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Recent questions and answers in Relations and Functions
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CBSE XII
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Math
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Relations and Functions
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
answered
Mar 21
by
hk0312109
1
answer
Differentiate ‘Cry’ and ‘cry’
cbsc
class 12
biology
biodiversity and its applications
sec-b
answered
Apr 9, 2019
by
priyanka.clay6
1
answer
Which one of the following is a bird flu virus?
cbse
class12
biology
zoology
neet
sec-a
answered
Feb 14, 2019
by
lpmvenkateswaran621
1
answer
Prove that relation R defined on the set N of natural numbers by \[x\;R\;y \Leftrightarrow 2x^2-3xy+y^2=0\] is not symmetric but it is reflexive.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q27
p4
math
sec-b
answered
Jan 24, 2018
by
nimmisivapuri.d5
1
answer
Let $f : A \rightarrow B$ be a given function. A relation R in the set A is given by $R = {(a,b) \varepsilon A \times A : f(a) = f(b)}.$ Check, if R is an equivalence relation.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q23
p4
math
sec-b
answered
Jan 24, 2018
by
nimmisivapuri.d5
1
answer
Draw a plot showing the variation of photo electric current against the intensity of incident validation on a given photo sensitive surface.
cbse
class12
physics
modelpaper
mock-test-series-2015
answered
Sep 4, 2017
by
throttlespec
1
answer
Let N denote the set of all natural numbers and R be the relation on N x N defined by $ (a,b)R(c,d) \Leftrightarrow ad(b + c) = bc(a + d).$ Show that R is an equivalence relation on N x N.
cbse
class12
additionalproblem
kvquestionbank2012
ch1
q21
p4
math
sec-b
answered
Jul 20, 2017
by
saurabh.kumarshukla1995
1
answer
Give an account of Hershey and Chase experiment. What did it conclusively prove? If both DNA and pro
cbse
class12
ch6
exemplar
theoryquestion
biology
sec-e
molecular basis of inheritance
answered
Jul 5, 2017
by
pady_1
1
answer
During reproduction, the chromosome number (2n) reduces to half (n) in the gametes and again the ori
cbse
class12
ch3
exemplar
theoryquestion
biology
sec-a
human reproduction
answered
Jun 14, 2017
by
pady_1
1
answer
An oil company has two depots A and B with capacities of 7000 L and 4000 L respectively. The company is to supply oil to three petrol pumps, D, E and F whose requirements are 4500L, 3000L and 3500L respectively. Assuming that the transportation cost of 10 litres of oil is Rs 1 per km, How should the delivery be scheduled in order that the transportation cost is minimum ? What is the minimum cost? The distance (In km) between the depots and the petrol pumps is given in the following table :
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Find the area of the region $\{ (x,y) : 0 \leq y \leq x^2, 0 \leq y \leq x+2 , 0 \leq x \leq 3\}$
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Find the image of the point (1, 3. 4) in the plane $x-y+z =5$. Hence show that the image lies on the plane $x -2y +z -7 = 0$
cbse
class12
maths
ch1
sec-e
answered
Dec 27, 2016
by
priyanka.c
1
answer
Radioactive wastes is to be disposed of in full enclosed lead boxes of inner volume $200 cm^3$. The base of the box has dimension in the ratio 2:1 . What is the inner length of the box. Find the minimum inner surface area of the box.
cbse
class12
maths
ch1
sec-e
answered
Dec 22, 2016
by
priyanka.c
1
answer
Rent -a-car has three different makes of vehicles P, Q and R for hire. These cars are located at stations A and B on either side of a city. Some cars are being rented. In total they have 150 cars. At station A, they have 20% of P, 40% of Q and 30% of R which is 46 cars in total. At station B they have 40% of P, 20% of Q and 50% of R which is 54 cars in total. How many of each cars types does Rent-a -car have ?
cbse
class12
maths
ch1
sec-e
answered
Dec 22, 2016
by
priyanka.c
1
answer
Integrate $\begin{align*} \int \frac{\sin(x+a)}{\sin (x+b)} dx\end{align*} $
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Express the matrix $A = \begin{bmatrix} 3 & 2 & 3 \\ 4 & 5 & 3 \\ 2 & 4 & 5 \end{bmatrix}$ as the sum of a symmetric and a skew symmetric matrix.
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
(a) The youngest is a girl.
(b) At least one is a girl.
Pre-natal *** determination is a crime. What will you do if you come to know that some of your known is indulging in pre-natal *** determination ?
