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Questions asked by thanvigandhi_1
Questions
5837
questions
1
answer selected
At what points of the ellipse \( 16x^2+9y^2=400\), does the coordinate decrease at the same rate at which the abscissa increases.
cbse
class12
modelpaper
2012
sec-a
q5
math
asked
Jan 11, 2013
0
answers
$ \int x^2 \bigg( 1-\large\frac{1}{x^2} \bigg) $$dx.$
cbse
class12
modelpaper
2012
sec-a
q6
math
asked
Jan 11, 2013
0
answers
Find the differential equation \( y=e^x+1\)
cbse
class12
modelpaper
2012
sec-a
q7
math
asked
Jan 11, 2013
0
answers
Represent graphically a displacement of 40 km , \( 30^{\circ} \) east of length.
cbse
class12
modelpaper
2012
sec-a
q8
math
asked
Jan 11, 2013
0
answers
Compute $ P (A/B)$if, $P(B)=0.5, P(A \cap B)=0.32.$
cbse
class12
modelpaper
2012
sec-a
q9
math
asked
Jan 11, 2013
0
answers
Evaluate : $ P(A \cup B)$ if $2P(A) = P(B)=\large\frac{5}{13}\: and \: $$P(A/B) =\large \frac{2}{5} $.
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Jan 11, 2013
0
answers
Let L be the set of all lines in XY - planes and R be the relation in L defined as R = \( { (L_1, L_2 ) : L_1 \: is \: parallel\: to\: L_2} \). Show the R is an equivalence relation. Find the set of all the lines related to the line \( y=2x+4.\)
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 11, 2013
1
answer
Using properties of determinants, prove the following : \( \begin{bmatrix} b+c & a & a \\ b & c+a & b \\ c & c & a+b \end{bmatrix} = 4abc.\)
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 11, 2013
0
answers
Using properties of determinants, prove the following : \( \begin{bmatrix} b+c & c+a & a+b \\ q+r & r+p & p+q \\ y+z & z+x & x+y \end{bmatrix} = 2 \begin{bmatrix} a & b & c \\ p & q & r \\ x & y & z \end{bmatrix}. \)
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 11, 2013
0
answers
If \( y=e^{\large a \: cos^{-1}\: x} ; -1 \: \leq \: x \leq \: 1\), show that $ (1+x^2) \large\frac{d^2y}{dx^2}-x\frac{dy}{dx}-$$a^2y=0.$
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 11, 2013
0
answers
If \( x \sqrt {1+y} + y \sqrt{1+x}=0 \: for \: -1 < x < 1\) Prove that : $\large \frac{dy}{dx}=\frac{1}{(1+x)^2} $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 11, 2013
0
answers
Find the equation of tangent to the curve \( x=sin \: 3t, \: y=cos\: 2t, \: at \: t=\large\frac{\pi}{4}. \)
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 11, 2013
0
answers
At what point will the tangent to the curve \( y=2x^3-15x^2+36x-21\) be parallel to x - axis? Also, find the equations of tangents to the curve at these points ?
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 11, 2013
0
answers
Evaluate : $ \int \sin x \sqrt {1+\cos2x} dx.$
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 11, 2013
0
answers
Evaluate : $ \int \large\frac{x^2+x+1}{(x+2)(x+1)^2}$$dx.$
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 11, 2013
0
answers
Evaluate : $ \int \large\frac{dx}{x[6(log \: x)^2]+7( log \: x)+2}$$dx.$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 11, 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 11, 2013
1
answer
Solve the following differential equation $ x(1+y^2)dx-y(1+x^2)dy=0 $ given that $ y=0, \: when \: x=1$
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 11, 2013
0
answers
Solve the following differential equation $\large\frac{dy}{dx}$$+\sec x.y = \tan \: x. $
cbse
class12
modelpaper
2012
sec-b
q19
math
asked
Jan 11, 2013
0
answers
Find the magnitude of two vectors $ \overrightarrow a \: and \overrightarrow b $ having the same magnitude and such that the angle between them is $ 60^{\circ} $ and their scalar product is $\large\frac{1}{2}$.
