class12
bookproblem
ch8
misc
q11
p375
sec-b
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in $ \Large \int \normalsize \sqrt{x^2-8x+7} \: dx$ is equal to\[ \begin{array}{l} (A)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}+9\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \\ (B)\frac{1}{2}(x+4)\sqrt{x^2-8x+7}+9\;log\mid x+4+\sqrt{x^2-8x+7}\mid + \; C \\ (C) \frac{1}{2}(x-4)\sqrt{x^2-8x+7}-3\sqrt2log\mid x-4+\sqrt{x^2-8x+7}\mid+ \; C \\ (D)\frac{1}{2}(x-4)\sqrt{x^2-8x+7}-\frac{9}{2}\;log\mid x-4+\sqrt{x^2-8x+7}\mid + \; C \end{array}\]
cbse
class12
bookproblem
ch7
sec7
q11
p330
sec-a
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
Find the area of the region bounded by the curve $y^2 = 4x$ and the line $x = 3$.
cbse
class12
bookproblem
ch8
sec1
q11
p366
sec-b
easy
math
asked
Dec 4, 2012
by
thanvigandhi_1
1
answer
Evaluate the definite integral\[\int\limits_2^3\frac{dx}{x^2-1}\]
cbse
class12
bookproblem
ch7
sec9
q11
p338
sec-a
easy
math
asked
Dec 4, 2012
by
sreemathi.v
1
answer
By using the properties of definite integrals,evaluate the integral $\begin{align*}\int\limits_\frac{\Large -\pi}{\Large 2}^\frac{\Large \pi}{\Large 2}\sin^2\;x\;dx \end{align*}$
cbse
class12
bookproblem
ch7
sec11
q11
p347
sec-a
easy
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
Integrate the function\[\int\frac{1}{\cos(x+a)\cos(x+b)}\]
cbse
class12
bookproblem
ch7
misc
q11
p352
sec-b
difficult
math
asked
Dec 3, 2012
by
sreemathi.v
1
answer
The number of arbitrary constants in the general solution of a differential equation of fourth order are
cbse
class12
bookproblem
ch9
sec2
q11
p385
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Which of the following differential equations has $y\;=\;c_1e^x+c_2e^{-x}$ as the general solution?
cbse
class12
bookproblem
ch9
sec3
q11
p391
easy
sec-a
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find a particular solution satisfying the given condition $(x^3+x^2+x+1)\large\frac{dy}{dx}$$=2x^2+x;y=1\;when\;x=0$
cbse
class12
bookproblem
ch9
sec4
q11
p396
medium
sec-b
math
asked
Nov 30, 2012
by
sreemathi.v
1
answer
Find the particular solution satisfying the given condition $(x+y)dy+(x-y)dx=0;\;y=1;\;when\;x=\;1$
cbse
class12
bookproblem
ch9
sec5
q11
p406
medium
sec-b
math
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Find the general solution of the differential equation $y\;dx+(x-y^2)dy=0$
cbse
class12
bookproblem
ch9
sec6
q11
p414
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
Using properties of determinants, prove that: $\begin{vmatrix} \alpha & \alpha^2 & \beta+\gamma\\ \beta & \beta^2 & \alpha+\gamma\\ \gamma & \gamma^2 & \alpha+\beta \end{vmatrix} = (\beta-\gamma) (\gamma - \alpha) (\alpha-\beta) (\alpha+\beta+\gamma)$
cbse
class12
bookproblem
ch4
misc
q11
p142
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Solve system of linear equations, using matrix method:\[\] \[2x+y+z=1\] \[x-2y-z = \frac{3}{2}\] \[3y-5z=9\]
cbse
class12
bookproblem
ch4
sec6
q11
p136
difficult
sec-c
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
prove that \[tan^{-1} \left ( \frac {{\sqrt {1+x}}-{\sqrt {1-x}}}{{\sqrt {1+x}}+{\sqrt {1-x}}} \right ) = \frac {\pi}{4} -\frac{1}{2} cos^{-1}x,-\frac{1}{\sqrt2} \leq x \leq 1 \]
cbse
class12
bookproblem
ch2
misc
q11
p52
sec-b
medium
modelpaper
2012
q12
math
asked
Nov 29, 2012
by
vaishali.a
1
answer
Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1&0&0 \\ 0&cos\alpha&sin\alpha \\ 0&sin\alpha&-cos\alpha \\ \end{bmatrix} \]
cbse
class12
bookproblem
ch4
sec5
q11
p132
easy
sec-b
math
asked
Nov 29, 2012
by
balaji.thirumalai
1
answer
Find a particular solution of the differential equation \((x-y)(dx+dy) = dx - dy\),given that \( y=\;-1\),when \( x=\;0\)
cbse
class12
bookproblem
ch9
misc
q11
p420
medium
math
sec-b
asked
Nov 29, 2012
by
sreemathi.v
1
answer
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
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
A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10 m. Find the dimensions of the window to admit maximum light through the whole opening.
cbse
class12
bookproblem
ch6
misc
q11
p243
sec-c
medium
math
asked
Nov 28, 2012
by
thanvigandhi_1
1
answer
Show that the set of all matrices of the form $\bigl(\begin{smallmatrix} a & 0 \\ 0 & 0 \end{smallmatrix} \bigr) $, $a \in R$ − {0} forms an abelian group under matrix multiplication.
