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Recent questions and answers in Sets, Relations and Functions
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JEEMAIN and NEET
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Mathematics
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Sets, Relations and Functions
determine whether even or odd : f(x+y)+f(x-y)=2f(x).f(y) ; where f(0) is not zero and x,y belongs to set of Real numbers
answered
May 20, 2016
by
asthajagia
1
answer
The value of c for which conclusion of Mean value theorem holds for the function $f(x)= \log _e^x$ on the interval $[1,3]$ is
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
If $\overrightarrow{a} \times \overrightarrow{b}=c, \overrightarrow{b} \times \overrightarrow{c}= \overrightarrow{a}$ and $\overrightarrow{c} \times \overrightarrow{a}= \overrightarrow{b}$ then $(\overrightarrow{a} . \overrightarrow{b} \times \overrightarrow{c}) + \overrightarrow{b} . (\overrightarrow{c} \times \overrightarrow{a})+ \overrightarrow{c}. (\overrightarrow{a} \times \overrightarrow{b})$ is equal to
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
The Cartesian equation of the plane passing through the line of intersection of the planes. $ \overrightarrow{r} .( 2 \hat i -3 \hat j+4 \hat k) =1$ and $ \overrightarrow{r} .( 2 \hat i - \hat j+ \hat k)+8 =0$ and passing through $(1, 1, 1).$
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
Consider the planes $3x-6y+2z+5=0$ and $4x-12y +3z=3$ . The plane $67x-16xy+4xz+44=0$ bisects the angle between the given planes which
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
The reflection of the point $P(1,0,0)$ in the $ \large\frac{x-1}{2} =\frac{y+1}{-3} =\frac{z+10}{8}$ is
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
Equation of a plane binding the cycle between the planes $2x-y+2z+3=0$ and $ 3x-2y+6z+8$ is
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
Let $P,Q,R $ and $S$ be the points on the plane with position vectors $-2 \hat i -\hat j ,4 \hat i, 3 \hat i +3 \hat j$ and $3 \hat i +2 \hat j$ respectively . The quadrilateral $PQRS$ must be a
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
Equation of the plane containing the straight line $ \large\frac{x}{2}= \frac{y}{3} =\frac{z}{4}$ and perpendicular to the plane containing the straight lines $ \large\frac{x}{3}=\frac{y}{4} =\frac{z}{2}$ and $\large\frac{x}{4}=\frac{y}{2} =\frac{z}{3}$ is
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
The equation of the plane passing through the line of intersection of the planes $x+2y+3z=2$ and $x-y+z=3$ and at a distance $\large\frac{2}{\sqrt 3}$ from the point $(3,1,-1)$ is
jeemain
math
sets-relations-and-functions
answered
Feb 15, 2016
by
meena.p
1
answer
The foci of an ellipse are $(0, \pm 1)$ and minor axis is of unit length . The equation of the ellipse
jeemain
math
sets-relations-and-functions
answered
Feb 1, 2016
by
meena.p
1
answer
If $z= \sqrt {5+12i }+\sqrt{12i-5}$ then the principal of org (z) can be
jeemain
math
sets-relations-and-functions
answered
Feb 1, 2016
by
meena.p
1
answer
In the expansion of $(a-b)^2 , n \leq 5, $ the sum 5th and 6th term is zero, then $\large\frac{a}{b}$ is equal to
jeemain
math
sets-relations-and-functions
answered
Feb 1, 2016
by
meena.p
1
answer
If $ \sin ^{-1} \bigg( \large\frac{x}{5}\bigg) $$ + cosec^{-1} \bigg( \large\frac{5}{4}\bigg)=\frac{\pi}{2}$, then x is
jeemain
math
sets-relations-and-functions
answered
Feb 1, 2016
by
meena.p
1
answer
Let $f(x)=\{(3 \sin^2(10x +11)-7)^2\}$ for $x \in R$ . Then the maximum value of the function f is
jeemain
math
sets-relations-and-functions
answered
Feb 1, 2016
by
meena.p
1
answer
If $ y= \sqrt{e^{\sqrt x}}$ , then $\large\frac{dy}{dx}$ is
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
Two vertices of an equilateral triangle are $(-1,0) (1,0)$ qand the third vertex lies above the x -axis . Then the equation of the circum circle is
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
The minimum area of triangle formed by the tangent to the ellipse $\large\frac{x^2}{a^2} +\frac{y^2}{b^2} $$=1$ and coordinating axes is :
jeemain
math
conics
answered
Jan 28, 2016
by
meena.p
1
answer
If $ \sin x + \cos y = \large \frac{1}{3}$ and $\cos x + \sin y = \frac{1}{2}$, then $\tan \frac{(x-y)}{2}$
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
The number of distinct roots of $\begin{bmatrix} \sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & cos x & \sin x \end{bmatrix}$ is a
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
The inverse of the following statement If $x=3,$ then $x^2=9$ is
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
The number of five digit number formed with out repetition , divisible by 6 with digits $0,1,2,3,4,5$ is
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
Equation of a line passing through $(-1,2,-3)$ and perpendicular to the place $2x+3y+z+5=0$ is
jeemain
math
