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Recent questions tagged q16
Questions
Show that Sin | x | is continuous.
cbse
class12
additionalproblem
kvquestionbank2012
ch5
q16
p12
easy
math
sec-a
asked
Jan 25, 2013
by
meena.p
1
answer
Assuming that petrol burnt per hour in driving a motorboat varies as the cube of its velocity. Show that the most economical speed when going against a current of p km/hour is \( \large\frac{3p}{2}\) km/hour.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 25, 2013
by
thanvigandhi_1
0
answers
If , Y = $ x^4 - \ frac$ {x$^3} ${3} when denotes the number of hours worked and denotes the amount (in Rupees) earned. Then find the value of (in interval) for which the income remains increasing? Explain the importance of earning in life?
cbse
class12
valuebasedproblems2012
relations-and-functions
ch1
q16
math
sec-b
asked
Jan 24, 2013
by
shanthinig
0
answers
Find the points on the curve \( 3x^2-y^2=8\), where the normal is parallel to line \( x+3y=4.\)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
If $ A=\begin{bmatrix} 3 & 1 \\ 7 & 5 \end{bmatrix}$ find x and y such that $ A^2+xl=yA.\;Find\;A^{-1}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch3
q16
p8
math
sec-b
asked
Jan 24, 2013
by
meena.p
1
answer
If R is a relation in N x N, show that the relation R defined by : (a, b)R(c, d)if and only if ad = bc is an equivalence relation.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 24, 2013
by
thanvigandhi_1
0
answers
In any Triangle ABC, if $ A=\tan^{-1}2\;and\;B=\tan^{-1}3,$prove that $C=\frac{\pi}{4}$
cbse
class12
additionalproblem
kvquestionbank2012
ch2
q16
p5
medium
sec-b
math
asked
Jan 24, 2013
by
meena.p
1
answer
Let $f:R_+\rightarrow[-5,\infty) $ given by $f(x)=9x^2+6x-5.$ show that f is invertiable with $ f^{-1}(y)=\frac{\sqrt{y+6}-1}{3}.$
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q16
p3
math
sec-b
asked
Jan 23, 2013
by
meena.p
1
answer
Find the values of a and b, so that the function f given by $ f(x) = \left\{ \begin{array}{l l} 1, & \quad if { x \leq 3}\\ ax+b, & \quad if { 3<x<5} \\ 7, & \quad if {x \geq 5} \end{array} \right. $ is continuous at x = 3 and x = 5.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Differentiate \( sin(x^x)\) w.r.t. $ \tan^{-1} \sqrt{ \large\frac{1-x^2}{1+x^2}} $
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 23, 2013
by
thanvigandhi_1
0
answers
Differentiate \( tan^{-1} \bigg[ \large\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}} \bigg] \) w.r.t. \( sin^{-1} \bigg( \large\frac{2x}{1+x^2} \bigg). \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 21, 2013
by
thanvigandhi_1
0
answers
Solve: $x^2\Large \frac{dy}{dx}\normalsize =x^2+xy+y^2$
cbse
class12
ch9
sec-b
q16
p194
short-answer
exemplar
medium
math
asked
Jan 18, 2013
by
sreemathi.v
1
answer
If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ represent the vertices of a triangle,then show that $\frac{1}{2}\mid\overrightarrow{b}\times\overrightarrow{c}+\overrightarrow{c}\times\overrightarrow{a}+\overrightarrow{a}\times\overrightarrow{b}\mid$ gives the vector area of the triangle .Hence deduce the condition that the three points $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are collinear.Also find the unit vector normal to the plane of the triangle.
cbse
class12
ch10
q16
p216
exemplar
difficult
sec-b
math
asked
Jan 17, 2013
by
sreemathi.v
1
answer
Show that \( y = \log (1+x)-\large\frac{2x}{2+x}\) is an increasing function of x for all value of x > -1.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 17, 2013
by
thanvigandhi_1
0
answers
Show that the line $ \large\frac{x}{a}+\frac{y}{b}$$=1$ touches the curve \(y=be^{\large\frac{-x}{a}}\) at the point where it crosses the y - axis.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 17, 2013
by
thanvigandhi_1
0
answers
Using differentials, find the approximate value of \( \sqrt {0.037}\).
