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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
Find the equation of tangent to the curve \( y = \sqrt {3x-2}\) which is parallel to the line \( 4x-2y+5=0\).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 3, 2013
0
answers
Find the intervals in which the function f given by $ f(x) = x^3 + \large\frac{1}{x^3}$$, x \neq 0 $ is, (i) increasing, (ii) decreasing.
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 3, 2013
0
answers
Evaluate : \[ (i) \int \: \sqrt {x^2+4x+8} dx \] \[ (ii) \int \: \sqrt {(x-5)(7-x)} dx \] \[ (iii) \int \: \sqrt {14x-20-2x^2} dx \] \[ (iv) \int \: \sqrt {4ax-x^2} dx \]
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 3, 2013
0
answers
Evaluate $ \int\large\frac{dx}{x[6(\log x)^2+7(\log x)+2]} $
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 3, 2013
0
answers
Evaluate $\int\: tan^{-1} \sqrt {\large\frac{1-sinx}{1+sinx}}$$dx.$
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 3, 2013
0
answers
Solve the following differential equation : \( \frac{dy}{dx} = \frac{x(2y-x)}{x(2y+x)}, \) if y = 1 when x = 1.
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 3, 2013
0
answers
Find the particular solution, satisfying the given condition for the differential equation $ \large\frac{dy}{dx} - \frac{y}{x} +$$ cosec \bigg(\large \frac{y}{x} \bigg)$$ = 0, y = 0\: when \: x = 1$
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 3, 2013
0
answers
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
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
0
answers
There are two bags I and II. Bag I contains 2 white and 3 red balls and Bag II contains 4 white and 5 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
q21
math
asked
Jan 3, 2013
1
answer
Find \( \mu\) variance for the following distribution :
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Jan 3, 2013
0
answers
Give example of relations which are : \[ \begin{array} (i)\: Symmetric \: but \: neither \: reflexive \: nor\: transitive \\ (ii) \: Transitive\: but\: neither\: reflexive\: nor\: symmetric \\ (iii)\: Reflexive \: and\: symmetric\: but\: not \: transitive \\ (iv)\: Reflexive \: and transitive\: but\: not\: symmetric \\ (v)\: Symmetric\: and\: transitive\: but \: not\: reflexive \end{array}\]
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 3, 2013
0
answers
Let \( A = \begin{bmatrix} 0 & 1 \\ 0 & 0 \end{bmatrix} \) , show that \( (aI + bA)^n = a^nI+na^{n-1}bA, \) where I is the identity matrix of order zero \( n \in N. \) If $ \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix} $ prove that : $ \begin{bmatrix} 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \\ 3^{n-1} & 3^{n-1} & 3^{n-1} \end{bmatrix}, n \in N. $
cbse
class12
modelpaper
2012
sec-c
q24
difficult
math
asked
Jan 3, 2013
1
answer
If A and B are square matrices of the same order such that AB = BA, then proved by induction that \( AB^n = ^nA.\) Further, prove that \( (AB)^n = A^nB^n\) for all \( n \in N.\)
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 2, 2013
0
answers
Show that the rectangle of maximum, area that can be inscribed in a circle is a square.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 2, 2013
0
answers
Find the equation of the tangent to the curve \( y = \sqrt {3x-2} \) which is parallel to the line \( 4x-2y+5 = 0\).
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 2, 2013
0
answers
Using integration, find the area lying above x - axis included, between the circle \( x^2+y^2 = 8x\) and the parabola \(y^2 = 4x\)
cbse
class12
modelpaper
2012
sec-c
q26
math
asked
Jan 2, 2013
0
answers
Find the distance of the point ( -2, 3, -4 ) from the line \(\large \frac{x+2}{3}=\frac{2y+3}{4}=\frac{3z+4}{5}\), measured parallel to the plane \( 4x+12y-3z+1=0\).
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 2, 2013
0
answers
Find the co-ordinates of the image of the point ( 1, 3, 4 ) in the plane \( 2x-y+z+3=0\)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 2, 2013
0
answers
Reshma wishes to mix two types of food P and Q in such a way that the vitamin contents of the mixture contains atleast 8 units of vitamin A and 11 units of vitamin B. Food P costs Rs. 60/kg and food Q costs Rs. 80/kg. Food P contains 3 units/kg of vitamin A and 5 units of vitamin B, while food Q contains 4 units/kg of vitamin A and 2 units/kg of vitamin B. Determine the minimum cost of the mixture.
cbse
class12
modelpaper
2012
sec-c
q29
math
asked
Jan 2, 2013
1
answer
Show that the relation R in the set R of real numbers, defined as \( R = {( a, b ) : a \leq b^2}\), is neither reflexive, nor symmetric , nor transitive.
cbse
class12
modelpaper
2012
sec-a
q1
math
asked
Jan 2, 2013
0
answers
Find the value of \( cosec^{-1} (2) \)
cbse
class12
modelpaper
2012
sec-a
q2
math
asked
Jan 2, 2013
1
answer
Find the value of y if $\begin{bmatrix} x-y & 2 \\ x & 5 \end{bmatrix} = \begin{bmatrix} 2 & 2 \\ 3 & 5 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 2, 2013
1
answer
In the matrix $A=\begin{bmatrix} 2 & 5 & 19 & -7 \\ 35 & -2 & \frac{5}{2} & 12 \\ \sqrt 3 & 1 & -5 & 17 \end{bmatrix} $Write (i) The order of the matrix .
cbse
class12
modelpaper
2012
sec-a
q4
q4-1
ch3
easy
math
asked
Jan 2, 2013
1
answer
Write the value of following determinants : $ \begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & 2a-b & b-c \end{vmatrix} $
cbse
class12
modelpaper
2012
sec-a
q5
math
asked
Jan 2, 2013
0
answers
A balloon which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the radius is 10 cm.
