Plotting

Q.

The equation $\sin x=x^2+x+1$ has

1. one root

2. no real root

3. An infinite number of roots

4. None of these

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

1. 
2. 
3. 
4. 

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

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

Q. Which of the following options has (have) the correct combination of the function and its graph?

1. $y=-3(x-\frac{1}{2}),x\le 2$
   
2. $y=3$
   
3. $y=2x-3,x>-4$
   
4. $y=-5x$
   

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

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

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

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. $A(-a,0)$ 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. $x^2-y^2=a^2$
3. $x^2+y^2=2a^2$
4. $2x^2{y}^2=2a^2$