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Evaluate $\begin{align*} \int \limits_{-1}^{3/2} |x \sin {\pi \; x}| dx \end{align*}$
cbse
class12
maths
ch1
sec-c
answered
Dec 22, 2016
by
priyanka.c
1
answer
Find the condition that the curves $2x= y^2$ and $2xy = k $ intersect orthogonally.
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
Differentiate $x ^{\sin ^{-1} x}$ w.r.t $\sin^{-1} x$
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
For what value of $a$ and $b$ is the function $f(x) = \begin{cases} x^2 ,& x \leq c \\ ax+b , & x> c \end{cases} $ is differentiable at $x=c$
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
On the set $R -\{ -1\} $ a binary operation $\ast$ is defined by $a \ast b = a + b + ab$ for all $a,b \in R - \{-1\}$. Prove that $\ast$ is commutative as well as associative on $R -\{-1\}$. Find the identity element on $\ast$ if any.
cbse
class12
maths
ch1
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
Evaluate : $\tan \begin{bmatrix} \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{a}{b} \end{bmatrix} + \tan \begin{bmatrix} \frac{\pi}{4} - \frac{1}{2} \cos^{-1} \frac{a}{b} \end{bmatrix}$
cbse
class12
maths
ch2
sec-c
answered
Dec 21, 2016
by
priyanka.c
1
answer
Using differentials, find the appropriate value of $[0.009] ^ {\frac{1}{3}}$
cbse
class12
maths
ch1
sec-b
answered
Dec 20, 2016
by
priyanka.c
1
answer
If $\overrightarrow {b} \times \overrightarrow {c} = \overrightarrow {c} \overrightarrow {a} \neq 0$, then $\overrightarrow{a} + \overrightarrow {b} = k \overrightarrow {c}$ where k is any scalar.
Is it true or false .
cbse
class12
maths
ch1
sec-b
answered
Dec 20, 2016
by
priyanka.c
1
answer
From the differential equation of the family of curves $y = A \sin 2x + B \cos 2x$
cbse
class12
maths
ch1
sec-b
answered
Dec 20, 2016
by
priyanka.c
1
answer
If $f'(x) = 6x^2+2,$ find $f(x)$, given that $f(x) = 7$ when $x=1$
cbse
class12
maths
ch7
sec-b
answered
Dec 20, 2016
by
priyanka.c
1
answer
If $y = 7x -x^3$ and $x$ increases at the rate of 4 units per second. How fast is the slope of the curve changing when $x=2$
cbse
class12
maths
ch1
sec-b
answered
Dec 20, 2016
by
priyanka.c
1
answer
Determine the order and degree in the differential equation. Also state if it is a linear or non linear.
$y +\frac{dy}{dx} = \frac{1}{4} \int y dx $
cbse
class12
maths
ch1
sec-a
answered
Dec 20, 2016
by
priyanka.c
1
answer
Let $\ast \; R \times R \to R$ given by $(a,b) \to a + 4b^2$ is a binary operation, compute $-5 \ast (2 \ast 0).$
cbse
class12
maths
ch1
sec-a
answered
Dec 20, 2016
by
priyanka.c
1
answer
A cooperative society of farmers has 50 hectors of land to grow two crops X and Y. The profit from crops X and Y are estimated on Rs.10,500 and Rs.9000 respectively. To control weeds, a liquid herbicide has to be used crops X and Y at rate of 20 litres and 10 litres per hectors. Further no more than 800 litres of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximize the total profit of the society ?
cbse
class12
maths
ch1
sec-e
answered
Dec 19, 2016
by
priyanka.c
1
answer
Find the area bounded by the lines. $x +2y = 2, y = x +1$ and $2x +y= 7$
cbse
class12
maths
ch1
sec-e
answered
Dec 12, 2016
by
priyanka.c
1
answer
Find absolute maximum and minimum value a function given by $f(x) = 12x^{\frac{4}{3}} - 6x^{\frac{1}{3}} , x \in [-1,1]$
cbse
class12
maths
ch1
sec-c
answered
Dec 12, 2016
by
priyanka.c
1
answer
Define standing crop.
cbse
class12
biology
botany
sec-a
answered
Dec 8, 2016
by
meena.p
1
answer
Define a binary operation $\ast$ on the set {0, 1, 2, 3, 4, 5} as \[a*b=\left \{ \begin{array} {1 1} a+b, & \quad \text{ if a+b<6} \\ a+b-6, & \quad { if a+b \geq 6} \end{array} \right.\] show that the zero is the identity for this operation and each element $a \neq 0$ of the set is invertible with $6-a$ being the inverse of $a$.
