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Recent questions tagged sec-a
Questions
Find the slope of the normal to the curve $ x = 1 - a \sin\theta, y = b \cos^2\theta$ at $ \theta = \Large {\frac{\pi}{2}}$
cbse
class12
bookproblem
ch6
sec3
q6
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $y = x^3 - 3x + 2$ at the point whose $x$ - coordinate is $3$.
cbse
class12
bookproblem
ch6
sec3
q4
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to curve $ y = x^3 - x + 1$ at the point whose $x$ - coordinate is $2$.
cbse
class12
bookproblem
ch6
sec3
q3
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $\normalsize y =\large { \frac{x-1}{x-2},} \normalsize x \neq 2\; at\;x = 10$
cbse
class12
bookproblem
ch6
sec3
q2
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the slope of the tangent to the curve $y = 3x^4 – 4x \; at\; x = 4.$
cbse
class12
bookproblem
ch6
sec3
q1
p211
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function given by \(f (x) = x^3 – 3x^2 + 3x - 100\) is increasing in \(R.\)
cbse
class12
bookproblem
ch6
sec2
q18
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function \(f\) given by $f (x) = \log \cos\: x$ is strictly decreasing on $ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly increasing on, $\left( \large {\frac{\pi}{2},} \normalsize \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q17
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the function $f$ given by $f (x) = \log \sin x$ is strictly increasing on$ \left(0, \: \large {\frac{\pi}{2}}\right)$ and strictly decreasing on $\left( \large {\frac{\pi}{2}}, \pi\right)$
cbse
class12
bookproblem
ch6
sec2
q16
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
For what values of $x$,
$\begin{bmatrix} 1 & 2 & 1 \end{bmatrix} \begin{bmatrix} 1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x \end{bmatrix}$ = 0 ?
cbse
class12
bookproblem
ch3
misc
q7
p100
easy
shortanswer
sec-a
math
asked
Nov 23, 2012
by
pady_1
1
answer
Prove that the function \(f\) given by \(f (x) = x^2 – x + 1\) is neither strictly increasing nor strictly decreasing on \((– 1, 1).\)
cbse
class12
bookproblem
ch6
sec2
q11
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Prove that the logarithmic function is strictly increasing on $(0, \infty).$
cbse
class12
bookproblem
ch6
sec2
q10
p206
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is neither increasing nor decreasing in $(0, \pi)$
cbse
class12
bookproblem
ch6
sec2
q3c
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f (x) = \sin x$ is strictly decreasing in $(\large {\frac{\pi}{2}},$$ \pi)$
cbse
class12
bookproblem
ch6
sec2
q3
q3b
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = \sin \;x\) is strictly increasing in $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q3
q3a
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by $f(x) = e^{2x}$ is strictly increasing on $R$.
cbse
class12
bookproblem
ch6
sec2
q2
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that the function given by \(f (x) = 3x + 17\) is strictly increasing on \(R\).
cbse
class12
bookproblem
ch6
sec2
q1
p205
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the total revenue in Rupees received from the sale of $x$ units of a product is given by $Rx = 3x^2 +36x + 5$. The marginal revenue, when $x = 15$ is
cbse
class12
bookproblem
ch6
sec1
q18
p199
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Choose the correct answer in the rate of change of the area of a circle with respect to its radius $r$ at $r = 6$ cm is
cbse
class12
bookproblem
ch6
sec1
q17
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The total revenue in Rupees received from the sale of $x$ units of a product is given by $ R(x) = 13x^2 + 26x + 15.$ Find the marginal revenue when $x = 7$.
cbse
class12
bookproblem
ch6
sec1
q16
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $ C(x) = 0.007x^3 - 0.003x^2 + 15x + 4000.$ Find the marginal cost when 17 units are produced.
cbse
class12
bookproblem
ch6
sec1
q15
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Sand is pouring from a pipe at the rate of $12 cm^3/s$. The falling sand forms a cone on the ground in such a way that the height of the cone is always one-sixth of the radius of the base. How fast is the height of the sand cone increasing when the height is 4 cm?