cbse
class12
modelpaper
2012
sec-b
q20
math
asked
Jan 11, 2013
0
answers
A man is known to speak the truth 3 out of 5 times. He throws a dice and reports that it is 1. Find the probability that it is actually 1.
cbse
class12
modelpaper
2012
sec-b
q21
math
asked
Jan 11, 2013
0
answers
Two bags A and B contain 2 white, 4 red and 3 white, 3 red balls respectively. One of the bags is selected at random and a ball is drawn from it. If the selected ball is of white colour, find the probability that it is drawn from bag A.
cbse
class12
modelpaper
2012
sec-b
q22
math
asked
Jan 11, 2013
1
answer
Let A = R-{3} and B = R-{1}. Consider the function\( f:A \rightarrow B\) defined by \( f(x)=\large\frac{x-2}{x-3}\). Is f one-one and onto? Justify your answer.
cbse
class12
modelpaper
2012
sec-c
q23
math
asked
Jan 11, 2013
0
answers
Solve, using matrices : $ 2x-y+3z=5;3x+2y-z=7 ; 4x+5y-5z = 9$
cbse
class12
modelpaper
2012
sec-c
q24
math
asked
Jan 11, 2013
1
answer
Using matrix solve the following system of linear equations : $ 2x+y+z=3 ; 3x-y+z=0 ;x-2y+3z = -6$
cbse
class12
modelpaper
2012
sec-c
q24
medium
math
asked
Jan 11, 2013
0
answers
Find the largest possible area of the right-angled triangle whose hypotenuse is 5 cm.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 11, 2013
0
answers
Prove that the radius of the right circular cylinder of the greatest curved surface that can be inscribed in a given cone is half of the radius of the cone.
cbse
class12
modelpaper
2012
sec-c
q25
math
asked
Jan 11, 2013
0
answers
Find the region included between the parabola \( y^2=x \) & the line \( x+y=2.\)
cbse
class12
modelpaper
2012
sec-c
q26
math
asked
Jan 11, 2013
0
answers
Find the shortest distance between the lines : $\overrightarrow r = (1+2\lambda ) \hat i + (2+3\lambda)\hat j + (3+4\lambda)\hat k $ and $ \overrightarrow r = (2+3\mu ) \hat i + 4(1+\mu)\hat j + 5(1+\mu)\hat k $
cbse
class12
modelpaper
2012
sec-c
q27
math
asked
Jan 11, 2013
0
answers
Find the angle between the planes \( 4x+8y+z-8=0 \: and \: y+z-4=0. \)
cbse
class12
modelpaper
2012
sec-c
q28
math
asked
Jan 11, 2013
0
answers
Relation R is the set N of natural numbers defined as R = (x, y): y=x+5 and x < y}.
cbse
class12
modelpaper
2012
sec-a
q1
math
asked
Jan 10, 2013
0
answers
Find the value of $ \cos^{-1} \bigg( \large\frac{1}{2} \bigg)=$$2\sin^{-1} \bigg(\large \frac{1}{2} \bigg) $
cbse
class12
modelpaper
2012
sec-a
q2
math
asked
Jan 10, 2013
0
answers
Compute the following $ \begin{bmatrix} a & b \\ -b & a \end{bmatrix} + \begin{bmatrix} a & b \\ b & a \end{bmatrix} $
cbse
class12
modelpaper
2012
sec-a
q3
ch3
easy
math
asked
Jan 10, 2013
1
answer
Show that the matrix $A = \begin{bmatrix} 1 & -1 & 5 \\ -1 & 2 & 1 \\ 5 & 1 & 3 \end{bmatrix} $ is a symmetric matrix.
cbse
class12
modelpaper
2012
sec-a
q4
ch3
medium
math
asked
Jan 10, 2013
1
answer
If $ \begin{bmatrix} x & 2 \\ 18 & x \end{bmatrix} = \begin{bmatrix} 6 & 2 \\ 18 & 6 \end{bmatrix} $ then what is the value of x.