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 16, 2013
by
thanvigandhi_1
0
answers
Find the area of the region bounded by the curve $y^2=2x$ and $x^2+y^2=4x.$
cbse
class12
ch8
q16
p177
exemplar
sec-c
difficult
math
asked
Jan 16, 2013
by
sreemathi.v
1
answer
A window is in the form of a rectangle surmounted by a semicircular opening. The total perimeter of the window is 10m . Find the dimensions of the window to admit maximum light through the whole opening.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 15, 2013
by
thanvigandhi_1
0
answers
Evaluate the following $\int\frac{3x-1}{\sqrt{x^2+9}}dx$
cbse
class12
ch7
q16
p164
short-answer
exemplar
sec-b
medium
math
asked
Jan 14, 2013
by
sreemathi.v
1
answer
Evaluate : $ \int \sin x \sqrt {1+\cos2x} dx.$
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 11, 2013
by
thanvigandhi_1
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
by
thanvigandhi_1
0
answers
Prove that the curves $y^2=4x$ and $x^2+y^2-6x+1=0$ touch each other at the point (1,2).
cbse
class12
ch6
q16
p136
short-answer
exemplar
difficult
sec-b
math
asked
Jan 11, 2013
by
sreemathi.v
1
answer
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
by
thanvigandhi_1
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
by
thanvigandhi_1
0
answers
If \( u, v \: and \ w \) are function of \( x\) , then show that $ \large\frac{d}{dx}(u.v.w) = \frac{du}{dx}.v.w+u.\frac{dv}{dx}.w+u.v.\frac{dw}{dx}$In two ways first by repeated application or product rule, secondly by logatithmic differentiation.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 10, 2013
by
thanvigandhi_1
0
answers
Find the derivaties of the function given by \( f(x)=(1+x)(1+x^2)(1+x^4)(1+x^8)\) and hence find \( f(1) \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 9, 2013
by
thanvigandhi_1
0
answers
A bag contains 4 white and 5 black balls.Another bag contains 9 white and 7 black balls.A ball is transferred from the first bag to the second and then a ball is drawn at random from the second bag.Find the probability that the ball drawn is white.
cbse
class12
ch13
q16
273
short-answer
exemplar
sec-a
easy
math
asked
Jan 9, 2013
by
sreemathi.v
1
answer
A manufacture of electronic circuits has a stock of 200 resistors,120 transistors and 150 capacitors and is required to produce two types of circuits A and B .Type A requires 20 resistors,10 transistors and 10 capacitors .Type B requires 10 resistors,20 transistors and 30 capacitors.If the profit on type A circuit is Rs 50 and that an type B circuit is Rs 60,how many of circuits of type A and type B,should be produced by the manufacturer so as to maximize his profit?Determine the maximum profit.
cbse
class12
ch12
q16
p253
exemplar
sec-c
difficult
math
asked
Jan 7, 2013
by
sreemathi.v
1
answer
Find the derivative of \( \sin (3x+2)\) w.r.t \(x\) from the first principal.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 7, 2013
by
thanvigandhi_1
0
answers
If \( y = \sqrt{\large\frac{(x-1)(x-2)}{(x-3)(x-4)(x-5)}} \) then find \( \large\frac{dy}{dx} \).
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int \large\frac{(x-4)e^x}{(x-2)^3}$$dx$
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Evaluate : $ \int\large \frac{e^x}{\sqrt {5-4e^x-e^{2x}}}$$dx $
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Jan 4, 2013
by
thanvigandhi_1
0
answers
Find the foot of perpendicular from the point(2,3,-8)to the line $\Large \frac{4-x}{2}\;=\frac{y}{6}\;=\frac{1-z}{3}$.Also,find the perpendicular distance from the given point to the line.