cbse
class12
bookproblem
ch6
sec1
q14
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A balloon, which always remains spherical, has a variable diameter $\large\frac{3}{2}$$(2x+1)$. Find the rate of change of its volume with respect to $x.$
cbse
class12
bookproblem
ch6
sec1
q13
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
The radius of an air bubble is increasing at the rate of $ \large\frac{1}{2}$ cm/s. At what rate is the volume of the bubble increasing when the radius is $1\; cm$?
cbse
class12
bookproblem
ch6
sec1
q12
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A particle moves along the curve $ 6y = x^3 +2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.
cbse
class12
bookproblem
ch6
sec1
q11
p198
sec-a
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is $10\; cm$.
cbse
class12
bookproblem
ch6
sec1
q9
p198
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
A balloon, which always remains spherical on inflation, is being inflated by pumping in $900$ cubic centimetres of gas per second. Find the rate at which the radius of the balloon increases when the radius is $15\; cm$.
cbse
class12
bookproblem
ch6
sec1
q8
p198
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
The length $x$ of a rectangle is decreasing at the rate of $5\; cm/minute$ and the width y is increasing at the rate of $4\; cm/minute$. When $x = 8$ cm and $y = 6$ cm, find the rates of change of (a) the perimeter
cbse
class12
bookproblem
ch6
sec1
q7
q7-a
p198
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
The radius of a circle is increasing at the rate of $0.7\; cm/s$. What is the rate of increase of its circumference?
cbse
class12
bookproblem
ch6
sec1
q6
p198
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
A stone is dropped into a quiet lake and waves move in circles at the speed of $5 \;cm/s$. At the instant when the radius of the circular wave is $8 \;cm$, how fast is the enclosed area increasing?
cbse
class12
bookproblem
ch6
sec1
q5
p197
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
An edge of a variable cube is increasing at the rate of $3\; cm/s$. How fast is the volume of the cube increasing when the edge is $10\; cm$ long?
cbse
class12
bookproblem
ch6
sec1
q4
p197
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
The radius of a circle is increasing uniformly at the rate of $3\; cm/s.$ Find the rate at which the area of the circle is increasing when the radius is $10\; cm$.
cbse
class12
bookproblem
ch6
sec1
q3
p197
sec-a
easy
math
asked
Nov 22, 2012
by
thanvigandhi_1
1
answer
Find the number of all onto functions from the set $\{1, 2, 3, ... , n\}$ to itself.
cbse
class12
bookproblem
ch1
misc
q10
p30
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Given a non-empty set \(X\), consider the binary operation \(\ast : P(X) × P(X) \to P(X)\) given by \(A \ast B=A \cap B\; \forall A, \) \( B \;in\; P(X),\) where \(P(X)\) is the power set of \(X\). Show that \(X\) is the identity element for this operation and \(X\) is the only invertible element in \(P(X)\) with respect to the operation \(\ast\).
cbse
class12
bookproblem
ch1
misc
q9
p30
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
If the matrix A is both symmetric and skew symmetric, then
cbse
class12
bookproblem
ch3
misc
q14
p101
easy
shortanswer
sec-a
math
asked
Nov 22, 2012
by
pady_1
1
answer
If $A $ is a square matrix, such that $ A^2 = A $ , then $ (1 + A )^3 - 7A $ is equal to:
cbse
class12
bookproblem
ch3
misc
q15
p101
easy
shortanswer
sec-a
math
asked
Nov 22, 2012
by
pady_1
1
answer
Let $S=\{a,b,c\}\;$ and$ \;T = \{1,2,3\}$. Find the inverse of the following function \(F\) from \(S\) to \(T\), if it exists - \[\;\; F=\{(a,3), (b,2), (c,1)\}\]
cbse
class12
bookproblem
ch1
misc
q11
q11-1
p30
easy
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Given a non empty set $X$, consider $P(X)$ which is the set of all subsets of $X$. Define the relation $R$ in $P(X)$ as follows: For subsets $A,\; B$ in $ P(X),\; ARB$ if and only if $ A \subset B $ Is $R$ an equivalence relation on $P(X)$?
