Plotting

Q. Area under the curve $y=x^2-4x$ within the x-axis and the line x=2, is

1. $Cannotbecalculated$
2. $\frac{16}{3}sq.unit$
3. $-\frac{16}{3}sq.unit$
4. $\frac{4}{7}sq.unit$

Q. If $a,b,c$ are three consecutive terms of an AP and $x,y,z$ are three consecutive terms of a GP, then the value of $x^{b-c}.y^{c-a}.z^{a-b}$ is

1. $0$
2. $xyz$
3. $-1$
4. $1$

Q. Number of solution(s) of the equation |ln x|=|sinx| is/are

1. 1
2. 3
3. 2
4. 4

Q. $\mathrm{If}\mathrm{the}\mathrm{graph}\mathrm{of}y=x^3\mathrm{is}$$\mathrm{then}\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{graph}\mathrm{of}y=(x+1{)}^3?$

1. 
2. 
3. 
4. 

Q. The locus of the moving point $P$ such that $2PA=3PB$, where $A$ is $(0,0)$ and $B$ is $(4,-3)$, is

1. $5x^2+5y^2+72x+54y+225=0$
2. $5x^2+5y^2-72x+54y-225=0$
3. $5x^2+5y^2-72x-54y+225=0$
4. $5x^2+5y^2-72x+54y+225=0$

Q. Number of solution(s) of the equation $\left({\log }_{10}x\right|=\left(\mathrm{sinx}\right|$ is/are

1. 4
2. 5
3. 6
4. 3

Q.

Formation of the differential equation of equation of all the parabolas having their axes of symmetry coincident with the X-axis is:

1. 

2. 

3. 

4. 

Q. Number of solution(s) possible for equation $\sin \left(x\right)={\log }_{10}\left(x\right)$ is/are

1. 1
2. 2
3. 3
4. more than 3

Q. A sphere of constant radius $k$ passes through the origin and meets the axes at $A,B$ and $C,$ then the centroid of $\Delta ABC$ lies on the sphere

1. $x^2+y^2+z^2=\frac{k^2}{9}$
2. $x^2+y^2+z^2=\frac{2k^2}{9}$
3. $x^2+y^2+z^2=\frac{k^2}{3}$
4. $x^2+y^2+z^2=\frac{4k^2}{9}$

Q. The locus of the point $P({\cos }^{2}t,2\sin t),t\in R$ is

1. $y^2+4x=4$
2. $y^2=4x$
3. $y^2+4x=1$
4. $y^2=4x+1$

Q. Number of solution(s) possible for the equation $\ln \left(x\right)=\sin \left(x\right)$ is/are

1. 1
2. 2
3. 3
4. 4

Q. The graph of $-f\left(x\right)$ will be the mirror image of the graph of $f\left(x\right)$ about the $x-$ axis.

1. True
2. False

Q. If $A\equiv (9,-1)$ and $B\equiv (-9,5)$, then the locus of moving point $P$ such that $|\overline{AP}|:|\overline{BP}|=1:2$, where $|\overline{AP}|$ denotes the length of $AP$, is

1. $(x-15{)}^2+(y+3{)}^2=180$
2. $(x-15{)}^2+(y+3{)}^2=160$
3. $(x+15{)}^2+(y-3{)}^2=160$
4. $(x-3{)}^2+(y-15{)}^2=160$

Q. A rod of length $3l$ units, slides with its ends $A$ and $B$ on the $x$ and $y$ axes respectively. Then the locus of the centroid of $△OAB$ is
(Here, $O$ is the origin.)

1. $x^2+y^2=l^2$
2. $x^2+y^2=9l^2$
3. $3x^2+3y^2=l^2$
4. $x^2+y^2=3l^2$

Q. Let $A(6,-5)$ and $B(-6,1)$ be the two vertices of the triangle $ABC$, if the locus of centroid of $△ABC$ is $2x+5y=1$, then the locus of vertex $C$ is

1. $2x-5y=21$
2. $5x+2y=19$
3. $5x-2y=17$
4. $2x+5y=23$

Q. If the locus of a point $P$ which is collinear with the points $A(2,3)$ and $B(4,7)$ is $ax+by=1$, then the value of $a^2+b^2$ is

Q. Number of solution(s) possible for the equation ${\log }_{10}x=\left|\sin x\right|$ is/are

1. 2
2. 3
3. 4
4. 5

Q. If $A=(5,0)$ and $B=(0,4)$, then the locus of moving point $P$ such that $|PA{|}^2-|PB{|}^2=9$ is

1. $4x-5y=0$
2. $5x-4y=0$
3. $5x+4y=0$
4. $4x+5y=0$

Q. The number of solutions of $[\sin x+\cos x]=3+[-\sin x]+[-\cos x]$ in the interval $[0,2\pi ]$ is (where $[.]$ denotes the greatest integer function.)

1. $0$
2. $4$
3. $3$
4. Infinitely many

Q. $A(-a,0)$ and $B(a,0)$ are two fixed points. The locus of a point $P$ such that $\angle APB$ is a right angle, is

1. $x^2-y^2=a^2$
2. $x^2+y^2=2a^2$
3. $2x^2{y}^2=2a^2$
4. $x^2+y^2=a^2$

Q. The function $f:R\to R$ defined by $f\left(x\right)=6^x+6^{\left|x\right|}$ is
(a) one-one and onto
(b) many one and onto
(c) one-one and into
(d) many one and into

Q. Locus of the point whose sum of distances from the origin and the $x-$ axis is $4$ units is

1. $x^2=8(2-y),y\ge 0$
2. $x^2=8(2+y),y\ge 0$
3. $x^2=8(2+y),y<0$
4. $x^2=8(2-y),y<0$

Q. A rod of length $3l$ units, slides with its ends $A$ and $B$ on the $x$ and $y$ axes respectively. Then the locus of the centroid of $△OAB$ is
(Here, $O$ is the origin.)

1. $x^2+y^2=l^2$
2. $x^2+y^2=9l^2$
3. $3x^2+3y^2=l^2$
4. $x^2+y^2=3l^2$

Q. Which one is the graph of $q=\mathrm{xcos}\left(x\right)$?

1. 
2. 
3. 
4. 

Q. The graph of xy = 1 is symmetric about

1. x-axis
2. y-axis
3. line y = x
4. origin

Q. Number of solution(s) possible for the equation $\ln \left(x\right)=\sin \left(x\right)$ is/are

1. 1
2. 2
3. 3
4. 4

Q. Which one is the graph of $q=\mathrm{xcos}\left(x\right)$?

1. 
2. 
3. 
4. 

Q. Let $\overline{a},\overline{b},\overline{c}$ be three vectors such that $\overline{a}\times \overline{b}=\overline{c}$ and $\overline{c}\times \overline{a}=\overline{b}$, then

1. $\overline{a}.\overline{b}=|\overline{c}{|}^2$
2. $\overline{c}.\overline{a}=|\overline{b}{|}^2$
3. $\overline{b}.\overline{c}=|\overline{a}{|}^2$
4. $\overline{a}\parallel \overline{b}\times \overline{c}$

Q. Number of solution(s) of the equation $\left({\log }_{10}x\right|=\left(\mathrm{sinx}\right|$ is/are

1. 3
2. 4
3. 5
4. 6

Q. The locus of the point $P({\cos }^{2}t,2\sin t),t\in R$ is

1. $y^2=4x$
2. $y^2=4x+1$
3. $y^2+4x=1$
4. $y^2+4x=4$