cbse
class12
ch11
q16
p236
exemplar
medium
sec-c
math
asked
Jan 3, 2013
by
sreemathi.v
1
answer
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
by
thanvigandhi_1
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
by
thanvigandhi_1
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
by
thanvigandhi_1
0
answers
Find the values of $a$ and $b$ such that the function $f$ defined by $f(x)=\left \{\begin{array}{1 1}\large\frac{x-4}{|x-4|}\normalsize+a, & if\;x<4\\a+b, & if\;x=4\\\large\frac{x-4}{|x-4|}\normalsize +b, & if\;x>4\end{array}\right.$ is a continuous function at $x=4.$
cbse
class12
ch5
q16
p108
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
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
by
thanvigandhi_1
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
by
thanvigandhi_1
0
answers
For the curve \( y = 4x^3 - 2x^5 \), find all the points at which the tangent passes through origin.
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Two equal sides of an isosceles triangle with fixed base 'a' are decreasing at the rate of 9 cm/second. How fast is the area of the triangle decreasing when the two sides are equal to 'a'.
cbse
class12
modelpaper
2011
sec-b
q16
math
asked
Dec 29, 2012
by
thanvigandhi_1
0
answers
Using differentials, find the approximate value of \( \sqrt {25.2} \)
cbse
class12
modelpaper
2011
sec-b
q16
math
asked
Dec 28, 2012
by
thanvigandhi_1
0
answers
show that the $\Delta$ABC is an isosceles triangle if the determinant\[\Delta=\begin{bmatrix}1 & 1& 1\\1+\cos A & 1+\cos B & 1+\cos C\\\cos^2A+\cos A & \cos^2B+\cos B & \cos^2C+\cos C\end{bmatrix}=0\]
cbse
class12
ch4
sec-c
q16
p78
short-answer
exemplar
difficult
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
Find the intervals inwhich the following function is strictly increasing or strictly decreasing \( f(x) = 20 - 9x + 6x^2 - x^3 \)
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
Find the intervals in which the function f given by $ f(x) = \large\frac{4sin x - 2x - x\cos\: x}{2+ cos\: x} $ is $\text { (i) increasing (ii) decreasing } $
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 25, 2012
by
thanvigandhi_1
0
answers
If \( \overrightarrow u = 2\hat i + 2\hat j - \hat k \) and \( \overrightarrow v = 6\hat i - 3\hat j + 2\hat k \), then a unit vector perpendiculat to both \( \overrightarrow u \) and \( \overrightarrow v \) is \[ \begin{array} (A) \: \hat i - 10\hat j - 18\hat k \quad & (B) \: \frac{1}{\sqrt {17}} \bigg( \frac{1}{5}\hat i - 2\hat j -\frac{18}{5}\hat k \bigg) \\ (C)\: \frac{1}{\sqrt {473}} \bigg( 7\hat i - 10\hat j -18\hat k \bigg) \quad & (D)\: \frac{1}{\sqrt {425}} \bigg( \hat i - 10\hat j -18\hat k \bigg) \end{array} \]
cbse
class12
modelpaper
2012
sec-b
q16
math
asked
Dec 24, 2012
by
thanvigandhi_1
0
answers
Show by an example that for $A\neq 0,B\neq 0,AB=0.$
cbse
class12
ch3
q16
p54
short-answer
exemplar
easy
sec-a
math
asked
Dec 22, 2012
by
sreemathi.v
1
answer
On a multiple choice examination with three possible answers ( out of which only one is correct ) for each of the five questions, what is the probability that the candidate would get four or more correct answers just by guessing?
cbse
class12
modelpaper
2009
sec-b
q16
math
asked
Dec 21, 2012
by
thanvigandhi_1
0
answers
What does $\tan^{-1}{\frac{1}{4}}+\tan^{-1}{\frac{2}{9}}$ reduce to?
cbse
class12
ch2
q16
p36
exemplar
medium
sec-b
math
asked
Dec 20, 2012
by
sreemathi.v
1
answer
Find the equation of tangent to the curve \( x = \sin 3t, y = \cos 2t, at\: t = \large\frac{\pi}{4} \)
cbse
class12
modelpaper
2008-1
sec-b
q16
math
asked
Dec 20, 2012
by
thanvigandhi_1
0
answers
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