cbse
class12
modelpaper
2012
sec-a
q6
math
asked
Jan 2, 2013
0
answers
Evaluate : $ \int \: \large\frac{cos\sqrt x}{\sqrt x}$$dx $
cbse
class12
modelpaper
2012
sec-a
q7
math
asked
Jan 2, 2013
0
answers
Show that the vectors : $ \overrightarrow a = -4\hat i - 6\hat j - 2\hat k, \overrightarrow b = -\hat i + 4\hat j + 3\hat k \: and \: \overrightarrow c = -8\hat i - \hat j + 3\hat k $ are coplanar.
cbse
class12
modelpaper
2012
sec-a
q8
math
asked
Jan 2, 2013
0
answers
Find the sum of the vectors : $ \overrightarrow a = \hat i - 2\hat j + \hat k, \overrightarrow b = -2\hat i + 4\hat j + 5\hat k \: and \: \overrightarrow c = \hat i - 6\hat j - 7\hat k $
cbse
class12
modelpaper
2012
sec-a
q9
math
asked
Jan 2, 2013
0
answers
Find the equation of the plane passing through the point ( 1, -1, 2 ) having ( 2, 3, 2 ) as direction ratios of normal to the plane?
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Jan 2, 2013
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} \forall \: n \: \in\: N. \right.$ Find whether the function f is bijective.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 2, 2013
0
answers
Prove that : \( tan^{-1}\bigg(\frac{1}{3} \bigg)+tan^{-1}\bigg(\frac{1}{5}\bigg)+tan^{-1}\bigg(\frac{1}{7}\bigg)+tan^{-1}\bigg(\frac{1}{8}\bigg)=\large\frac{\pi}{4} \)
cbse
class12
modelpaper
ch2
2012
sec-b
q12
difficult
math
asked
Jan 2, 2013
1
answer
Using properties of determinants, show that $\begin{bmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{bmatrix} = (a + b + c )^3 $
cbse
class12
modelpaper
2012
sec-b
q13
ch4
bookproblem
sec2
q11-1
p120
math
asked
Jan 2, 2013
0
answers
Using properties of determinants, show that $ \begin{bmatrix} b+c & a & b \\ c+a & c & a \\ a+b & b & c \end{bmatrix} = (a + b + c )(a-c)^2 $
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 2, 2013
0
answers
If f(x) , defined by the following, is continuous at x = 0 , find the value of a, b and c. $f(x)=\left \{\begin{array}{1 1}\large\frac{\sin(a+1)x+\sin x}{x}, & if\;x< 0\\c, & if\;x= 0\\ \large\frac{\sqrt{x+bx^2}-\sqrt x}{bx^{\large\frac{3}{2}}}, & if\;x>0\end{array}\right.$
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 2, 2013
0
answers
If \( x = a \bigg( \cos \theta +\ log \tan\large \frac{\theta}{2} \bigg)\) and \( y = a\sin\: \theta\), find the value of \( \large\frac{dy}{dx}\) at \( \theta = \large\frac{\pi}{4} \).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 2, 2013
0
answers
Find the intervals in which the function \( f(x) = \large\frac{4x^2+1}{x} \) is, (i) increasing, (ii) decreasing.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 2, 2013
0
answers
Find the equation of the tangent and the normal to the curve \( y = x^2+4x+1 \) at the point whose x - coordinate is 3.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 2, 2013
0
answers
Evaluate : \[ (i) \int \: (x-3) \sqrt {x^2+4x+3} dx \] \[ (ii) \int \: (3x+5) \sqrt {2x^2+3x+7} dx \] \[ (iii) \int \: (x-4) \sqrt {4+x-x^2} dx \] \[ (iv) \int \: (5x-1) \sqrt {6+5x-2x^2} dx \]
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 2, 2013
0
answers
Evaluate : $ \int \: \large\frac{1}{\cos(x+a)\cos(x+b)}$$dx $
cbse
class12
modelpaper
2012
sec-b
q18
math
asked
Jan 2, 2013
0
answers
Evaluate : $ \int \:\large \frac{e^x}{(1+e^x)(2+e^x)}$$dx. $
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 2, 2013
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
0
answers
Find the vector and cartesian equation of the sphere described on the join of the points (2, -3, 4 ) and (-5, 6, -7 ) as the extremities of a diameter.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 2, 2013
0
answers
Find the root of the perpendicular drawn from the point P(1, 6, 3) on the line $\large \frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}. $ Also, find its distance from P.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 2, 2013
0
answers
12 cards, numbered 1 to 12, are placed in a box, mixed up throughly and then a card is drawn at random from the box. If it is known that the number on the drawn card is more than 3, find the probability that it is an even number.
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Jan 2, 2013
0
answers
Using matrices, solve the following system of equations : $ 2x-3y+5y = 11 ; 3x+2y-4z = -5 ; x+y-2z = -3 $
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 2, 2013
0
answers
Using elementary transformations, find the inverse of the following matrix : $ \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 7 \\ -2 & -4 & -5 \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-c
q23
ch3
easy
math
asked
Jan 2, 2013
1
answer
A tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2m and volume is \( 8m^3\) . If building of tank cost Rs. 70 per sq. metre for the base and Rs. 45 per sq. metre for sides, what is the cost of least expensive tank?
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 2, 2013
0
answers
Find the volume of the largest cylinder that can be inscribed in a sphere of radius r.
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 2, 2013
0
answers
Using integration, find the area of the triangular region whose sides have the equation \( y = 2x+1, y = 3x+1\: and \: x = 4 \).
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 2, 2013
0
answers
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