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Recent questions tagged cbse
Questions
If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix} $ show that $A^2 - 5A + 7I = 0$
cbse
class12
bookproblem
ch3
misc
q8
p100
easy
shortanswer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Find $x$, if $ \begin{bmatrix} x & -5 & -1 \end{bmatrix} \begin{bmatrix} 1 & 0 & 2 \\ 0 & 2 & 1 \\ 2 & 0 & 3 \end{bmatrix} \begin{bmatrix} x \\ 4 \\ 1 \end{bmatrix} = 0 $
cbse
class12
bookproblem
ch3
misc
q9
p100
medium
shortanswer
sec-b
math
asked
Nov 23, 2012
by
pady_1
1
answer
Which of the following functions are strictly decreasing on $\left(0, \: \large {\frac{\pi}{2}}\right)$
cbse
class12
bookproblem
ch6
sec2
q12
p206
sec-b
medium
math
asked
Nov 23, 2012
by
thanvigandhi_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
Prove that \( y =\large { \frac{4\sin\theta}{(2+\cos\theta)}}-\normalsize \theta\) is an increasing function of \(\theta\) in $\left[0, \: \large {\frac{\pi}{2}}\right]$
cbse
class12
bookproblem
ch6
sec2
q9
p205
sec-b
easy
modelpaper
2012
q15
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the values of $x$ for which $y = [x(x – 2)]^2$ is an increasing function.
cbse
class12
bookproblem
ch6
sec2
q8
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Show that $ y = log(1+x)-\large {\frac{2x}{2+x}}, \normalsize x > – \normalsize 1$, is an increasing function of $x$ throughout its domain.
cbse
class12
bookproblem
ch6
sec2
q7
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the following functions are strictly increasing or decreasing: $(a) \;x^2 + 2x - 5$
cbse
class12
bookproblem
ch6
sec2
q6
q6-a
p205
sec-b
easy
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function f given by $f (x) = 2x^3 – 3x^2 – 36 x + 7$ is (a) strictly increasing and (b) strictly decreasing ?
cbse
class12
bookproblem
ch6
sec2
q5
p205
sec-b
easy
modelpaper
2012
q16
math
asked
Nov 23, 2012
by
thanvigandhi_1
1
answer
Find the intervals in which the function $f$ given by $f (x) = 2x^2 - 3x$ is $(a) $ strictly increasing
cbse
class12
bookproblem
ch6
sec2
q4
q4-b
p205
sec-b
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 ladder 5 m long is leaning against a wall. The bottom of the ladder is pulled along the ground, away from the wall, at the rate of 2cm/s. How fast is its height on the wall decreasing when the foot of the ladder is 4 m away from the wall ?
cbse
class12
bookproblem
ch6
sec1
q10
p198
sec-b
medium
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
A manufacturer produces three products \( x, y, z \) which he sells in two markets. Annual sales are indicated below: \[ \begin{array} { c c } \textbf{Market} & \textbf{Products} \\ I & 10,000 \quad 2,000 \quad 18,000 \\ II & 6,000 \quad 20,000 \quad 8,000 \end{array} \]
If unit sale prices of x, y and z are Rs 2.50, Rs 1.50 and Rs 1.00, respectively, find the total revenue in each market
cbse
class12
bookproblem
ch3
misc
q10
p101
easy
10-1
sec-b
math
asked
Nov 22, 2012
by
pady_1
1
answer
Define a binary operation \(\ast\) on the set \(\{0, 1, 2, 3, 4, 5\}\) as \[ a \ast b = \left\{ \begin{array} {1 1} a+b, & \quad \text{ if a$+$b $<$ 6} \\ a+b-6, & \quad \text{ if a+b $\geq$ 6} \\ \end{array} \right. \] Show that zero is the identity for this operation and each element $a\neq0$ of the set is invertible with $6-a$ being the inverse of $a$.
cbse
class12
bookproblem
ch1
misc
q14
p30
sec-b
medium
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Find the matrix \( X \) so that \( X \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \end{bmatrix} \: = \: \begin{bmatrix} -7 & -8 & -9 \\ 2 & 4 & 6 \end{bmatrix} \)
cbse
class12
bookproblem
ch3
misc
q11
p101
easy
shortanswer
sec-b
math
asked
Nov 22, 2012
by
pady_1
1
answer
Given a non-empty set \( X,\) let \(\ast :\; P(X)\; \times\; P(X) \to P(X) \) be defined as \(A \ast B = \; ( A-B)\; \cup \; (B-A),\; \forall A, B \in \; P(X).\). Show that the empty set \(\emptyset \) is the identity for the operation $\ast$ and all the elemnets \(A\) of \( P(X) \) are invertible with \( A^{-1} \;= A\).
cbse
class12
bookproblem
ch1
misc
q13
p30
medium
sec-b
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
Consider the binary operation $\ast :\; R \times R \rightarrow R$ and $o :\; R \times R \rightarrow R$ defined as $a \ast b = | a \text{-b}|$ and \(\;a\;o\;b=a, \forall a,\;b \in R.\) Show that \(\ast\) is commutative but not associative, \(o\) is associative but not commutative. Further, show that \(\forall\; a,\; b,\; c \in R,\; a\; \ast\; (b\; o\; c) = (a \ast b) \;o\; (a \ast c)\). [If it is so, we say that the operation $\ast$ distributes over $o$]. Does $o$ distribute over? Justify your answer.
cbse
class12
bookproblem
ch1
misc
q12
p30
sec-b
medium
math
asked
Nov 22, 2012
by
vaishali.a
1
answer
If \(A\) and \(B\) are square matrices of the same order such that \(AB = BA \), then prove by induction that \(AB^n = B^nA \). Further, prove that \( (AB)^n = A^nB^n \: \) for all \( n ∈ N. \)
cbse
class12
bookproblem
ch3
misc
q12
p101
long-answer
difficult
sec-c
math
asked
Nov 22, 2012
by
pady_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
Let \(f:W \to W\) be defined as $f(n)=n$ - $1$, if \(n\;is\;odd\;and\; f(n)=n+1,\;if\;n\;is\; even.\) Show that \(f\) is invertible. Find the inverse of \(f\). Here, \(W\) is the set of all whole numbers.
cbse
class12
bookproblem
ch1
misc
q2
p29
medium
sec-b
math
modelpaper-2014
q15
asked
Nov 21, 2012
by
vaishali.a
1
answer
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