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Recent questions tagged short-answer
Questions
Differentiate the following w.r.t x: $\tan^{-1}\bigg(\large {\frac {a \cos x - b \sin x}{b \cos x + a \sin x}}\bigg)$, where $\frac{-\pi}{2} < x < \frac{\pi}{2}$ and $\frac{a}{b} \tan x > -1$
cbse
class12
ch5
q40
p110
short-answer
exemplar
sec-a
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x:$\tan^{-1}(\sec x+\tan x),\large \frac{-\pi}{2}<$$x<\large\frac{\pi}{2}$.
cbse
class12
ch5
q39
p110
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x:$\tan^{-1}\bigg(\sqrt{\large\frac{1-\cos x}{1+\cos x}}\bigg),$$\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.
cbse
class12
ch5
q38
p110
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $\sin^{-1} \big[\large\frac{1}{\sqrt 2}$$\sin x+\large\frac{1}{\sqrt 2}$$\cos x\big],\large\frac{-\pi}{4}<$$x<\large\frac{\pi}{4}$.
cbse
class12
ch5
q37
p110
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$: $(x+1)^2(x+2)^3(x+3)^4$.
cbse
class12
ch5
q36
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x: $\sin^mx.\cos ^nx$.
cbse
class12
ch5
q35
p109
short-answer
exemplar
sec-a
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x: $(\sin x)^{\large\cos x}$.
cbse
class12
ch5
q34
p109
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x: $\sin^{-1}\bigg|\large\frac{1}{\sqrt {x+1}}\bigg|$.
cbse
class12
ch5
q33
p109
short-answer
exemplar
sec-b
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $\sin (x^2)+\sin^2x+\sin^2(x^2)$.
cbse
class12
ch5
q32
p109
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $\cos\bigg(\tan\sqrt {x+1}\bigg)$.
cbse
class12
ch5
q31
p109
short-answer
exemplar
sec-a
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t x: $\sin^n(ax^2+bx+c)$.
cbse
class12
ch5
q30
p109
short-answer
exemplar
sec-a
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $\sin\sqrt x+\cos^2\sqrt x$.
cbse
class12
ch5
q29
p109
short-answer
exemplar
sec-b
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $log\begin{bmatrix}log\bigg(log x^5\bigg)\end{bmatrix}$.
cbse
class12
ch5
q28
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ : $log\bigg(x+\sqrt{ x^2+a}\bigg)$.
cbse
class12
ch5
q27
p109
short-answer
exemplar
sec-b
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$ :$\large \frac{8^x}{x^8}$
cbse
class12
ch5
q26
p109
short-answer
exemplar
sec-a
medium
math
sec4
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Differentiate the following w.r.t $x$: $2^{\large \cos^2x}$
cbse
class12
ch5
q25
p109
short-answer
exemplar
sec-a
medium
math
sec4
asked
Dec 31, 2012
by
sreemathi.v
1
answer
A function $f\;:\;R\rightarrow R$ satisfies the equation $f(x+y)=f(x)f(y)$ for all $x,y\in R,f(x)\neq 0.$ Suppose that the function is differentiable at $x=0$ and $f'(0)=2$.Prove that $f'(x)=2f(x).$
cbse
class12
ch5
q24
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Show that $f(x)=|x-5|$ is continuous but not differentiable at $x=5$
cbse
class12
ch5
q23
p109
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}1+x, & if\;x\leq 2\\5-x, & if\;x>2\end{array}\right.$at $x=2$.
cbse
class12
ch5
q22
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the differentiability of $f$,where $f$ is defined by $f(x)=\left \{\begin{array}{1 1}x^2\sin\large\frac{1}{x}, & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at $x=0$
cbse
class12
ch5
q21
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the differentiability of f,where f is defined by $f(x)=\left \{\begin{array}{1 1}x[x], & if\;0\leq x<2\\(x-1)x, & if\;2\leq x<3\end{array}\right.$at $x=2$
cbse
class12
ch5
q20
p109
short-answer
exemplar
easy
sec-a
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Show that the function $f(x)=\mid \sin x+\cos x\mid$ is continuous at $x=\pi$.
cbse
class12
ch5
q19
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find all points of discontinuity of the function $f(t)=\large\frac{1}{t^2+t-2},$where $\;t=\large\frac{1}{x-1}.$
cbse
class12
ch5
q18
p109
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Given the function $ f(x)=\large\frac{1}{x+2}.$Find the points of discontinuity of the composite function $y=f(f(x)).$
cbse
class12
ch5
q17
p108
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
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
Prove that the function f defined by $ f(x)=\left \{\begin{array}{1 1}\large\frac{x}{\mid x\mid+2x^2}, & x\neq 0\\k, &x=0\end{array}\right.$remains discontinuous at x=0,regardless the choice of k.