tnstate
class12
bookproblem
ch9
sec2
exercise9-4
p190
q11
modelpaper
mar-2008
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
In a game, a man wins a rupee for a six and loses a rupee for any other number when a fair die is thrown. The man decided to throw a die thrice but to quit as and when he gets a six. Find the expected value of the amount he wins / loses.
cbse
class12
bookproblem
ch13
misc
p583
q11
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
2
answers
Find the probability of getting 5 exactly twice in 7 throws of a die.
cbse
class12
bookproblem
ch13
sec5
p578
q11
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.
cbse
class12
bookproblem
ch13
sec4
p571
q11
sec-b
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
cbse
class12
bookproblem
ch13
sec3
p557
q11
sec-c
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6. Find (i) P(A and B) (ii) P(A and not B) (iii) P(A or B) (iv) P(neither A nor B)
cbse
class12
bookproblem
ch13
sec2
p546
q11
sec-a
easy
math
asked
Nov 27, 2012
by
balaji.thirumalai
1
answer
It is given that at $x = 1$, the function $x^4 – 62x^2 + ax + 9$ attains its maximum value, on the interval $[0, 2].$ Find the value of $a.$
cbse
class12
bookproblem
ch6
sec5
q11
p233
sec-a
easy
math
asked
Nov 27, 2012
by
thanvigandhi_1
1
answer
If $ x\begin{bmatrix} 2 \\ 3 \end{bmatrix} + y\begin{bmatrix} -1 \\ 1 \end{bmatrix} = \begin{bmatrix} 10 \\ 5 \end{bmatrix} $, find the values of $x$ and $y$.
cbse
class12
bookproblem
ch3
sec2
q11
p81
easy
veryshort-answer
sec-a
math
asked
Nov 25, 2012
by
pady_1
1
answer
If $A, B$ are symmetric matrices of the same order, then $AB - BA$ is
cbse
class12
bookproblem
ch3
sec3
q11
p90
easy
shortanswer
sec-a
math
asked
Nov 23, 2012
by
pady_1
1
answer
Using elementary transformations, find the inverse of the matrix if it exists - $ \begin{bmatrix} 2 & -6 \\ 1 & -2 \end{bmatrix} $
cbse
class12
bookproblem
ch3
sec4
q11
p97
easy
shortanswer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Find the equation of all lines having slope \(2\) that are tangents to the curve $ y= \large\frac{1}{x-3}, $$\: x \neq 3$
cbse
class12
bookproblem
ch6
sec3
q11
p212
sec-a
medium
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by \(f (x) = x^2 – x + 1\) is neither strictly increasing nor strictly decreasing on \((– 1, 1).\)
cbse
class12
bookproblem
ch6
sec2
q11
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.
cbse
class12
bookproblem
ch6
sec1
q11
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the matrix \( X \) so that \( X \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \: = \: \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix} \)
cbse
class12
bookproblem
ch3
misc
q11
p101
easy
shortanswer
sec-b
math
asked
Nov 22, 2012
by
pady_1
1
answer
Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find the inverse of the following function \(F\) from \(S\) to \(T\), if it exists - \[\;\; F=\{(a,3), (b,2), (c,1)\}\]
cbse
class12
bookproblem
ch1
misc
q11
q11-1
p30
easy
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Let \(f:R \to R\) be defined as \(f(x)=10x+7.\)Find the function \(g:R \to R\) such that \(g\;o\;f = f\;o\;g = I_R.\)
cbse
class12
bookproblem
ch1
misc
q1
p29
sec-b
easy
modelpaper
2012
q11
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let $(A=N \times N \,and\, * )$ be the binary operation on $(A)$ defined by $( (a, b) * (c, d) = (a + c, b + d))$. Show that * is commutative and associative. Find the identity element for * on $( A )$, if any.
cbse
class12
bookproblem
ch1
sec4
q11
p25
sec-b
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Differentiate w.r.t. \(x\) the function in \( x^{\large x^2-3} + ( x - 3 )^{\large x^2} \), for \(x > 3\)
cbse
class12
bookproblem
ch5
misc
q11
p191
sec-c
medium
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Consider the binary operation \( \wedge\) on the set \(\{1, 2, 3, 4, 5\}\) defined by \(a \wedge b = min \{a, b\}\). Write the multiplication table of the operation \( \wedge\) .
cbse
class12
bookproblem
ch1
sec4
q3
p24
sec-a
easy
modelpaper
2012
q11
math
asked
Nov 20, 2012
by
vaishali.a
1
answer
If \( y = 5 \cos x - 3 \sin x \) , prove that \( \large\frac{d^2y}{dx^2}\normalsize + y = 0\)
cbse
class12
bookproblem
ch5
sec7
q11
p183
sec-a
easy
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
If $x = \sqrt {a^{\large sin^{-1}t}}, \: y = \sqrt {a^{\large cos^{-1}t}} $, show that $\frac {\large dy}{\large dx} = -\frac{\large y}{\large x} $
cbse
class12
bookproblem
ch5
sec6
q11
p181
medium
sec-c
math
asked
Nov 20, 2012
by
thanvigandhi_1
1
answer
Differentiate the functions given in w.r.t. $x : $ $ (x \cos x )^{\large x} + (x\sin x)^{\Large\frac{1}{x}} $
cbse
class12
bookproblem
ch5
sec5
q11
p178
sec-c
difficult
math
asked
Nov 17, 2012
by
thanvigandhi_1
1
answer
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