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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Prove that \( x^2-y^2 = c ( x^2-y^2 )^2 \) is the general solution of differential equation \(( x^3-3xy^2) dx = (y^3-3x^2y) dx\).
cbse
class12
modelpaper
2012
sec-c
q26
math
asked
Jan 2, 2013
0
answers
From the point P(1, 2, 4 ) a perpendicular is drawn on the plane \( 2x+y-2z+3 = 0 \). Find the equation of the length and coordinates of the foot of the \( \bot \)
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 2, 2013
1
answer
A farmer mixes two brands P and Q of cattle feed. Brand P costing Rs. 200 per bag contains 1.5 units of nutritional element A, 11.25 units of element B and 3 units of element C . The minimum requirements of nutrients A, B and C are 18 units, 45 units and 24 units, respectively. Determine the number of bags of each brand which should be mixed in order to produce a mixture having a minimum cost per bag? What is the minimum cost of the mixture per bag?
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 2, 2013
0
answers
Suppose, we have four boxes A, B, C and D containing coloured marbles as given below : One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A? box B? and box C?
cbse
class12
modelpaper
sec-c
q29
math
asked
Jan 2, 2013
0
answers
Relation R in the set of Z of all integers defined as R = {(x, y) : x-y is an integer }.
cbse
class12
modelpaper
2012
sec-a
q1
math
asked
Jan 2, 2013
1
answer
Using principle value, evaluate the following : $ \cos^{-1} \bigg( \cos\large\frac{2\pi}{3} \bigg)$$ + \sin^{-1} \bigg( \sin\large\frac{2\pi}{3} \bigg) .$
cbse
class12
modelpaper
2012
sec-a
q2
math
asked
Jan 2, 2013
1
answer
Find the value of x and y if : $2\begin{bmatrix} 1 & 3 \\ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \\ 1 & 8 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 2, 2013
1
answer
If matrix A = [ 1 2 3 ] Write AA' where A' is the transpose of matrix A.
cbse
class12
modelpaper
2012
sec-a
q4
math
asked
Jan 2, 2013
0
answers
Write the value of the determinant : $\begin{bmatrix} 2 & 3 & 4 \\ 5 & 6 & 8 \\ 6x & 9x & 12x \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q5
math
asked
Jan 2, 2013
1
answer
The radius of a circle is increasing uniformly at the rate of 3 cm per second. Find the rate in which the area of the circle is increasing when the radius is 10 cm.
cbse
class12
modelpaper
2012
sec-a
q6
math
asked
Jan 2, 2013
0
answers
\( \int \: \large\frac{x^3+5x^2-4}{x^2}\normalsize dx. \)
cbse
class12
modelpaper
2012
sec-a
q7
math
asked
Jan 2, 2013
0
answers
Find the value of the parallelopipped whose edges are $ \overrightarrow a = 2\hat i - 3\hat j + 4\hat k, \overrightarrow b = \hat i - 2\hat j - \hat k \: and \: \overrightarrow c = 2\hat i - \hat j + 2\hat k $
cbse
class12
modelpaper
2012
sec-a
q8
math
asked
Jan 2, 2013
0
answers
Find the scalar and vector components of the vector with initial point ( 2, 1 ) and terminal point ( -5, 7 ).
cbse
class12
modelpaper
2012
sec-a
q9
math
asked
Jan 2, 2013
1
answer
Write the direction cosines of a line equally inclined to the three coordinate axes.
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Jan 2, 2013
0
answers
(i) Is the binary operation * defined on set N, given a * b = \( \large\frac{a+b}{2} \) for all a, b \( \in\) N, comutative? (ii) Is the above binary operation * associative ?
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 2, 2013
0
answers
Write the following functions in the simplest form : \[ (i) tan^{-1} \bigg( \frac{\sqrt{1+x^2} - 1}{x} \bigg), x \neq 0 \] \[(ii) tan^{-1} \frac{1}{\sqrt{x^2-1}} ,| x | > 1 \]
cbse
class12
modelpaper
ch2
2012
sec-b
q12
easy
math
asked
Dec 31, 2012
1
answer
Using properties of determinants, prove the following: $ \begin{bmatrix} a^2+1 \quad & ab \quad & ac \\ ab \quad & b^2+1 \quad & bc \\ ca \quad & cb \quad & c^2+1 \end{bmatrix} = 1+a^2+b^2+c^2. $
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Dec 31, 2012
0
answers
Prove that : $ (i) \large \frac{d}{dx} $$(a^x) = a^x log_e a. \; (ii) \large\frac{d}{dx}$$ (e^x) = e^x. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Dec 31, 2012
0
answers
Find all the points of discontinuity of f, where $ f(x) = \left \{ \begin{array}{1 1} \large\frac{sinx}{x}, \quad & if\: x < 0 \\ x+1, \quad & if\: x \geq 0 \end{array}\right \}. $
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Dec 31, 2012
0
answers
A point source of light along a straight road is a height of 'a' metres. A boy 'b' metres in height is walking along the road. How fast is his shadow increasing if he is walking away from the light at the rate of c metres per minute.?