cbse
class12
ch5
q15
p108
short-answer
exemplar
easy
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the value of $k$ in the following so that the function $f$ is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos kx}{x\sin x}, & if\;x\neq 0\\\large\frac{1}{2}, & if\;x=0\end{array}\right.\;at\;x=0$
cbse
class12
ch5
q14
p108
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the value of $k$ in the following so that the function $f$ is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{\sqrt {1+kx}-\sqrt{1-kx}}{x}, & if\;-1\leq x< 0\\\large\frac{2x+1}{x-2}, & if\;0\leq x\leq 1\end{array}\right.\; at\; x=0$
cbse
class12
ch5
q13
p108
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the value of k in the following so that the function $f$ is continuous at the indicated point: $f(x)=\left \{\begin{array}{1 1}\frac{\large 2^{x+2}-16}{4^{\large x}-16}, & if\;x\neq 2\\k, & if\;x=2\end{array}\right.$ at $x=2$
cbse
class12
ch5
q12
p108
short-answer
exemplar
medium
sec-a
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find the value of k in the following so that the function f is continuous at the indicated point $f(x)=\left \{\begin{array}{1 1}3x-8, & if\;x\neq 5\\2k, & if\;x=5\end{array}\right.\;at\;x=5$
cbse
class12
ch5
q11
p108
short-answer
exemplar
sec-a
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether f(x) is continuous or discontinuous at the indicated point $f(x)= x ^2+x-1\;at\;x=1.$
cbse
class12
ch5
q10
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{x^2}{2}, & if\;0\leq x\leq 1\\2x^2-3x+\large\frac{3}{2}\normalsize,& if\;0< x\leq 2\end{array}\right.$ at $x=1$.
cbse
class12
ch5
q9
p107
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{e^ {\Large\frac{1}{x}}}{1+e^ {\Large\frac{1}{x}}},\normalsize & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$ at $x=0$.
cbse
class12
ch5
q8
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether $f(x)$ is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}( x-a)\sin\large\frac{1}{x-a},\normalsize & if\;x\neq 0\\0, & if\;x=0\end{array}\right.$ at $x=a$.
cbse
class12
ch5
q7
p107
short-answer
exemplar
sec-b
medium
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}\mid x\mid\cos\large\frac{1}{x}, \normalsize& if\;x\neq 0\\0, & if\;x=0\end{array}\right.$at x=0.
cbse
class12
ch5
q6
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find whether f(x) is continuous or discontinuous at the indicated point $f(x)=\left \{\begin{array}{1 1}x-4, & if\;x\neq 4\\2(x-4)\\0, & if\;x=4\end{array}\right.$at x=4.
cbse
class12
ch5
q5
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{2x^2-3x-2}{x-2} &\normalsize if\;x\neq 2\\5 & if\;x=2\end{array}\right.$ at x=2.
cbse
class12
ch5
q4
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}\large\frac{1-\cos 2x}{x^2} & \normalsize if\;x\neq 0\\5 & if\;x=0\end{array}\right.$at x=0.
cbse
class12
ch5
q3
p107
short-answer
exemplar
easy
sec-a
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the continuity of f(x) at the indicated point $f(x)=\left \{\begin{array}{1 1}3x+5 & if\;x\geq 2\\x^2 & if\;x<2\end{array}\right.$ at $x=2.$
cbse
class12
ch5
q2
p107
short-answer
exemplar
sec-b
easy
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Examine the continuity of the function $f(x)=x^3+2x^2-1$ at $x=1$
cbse
class12
ch5
q1
p107
short-answer
exemplar
easy
sec-b
math
asked
Dec 31, 2012
by
sreemathi.v
1
answer
Find $A^{-1}$ if $A=\begin{bmatrix}0 & 1 & 1\\1 & 0 & 1\\1 & 1 & 0\end{bmatrix}$ and show that $ A^{-1}=\Large \frac{A^2-3I}{2}$
cbse
class12
ch4
sec-c
q17
p79
short-answer
exemplar
medium
math
asked
Dec 26, 2012
by
sreemathi.v
1
answer
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
Show that the point(a+5,a-4),(a-2,a+3) and (a,a) do not lie on a straight line for any value of a.
cbse
class12
ch4
sec-b
q15
p78
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
If $a_1,a_2,a_3,....,a_r$ are in G.P., then prove that the determinant $\begin{vmatrix} a_{r-1} & a_{r-5} & a_{r-9} \\ a_{r-7} & a_{r-11} & a_{r-15} \\ a_{r-13} & a_{r-17} & a_{r-21} \end{vmatrix} is\; independent\; of\; r$
cbse
class12
ch4
sec-b
q14
p78
short-answer
exemplar
difficult
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Find the value of $\theta$ satisfying $\begin{bmatrix} 1 & 1 & \sin3\theta \\ -4 & 3 & \cos2\theta \\ 7 & -7 & -2 \end{bmatrix}\;=\;0$
cbse
class12
ch4
sec-b
q12
p78
short-answer
exemplar
difficult
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, Prove that$\begin{vmatrix} y+z & z & y \\ z & z+x & x \\ y & x & x+y \end{vmatrix}\;=\;4xyz$
cbse
class12
ch4
sec-b
q8
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, prove that: $\begin{vmatrix} y^2z^2 & yz &y+ z \\ z^2x^2 & zx & z+x \\ x^2y^2 & xy & x+y \end{vmatrix}\;=\;0$
cbse
class12
ch4
sec-b
q7
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix}$
cbse
class12
ch4
sec-b
q6
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} x+4 & x & x \\ x & x+4 & x \\ x & x & x+4 \end{vmatrix}$
cbse
class12
ch4
sec-b
q5
p77
short-answer
exemplar
easy
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
Using the properties of determinants, evaluate $\begin{vmatrix} 3x & -x+y & -x+z \\ x-y & 3y & z-y \\ x-z & y-z & 3z \end{vmatrix}$
cbse
class12
ch4
sec-b
q4
p77
short-answer
exemplar
medium
math
asked
Dec 24, 2012
by
sreemathi.v
1
answer
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