cbse
class12
bookproblem
ch1
misc
q8
p29
sec-a
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Give examples of two functions \(f: N \to N\) and \(g: N \to N\) such that \(g\;o\;f \) is onto but \(f\) is not onto.
cbse
class12
bookproblem
ch1
misc
q7
p29
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Give examples of two functions \(f : N \to Z \) and \(g: Z \to Z\) such that \(g\;o\;f\) is injective but \(g\) is not injective.
cbse
class12
bookproblem
ch1
misc
q6
p29
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Show that the function \(f : R \to R\) given by \(f (x) = x^3\) is injective.
cbse
class12
bookproblem
ch1
misc
q5
p29
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Show that the function f:R $\rightarrow \{ x \in$ R:-1$<$x$<$1 $\}$ defined by $f(x) = \frac {x} { 1+|\;x\;|}, x \in R$ is one-one and onto function.
cbse
class12
bookproblem
ch1
misc
q4
p29
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
If $(f:R \to R)$ is defined by $f(x) = x^2$ - $3x+2$. Find $f(f(x))$:
cbse
class12
bookproblem
ch1
misc
q3
p29
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Consider a binary operation $\ast$ on $N$ defined as $a \ast b = a^3 + b^3$. Choose the correct answer:
cbse
class12
bookproblem
ch1
sec4
q13
p26
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Find if the given operation has identity: $\;\; a \ast b = a^2 + b^2$
cbse
class12
bookproblem
ch1
sec4
p25
q10
q10-2
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
2
answers
Let $\ast$ be a binary operation on the set $Q$ of rational numbers as follows: $\;\; a \ast b = a-b$. Find which of the binary operations are commutative and which are associative.
cbse
class12
bookproblem
ch1
sec4
q9
q9-1
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Let $\ast$ be the binary operation on $N$ defined by $a \ast b=H.C.F. $ of a and b. Is $\ast$ commutative? Is $\ast$ associative? Does there exist identity for this binary operation on $N$?
cbse
class12
bookproblem
ch1
sec4
q8
p25
easy
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Differentiate w.r.t. x the function $cot^{-1} \begin{bmatrix} \frac{{\sqrt {1+sin \: x}} + {\sqrt{1-sin \: x}}} {{\sqrt {1+sin \: x}} - {\sqrt{1-sin \: x}}} \\[0.3em] \end{bmatrix}$, where $0 < x < \frac{\pi}{2}$
cbse
class12
bookproblem
ch5
misc
q6
p191
sec-a
medium
math
kvquestionbank2012
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Is $\ast$ defined on the set $\{1,2,3,4,5\}$ by $a\ast b=L.C.M$.of $a$ and $b$ a binary operation?
cbse
class12
bookproblem
ch1
sec4
q7
p25
sec-a
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
Find \(\large \frac{dy}{dx} \), if \( y = \sin^{-1}x + \sin^{-1} \: \sqrt {1-x^2} , -1 \leq x \leq 1 \)
cbse
class12
bookproblem
ch5
misc
q13
p191
sec-a
easy
math
asked
Nov 21, 2012
by
thanvigandhi_1
1
answer
Let $\ast '$ be the binary operation on the set $\{1, 2, 3, 4, 5\}$ defined by $a \ast ' b = H.C.F$ of a and b. Is the operation same as the operation $\ast$ defined in the table below? $\begin{matrix} *&1&2&3&4&5 \\ 1&1&1&1&1&1 \\ 2&1&2&1&2&1 \\ 3&1&1&3&1&1 \\ 4&1&2&1&4&1 \\ 5&1&1&1&1&5 \end{matrix}$
cbse
class12
bookproblem
ch1
sec4
q5
p25
sec-a
easy
math
asked
Nov 21, 2012
by
vaishali.a
1
answer
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