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 31, 2012
0
answers
The two equal sides of an isosceles triangles with fixed base b cm are decreasing at the rate of 3 cm/sec. How fast is the area decreasing when two equal sides are equal to the base.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 31, 2012
0
answers
Evaluate : $ \int \: \bigg[ \large\frac{1}{log \: x} - \large\frac{1}{(log\: x )^2} \bigg]$$ dx. $
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Dec 31, 2012
0
answers
Integrate : $\int \:\large \frac{x}{(x-1)^2(x+2)} $
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Dec 31, 2012
0
answers
Integrate : $ \int \: \large\frac{3x+5}{x^2-x^2-x-1} $
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Dec 31, 2012
0
answers
Integrate : $\int \: x(\ log x )^2dx.$
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Dec 31, 2012
0
answers
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
0
answers
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
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
0
answers
There are two bags I and II. Bag I contains 3 white and 4 red balls and Bag II contains 5 white and 6 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
q22
math
asked
Dec 31, 2012
0
answers
Show that the height of the cylinder of maximum volume that can be inscribed in a cone of height h is \( \large\frac{1}{3} \) h.
cbse
class12
modelpaper
2008-1
sec-c
q24
math
asked
Dec 29, 2012
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
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
0
answers
Solve the following differential equation : $ \large\frac{dy}{dx} = \large\frac{x(2y-x)}{x(2y+x)} $ if \( y = 1 \) when \( x = 1 \)
cbse
class12
modelpaper
2008-1
sec-b
q18
math
asked
Dec 29, 2012
0
answers
If $ A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & 2 \\[0.3em] 2 & 2 & 1 \end{bmatrix}$ what is $ A^2-4A-5I=0$
cbse
class12
modelpaper
2008-1
sec-b
q13
ch3
medium
math
asked
Dec 29, 2012
1
answer
A manufacturer can sell x items at a price of Rs. \( \bigg( 5 - \large \frac{x}{100} \bigg) \) each. The cost price of x items is Rs. $ \bigg( \large\frac{x}{5}$$ + 500 \bigg) $. Find the number of items he should sell to earn the maximum profit.
cbse
class12
modelpaper
2009
sec-c
q29
math
asked
Dec 29, 2012
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
0
answers
Evaluate : $ \int \mathrm \: x \sin^{-1}x \: dx $
cbse
class12
modelpaper
2009
sec-b
q14
math
asked
Dec 29, 2012
0
answers
If \( (\cos x)^y = (\sin y)^x \), find \( \large\frac{dy}{dx} \)
cbse
class12
modelpaper
2009
sec-b
q12
math
asked
Dec 29, 2012
0
answers
Find the intervals in which the function f given by $ f(x) = \sin x + \cos x, 0 \leq \: x \leq \: 2\pi, $is strictly increasing or strictly decreasing.
cbse
class12
modelpaper
2009
sec-b
q11
math
asked
Dec 29, 2012
0
answers
Prove that the curves \( y^2 = 4x\) and \( x^2 = 4y\) divide the area of the square bounded by \( x = 0, x = 4, y = 4\) and \(y = 0\) into three equal parts.
cbse
class12
modelpaper
2012
sec-c
q34
math
asked
Dec 29, 2012
0
answers
An open box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides. Find the volume of the largest such box.
cbse
class12
modelpaper
2012
sec-c
q33
math
asked
Dec 29, 2012
1
answer
If \( A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end {bmatrix} \), find \( A^{-1} \) . Using \( A^{-1} \) , solve the system of equations : $ 2x – 3y + 5z = 11 ,3x + 2y – 4z = –5 ,x + y – 2x = –3. $
cbse
class12
modelpaper
2009
sec-c
q32
ch4
bookproblem
sec6
q15
p137
math
asked
Dec 29, 2012
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
0
answers
Find the equation of the plane passing through the point (–1, 3, 2) and perpendicular to each of the planes \( x + 2y + 3z = 5\: and\: 3x + 3y + z = 0\)
cbse
modelpaper
2012
sec-b
q30
asked
Dec 29, 2012
0
answers
Find the equation of the curve passing through the origin and satisfying the differential equation \((1 + x^2) \frac{dy}{dx} + 2xy = 4x^2 \)
cbse
class12
modelpaper
2012
sec-b
q28
math
asked
Dec 29, 2012
0
answers
Find \[ \int \mathrm \: \frac{x^2+1}{x^2-5x+6} dx \]
cbse
class12
modelpaper
2012
sec-b
q26
math
asked
Dec 29, 2012
0
answers
Evaluate : $ \int\: \large\frac{dx}{(x^2-3x+2) \sqrt {x-1}} $
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Dec 29, 2012
0
answers
Using elementary transformation, find the inverse of $\begin{bmatrix} 1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-c
ch3
q23
easy
math
asked
Dec 29, 2012
1
answer
Evaluate :$ \int_1^4\: ( | x-1|+ | x-2 | + | x=3 | ) dx $
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Dec 29, 2012
0
answers
Let \( f : N \rightarrow N\) be defined by : $ f(n) = \left\{ \begin{array}{l l} \large \frac{n+1}{2} & \quad \text{if $n$ is odd}\\ \large \frac{n}{2} & \quad \text{ if $n$ is even} \end{array} for \: all\: n\: \in \: N. \right.$
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Dec 29, 2012
0
answers
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