cbse
class12
modelpaper
2012
sec-a
q5
ch3
easy
math
asked
Jan 10, 2013
1
answer
The radius of a circle is increasing at 0.7 cm/s. What is the rate of increase of its circumference?
cbse
class12
modelpaper
2012
sec-q
q6
math
sec-a
asked
Jan 10, 2013
0
answers
\( \int (ax^2+bx+c)dx.\)
cbse
class12
modelpaper
2012
sec-q
q7
math
sec-a
asked
Jan 10, 2013
0
answers
If \( \overrightarrow P (1, 5, 4) \: and \overrightarrow Q (4, 1, -2),\) find the dr. of \( \overrightarrow {PQ}.\)
cbse
class12
modelpaper
2012
sec-q
q8
math
sec-a
asked
Jan 10, 2013
0
answers
If \( | \overrightarrow a | = \sqrt 3, | \overrightarrow b | = 2 \: and \: \overrightarrow a . \overrightarrow b = 3. \) Find angle between \( \overrightarrow a \: and \: \overrightarrow b \).
cbse
class12
modelpaper
2012
sec-q
q9
math
sec-a
asked
Jan 10, 2013
0
answers
Find the equation of the plane which is perpendicular to the plane \( 5x+3y+6z+8=0\) and which contains the line of intersection of the planes \( x+2y+3z-4=0 \: and \: 2x+y-z+3=0.\)
cbse
class12
modelpaper
2012
sec-a
q10
math
asked
Jan 10, 2013
0
answers
Show that the relation R in the set \( A = { x \in Z:0 \leq x \leq 12},\) given by (i) R = { a, b : |a-b| is a multiple of 4 } (ii) R = {a, b ; a = b}. is equivalence relation. Find the set of all eleents related to 1 in each case.
cbse
class12
modelpaper
2012
sec-b
q11
math
asked
Jan 10, 2013
0
answers
Prove that : $ \cot^{-1} \bigg[\large \frac{\sqrt{1+\sin\: x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}} \bigg] = \large \frac{x}{2}; $$x \in \bigg( 0, \large\frac{\pi}{2} \bigg). $
cbse
class12
modelpaper
2012
sec-b
q12
math
asked
Jan 10, 2013
0
answers
Using properties of determinants, prove the following : \( \begin{bmatrix} 1 & 1 & 1 \\ a & b & c \\ bc & ca & ab \end{bmatrix} = (a-b)(b-c)(c-a). \)
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 10, 2013
0
answers
Using properties of determinants, prove the following : \( \begin{bmatrix} a+b+2c & a & b \\ c & b+c+2a & b \\ c & a & c+a+2b \end{bmatrix} = 2(a+b+c)^3. \)
cbse
class12
modelpaper
2012
sec-b
q13
math
asked
Jan 10, 2013
1
answer
Find \(\large \frac{dy}{dx} \) of following : $ y=(\sin \: x)^x+\sin^{-1} \sqrt x. $
cbse
class12
modelpaper
2012
sec-b
q14
math
asked
Jan 10, 2013
0
answers
Using Mathematical Induction prove that $ \large\frac{d}{dx}(x^n)$$=nx^{n-1}, \forall \: n \: \in \: N$ for all positive integers \( n \).
cbse
class12
modelpaper
2012
sec-b
q15
math
asked
Jan 10, 2013
0
answers
Find the intervals in which the function f given by \( f(x)=2x^3-3x^2-36x+7\) is : \[ \begin{array} ((i)\: strictly\: increasing \quad & (ii)\: strictly\: decreasing \end{array} \]
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 10, 2013
0
answers
Prove that the curves \( x=y^2\) and \( xy=k\) cut at right angles if \( 8k^2 = 1. \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 10, 2013
0
answers
Evaluate : $\int \large\frac{2\sin\: x+3\cos \: x}{3\sin \: x + 4 \cos \: x} $$dx.$
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 10, 2013
0
answers
Evaluate : $ \int \ (x+3) \sqrt {3-4x-x^2} dx. $
cbse
class12
modelpaper
2012
sec-b
q17
math
asked
Jan 10, 2013
0
answers
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