sets-relations-and-functions
answered
Jan 28, 2016
by
meena.p
1
answer
The side of a parallelogram are $2 \hat i +4 \hat j -5 \hat k$ and $ \hat i +2 \hat j +3 \hat k$, then the unit vector parallel to one of the diagonals is :
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
The length of the normals drawn from the point on the axis of the parabola $y^2 =8x $ whose distance from the focus is
jeemain
math
conics
answered
Jan 27, 2016
by
meena.p
1
answer
The solution of the differential equation $ \large\frac{dy}{dx} =\frac{xy}{x^2+y^2}$ is
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
If $\cos \alpha+\cos \beta + \cos \gamma=0= \sin \alpha +\sin \beta + \sin \gamma$ then $ \sin^2 \alpha +\sin ^2 \beta +\sin ^2 \gamma$
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
If $A=\begin{bmatrix} i & -i \\ -i & i \end{bmatrix}$ and $B=\begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$ then $A^8$ equals
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
If $a,b,c$ be the sides of a triangle ABC and if roots of the equation . $a(b-c)x^2+b(c-a)x+c(a-b)=0$ are equal , then $\sin ^2 \bigg(\large\frac{A}{2} \bigg) ,$$ \sin ^2 \bigg(\large\frac{B}{c} \bigg),$$ \sin ^2 \bigg(\large\frac{c}{2} \bigg) $are in
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
$\int\large\frac{dx}{(1+x^2) \sqrt {p^2+q^2(\tan^{-1}x)^2}}$=
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
If $\cos ^{-1} x > \sin ^{-1} x$, then x lies in the interval
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
The number of equivalence relation on the set $\{1,2,3\}$ containg $(1,2)\;and\;(2,1)$ is
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
Solve : $\lim \limits_{x \to \infty } [ \sqrt {x+\sqrt{x+\sqrt x}}-\sqrt {x} ]=$
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
An A.P consists of 23 terms.If the sum of the 3 terms in the middle is 141 and the sum of last 3 terms is 261, then the first term is :
jeemain
math
sets-relations-and-functions
answered
Jan 27, 2016
by
meena.p
1
answer
The variance of first 20 natural number is :
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
The value of $ \int \limits_{0}^{2\pi} \large\frac{x \sin ^{2n}x }{\sin ^{2n} x+ \cos ^{2n} x}= \pi^2$
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
The solution of $\large\frac{6x}{4x-1} < \frac{1}{2}$ is
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
$\lim_{x \to \infty } \bigg(\large\frac{3x-4}{3x+2}\bigg) ^{\large\frac{x+1}{3}}=$
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
The distance of the center of ellipse $x^2+2y^2-2=0$ to these tangent of the ellipse which are equally inclined from both the axis , is
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
There are three bags each containing 5 white balls and 2 black balls. Also there are 2 bags each containing 1 white ball and 4 black balls. A black ball is drawn at random , the chance that the ball is from the first bag is :
jeemain
math
sets-relations-and-functions
answered
Jan 22, 2016
by
meena.p
1
answer
is there any function which is continuous throughout but not differential at integral points
answered
Jun 29, 2015
by
pady_1
1
answer
find solutions of the equation [x][y]=x+y .
math
answered
Nov 24, 2014
by
pady_1
1
answer
If $f:[1,\infty )\rightarrow\:[2,\infty)$ is defined as $f(x)=x+\large\frac{1}{x}$ then find $f^{-1}(x)$.
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f:A\rightarrow B$ is defined as $f(x)=x^2-x+1$ so that $f(x)=f^{-1}(x)$ then the solution set of $x$ is ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
medium
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
If $A=\{x:x\in R\:\:and\:\:x\geq \large\frac{1}{2}\}$ and $B=\{x:x\in R\:\:and\:\:x\geq\large\frac{3}{4}\}$ and $f(x)=x^2-x+1$ so that $f(x)=f^{-1}x$ then the solution set of $x$ is ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
medium
asked
May 27, 2013
by
rvidyagovindarajan_1
0
answers
If $f:A\rightarrow B$, $3^{f(x)}+2^{-x}=4$ and $f(x)$ is bijection then the domain $A$ of $f(x)$ is ?
jeemain
math
class12
relations-and-functions
types of relations
medium
answered
May 27, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R$ is defined as $f(x)=x^2+1$ then $f^{-1}(x)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 24, 2013
by
rvidyagovindarajan_1
1
answer
If $f:R\rightarrow R$ is defined as $f(x)=3x-5$, then $f^{-1}(x)$ = ?
jeemain
math
class12
ch1
relations-and-functions
composition of functions
easy
answered
May 24, 2013
by
rvidyagovindarajan_1
1
answer
Range of $f(x)=\large\frac{x-[x]}{1+x-[x]}$ where $[x]$ is greatest integer function.
jeemain
math
class12
ch1
relations-and-functions
types of functions
medium
answered
May 21, 2013
by
rvidyagovindarajan_1
1
answer
Domain of $f(x)=\large\frac{1}{\sqrt {|x|-x}}$ = ?
jeemain
math
class12
ch1
relations-and-functions
types of functions
easy
answered
May 21, 2013
by
rvidyagovindarajan_1
1
answer
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