cbse
class12
maths
ch1
sec-c
answered
Dec 7, 2016
by
priyanka.c
1
answer
If $f : R \to R$ be given by $f(x) = (3-x^3)^{\frac{1}{3}}$, then evaluate $f o f(x)$
cbse
class12
maths
ch1
sec-a
answered
Dec 7, 2016
by
priyanka.c
1
answer
Find the approximate value of $f'(3.02)$ where $f(x) = 3x^2+5x+3$
cbse
class12
maths
ch6
sec-b
answered
Nov 25, 2016
by
priyanka.c
1
answer
The total cost C(x) in rupees associated with the production of x units of an item is given by $ C(x) = 0.007 x^3 - 0.003 x^2 + 15x + 4000$. Find the marginal cost when 10 units are produced.
cbse
class12
maths
ch6
sec-b
answered
Nov 23, 2016
by
priyanka.c
1
answer
Let A = {1, 2}. Find the number of possible binary operations defined on A.
cbse
class12
maths
ch1
sec-b
answered
Nov 23, 2016
by
priyanka.c
1
answer
A balloon which always remain spherical has a variable diameter$ \frac{3}{2} (2x+ 3)$ : Determine the rate of change of volume w.r.t x
cbse
class12
maths
sec-a
ch6
answered
Nov 23, 2016
by
priyanka.c
1
answer
Find the value of $\lambda$, so that the lines $\frac{1-x}{3} = \frac{7y - 14}{2 \lambda} = \frac{z-3}{2} \;and\; \frac{7-7 \lambda}{3 \lambda} = \frac{y-5}{1} = \frac{6-z}{5} $ are at right angle
cbse
class12
maths
sec-e
ch11
answered
Nov 22, 2016
by
priyanka.c
1
answer
Find the value of 'a ' so that the function f(x) is defined by $f(x) = \begin{cases} \frac{\sin ^2 a x}{x^2} & x \neq 0 \\ 1 , & x =0 \end{cases}$ may be continuous at x = 0
cbse
class12
maths
sec-e
ch5
answered
Nov 22, 2016
by
priyanka.c
1
answer
Verify Rolle's theorem for $f(x) = x^2 + 2$ in the interval [-2,2]
cbse
class12
maths
sec-e
ch5
answered
Nov 21, 2016
by
priyanka.c
1
answer
If $P(A) = 0.25, P(B) = 0.4 \; and \; P (A \cup B) = 0.5 \; find \; P (A \cap B) \;and \; P (A \cap \bar{B})$
cbse
class12
maths
sec-e
ch1
answered
Nov 21, 2016
by
priyanka.c
1
answer
A car stands from a point P at time t = 0 sec and stops at point Q. The distance x, in metres, covered by it, in t seconds in given by $x = t^2 (2 - \frac{t}{3})$. Find the time taken by it to reach Q and also find the distance between P and Q.
cbse
class12
maths
sec-e
ch6
answered
Nov 21, 2016
by
priyanka.c
1
answer
On Q the set of all rational numbers, a binary operation $\ast$ is defined by $a \ast b=\frac{ab}{5}$ for all $a, b \in Q $. Find the identity element $\ast$ in Q. Also prove that every non-zero element of Q is invertible.
cbse
class12
maths
sec-e
ch1
answered
Nov 20, 2016
by
priyanka.c
1
answer
Fine the maximum and minimum value of $f(x) = x + \sin 2x $ in the invervat $0, 2\pi $
cbse
class12
maths
sec-e
ch6
answered
Nov 19, 2016
by
priyanka.c
1
answer
Show that function $f : R \to R$ given by $f(x) = x^3 + x $ I a bijection.
cbse
class12
maths
sec-e
ch1
answered
Nov 18, 2016
by
priyanka.c
1
answer
If the function $ f: [1, \alpha) \ implies [ 1, \alpha)$ defined by $f(x) = 2^{x(x-1)}$ is invertible, find $f^{-1}(x)$
cbse
class12
maths
sec-e
ch1
answered
Nov 17, 2016
by
priyanka.c
1
answer
Let f : N $\to$ Y be a function defined as $f(x) = 4x + 3f(x)=4x+3$ where $Y = \{ y \in N ; y = 4x + 3Y=\{ y \in N; y= 4x+3$ for some $ x \in N \}x \in N \}$. If 'f' is invertible.
cbse
class12
maths
ch1
sec-e
answered
Nov 14, 2016
by
priyanka.c
1
answer
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