Distance Formula

Q. Find the distance between E and F.

1. 2.2 units
2. 2.9 units
3. 3.5 units
4. 1.3 units

Q. The area of a traingle is 5 square units, two of its verices are (2, 1) and (3, -2).The third vertex lies on y=x+3.The third vertex is

1. $(\frac{7}{2},\frac{3}{2})$
2. $(-\frac{3}{2},\frac{3}{2})$
3. $(\frac{7}{2},\frac{5}{2})$
4. $(-\frac{3}{2},\frac{13}{2})$

Q. Take any point O in the interior of a triangle PQR:
Is OP + OQ > PQ?
Is OP + OR > PR?
Is OQ+ OR > QR?

Q. Given the points $A(0,4)$ and $B(0,-4)$, the equation of the locus of the point $P$ such that $|AP-BP|=6$ is-

1. $9x^2-7y^2-63=0$
2. $9x^2-7y^2+63=0$
3. $7x^2-9y^2+63=0$
4. $7x^2-9y^2-63=0$

Q. The value of ${\left(\frac{x^a}{x^b}\right)}^{(a+b)}\times {\left(\frac{x^b}{x^c}\right)}^{(b+c)}\times {\left(\frac{x^c}{x^a}\right)}^{(c+a)}$ is equal to

1. 1
2. 0
3. $x^{abc}$
4. abc

Q. The shortest distance between line $y-x=1$ and curve $x=y^2$

1. $\frac{\sqrt{3}}{4}$
2. $\frac{3\sqrt{2}}{8}$
3. $\frac{8}{3\sqrt{2}}$
4. $\frac{4}{\sqrt{3}}$

Q. If $2^a+3^b=17$ and $2^{a+2}-3^{b+1}=5,$ then find the value of a and b.

1. $a=2andb=2.$
2. $a=3andb=2.$
3. $a=3andb=3.$
4. $a=3andb=4.$

Q. The distance between two points (x, a) and (x, b) with the same x- coordinate is given by:

1. |(x - a)|
2. |(a - b)|
3. None of the above
4. |(x - b)|

Q. Find the $6^{th}$ term of ${\left(1+\frac{x}{2}\right)}^{-5}$

Q. In the given figure, find the perimeter of the rectangular frame PQRS.

1. 30 units
2. 22 units
3. 26 units
4. 28 units

Q. The distance between the point $(1,2)$ and the point of intersection of the line $2x+y=2$ and $x+2y=2$ is

1. $\frac{\sqrt{17}}{3}$
2. $\frac{\sqrt{16}}{3}$
3. $\frac{\sqrt{17}}{5}$
4. $\frac{\sqrt{19}}{3}$
5. $\frac{\sqrt{19}}{5}$

Q. If line m is parallel to n, what is the value of x (in degrees)?

1. 45
2. 135
3. 125
4. 55

Q. If PEN is written as '+X' and ENT is written as 'X-' in a certain code, how is TEN written in the same code?

Q. If $AB=A$ and $BA=B$ then $B^2$ is equal to

1. $B$
2. $A$
3. $B^2$
4. $-B$

Q. Assertion(A): $(1,0)(\frac{1}{2},\frac{\sqrt{3}}{2})(\frac{1}{2},\frac{\sqrt{3}}{2})$ forms an equilateral triangle
Reason (R): The cube roots of unity taken as vertices of a triangle then the triangle is an equilateral triangle.

1. Both A and R are true but R is not the correct explanation of A
2. Both A and R are true and R is the correct explanation of A
3. A is true R is false.
4. A is false, R is true.

Q. $a$ and $b$ are real numbers between $0$ and $1.$ $A\equiv (a,1),B\equiv (1,b)$ and $C\equiv (0,0)$ are the vertices of a $△ABC$. If the $△ABC$ is equilateral, its area is equal to

1. $\frac{7\sqrt{3}-12}{4}$
2. $\frac{7\sqrt{3}+12}{4}$
3. $\frac{\sqrt{3}}{4}$
4. none of these

Q. If the values of $(a-b)$ and $ab$ are $6$ and $40$ respectively, find the values of $a^2+b^2$ and $(a+b{)}^2$

Q. The distance between two points (x, a) and (x, b) with the same x- coordinate is given by:

1. |(x - a)|
2. |(x - b)|
3. |(a - b)|
4. None of the above

Q. Distance between points P (11, 3) and Q (-7, 3) is

1. 12 units
2. 15 units
3. 18 units
4. 4 units

Q. Distance between points P (11, 3) and Q (-7, 3) is

1. 18 units
2. 4 units
3. 15 units
4. 12 units

Q. Suppose, $z_1,z_2,z_3$ are the vertices of an equilateral triangle inscribed in the circle $\left|z\right|=2.$ If $z_1=1+i\sqrt{3}$ then $z_2$ and $z_3$ are equal to

1. $-2,1-i\sqrt{3}$
2. $2,1-i\sqrt{3}$
3. $-2,1+i\sqrt{3}$
4. None of these

Q. If $a=-2,b=3$, evaluate the $a{b}^2$

1. -18
2. -27
3. 2
4. None of these