Q. Three of the six vertices of a regular hexagon are chosen at random. The probability that triangle formed by these vertices is equilateral is

1. $\frac{1}{20}$
2. $\frac{1}{5}$
3. $\frac{1}{2}$
4. $\frac{1}{10}$

Q. The divisor is $10$ times of quotient and $10$ times of remainder. If the quotient is $10$ then what is a dividend ?

1. $1010$
2. $1100$
3. $1001$
4. $101$

Q. In which district is the number of male teachers more than the number of female teachers?

1. $B$ only
2. $D$ only
3. Both $B$ and $E$
4. Both $E$ and $F$

Q. If sum of LCM and HCF of two number is $50$ and their LCM is $20$ more than their HCF, then the product of two numbers will be :

1. $525$
2. $425$
3. $625$
4. $325$

Q. What is the total number of male teachers in District $F$, female teachers in District $C$ and female teachers in District $B$ together?

1. $1180$
2. $1080$
3. $1020$
4. $1120$

Q. A $320m$ long rain moving at an average speed of $120km/h$ crosses a platform in $24$ seconds. A man crossed the same platform in $4$ minutes. The speed of the man in $m/s$ is

1. $2.0$
2. $1.6$
3. $1.5$
4. $2.4$

Q. If $\alpha ,\beta$ are the roots of the equation $2x^2-5x+16=0$ then the value of ${\left(\frac{{\alpha }^2}{\beta }\right)}^{\frac{1}{3}}+{\left(\frac{{\beta }^2}{\alpha }\right)}^{\frac{1}{3}}$ is :

1. $\frac{1}{4}$
2. $\frac{5}{4}$
3. $\frac{5}{12}$
4. $\frac{1}{3}$

Q. If $\times$ means $-,+$ means $÷,-$ means $\times$ and $÷$ means $+$ then what is the value of :

1. $1080$
2. $1030$
3. $1050$
4. $1090$

Q. What is the difference between the number of female teachers in district $F$ and total number of teachers (both male and female) in district $E$?

1. $625$
2. $775$
3. $675$
4. $725$

Q. In the given arrangement of numbers after removing all even numbers which is the middle most number
$185947125836592764529264123514283$

1. $7$
2. $6$
3. $5$
4. $9$

Q. If $\sin \alpha ,\cos \alpha ,\tan \alpha$ are in GP, GP means ${\cos }^2\alpha =\sin \alpha \tan \alpha$, then ${\cot }^6\alpha -{\cot }^2\alpha =$ ?

1. $0$
2. $1$
3. $4$
4. $2$

Q. If one root of quadratic equation ${(K+1)}^{}{x}^2-5x+2K=0$ is reciprocal of other, then the value of $K$ is :

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

Q. In a certain office, $\frac{1}{3}$ of the workers are women, $\frac{1}{2}$ of the same are married and $\frac{1}{3}$ of the married women have children. If $\frac{3}{4}$ of the men are married and $\frac{2}{3}$ of the married men have children, then what part of worker are without children?

1. $\frac{5}{18}$
2. $\frac{11}{18}$
3. $\frac{4}{9}$
4. $\frac{17}{36}$

Q. A regular polygon is drawn with $35$ diagonals. What will be its measure of interior angle ?

1. ${164}^o$
2. ${144}^o$
3. ${154}^o$
4. None of these

Q. What will be the ratio of volume of cube is to volume of sphere inscribed in the cube?

1. $3:\pi$
2. $6:5$
3. $2:\pi$
4. $6:\pi$

Q. The height of three towers are in the ratio of $5:6:7$. If a spider takes $15$ minutes to climb the smallest tower, how much time it will take to climb the highest one?

1. $18$ minutes
2. $21$ minutes
3. $15$ minutes
4. $54$ minutes

Q. The value of $\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\frac{1}{\sqrt{7}+\sqrt{8}}+\frac{1}{\sqrt{8}+\sqrt{9}}$ is :

1. $4$
2. $2$
3. $1$
4. $0$

Q. If $\frac{a^{n+1}+b^{n+1}}{a^n+b^n}$ is the AM (arithmetic mean) between '$a$' and '$b$', then find the value of $n$.

1. $1$
2. $2$
3. $3$
4. $0$

Q. If $a_8=a_1+a_2+a_3+.......+a_7$
$b_8=b_1+b_2+b_3+......+b_7$
.................
..................
$h_8=h_1+h_2+h_3+.....+h_8=$
What is $a_8+b_8+....+h_8=$

1. $1596$
2. $2080$
3. $399$
4. $741$

Q. The numbers of female teachers in District $D$ is approximately what percent of the total number of teachers (both male and female) in District $A$?

1. $70$
2. $90$
3. $75$
4. $80$

Q. Eight members of a group shake hands with one another once. How many shakes were done altogether?

1. $64$
2. $28$
3. $18$
4. $16$

Q. What is the ratio of the number of male teachers in district $C$ to number of female teachers in district $B$?

1. $11:15$
2. $15:11$
3. $15:8$
4. $8:15$

Q. If $n$ is a natural number the $9^{2n}-4^{2n}$ is always divisible by :

1. $13$
2. Both $5$ and $13$
3. $5$
4. None of the above

Q. If in a business, Alok gains $75$% more profit than Akash, then by what percentage profit of Akash is less than the profit of Alok?

1. $25$%
2. $12.63$%
3. $42.85$%
4. $30.8$%

Q. The two vertices of a triangle are $(4,-2)$ and $(2,-6)$. If centroid of a triangle is $(0,1)$ then third vertex of triangle will be :

1. $(11,-6)$
2. $(-6,11)$
3. $(6,-11)$
4. $(6,11)$

Q. Value of ${[{\left(0.111\right)}^3+{\left(0.222\right)}^3-{\left(0.333\right)}^2{+\left(0.333\right)}^2\left(0.222\right)]}^2$ will be :

1. $222$
2. $0$
3. $333$
4. $2$

Q. If $5\tan \theta =3$, then $\frac{5\tan \theta -3\cos \theta }{5\tan \theta +3\cos \theta }=$ ?

1. $\frac{5}{3}$
2. $\frac{4}{5}$
3. No solution
4. $0$
5. $\frac{3}{5}$

Q. A clock is set right at $5$ a.m. The clock loses $16$ minutes in $24$ hours. What will be the right time when the clock indicates $10$ p.m on the 4th day?

1. $8$ p.m
2. $9$ p.m
3. $11$ p.m
4. $10$ p.m

Q. Find the missing letter:

$3$	$L$	$4$
$1$	$Q$	$17$
$5$	?	$4$

1. $V$
2. $P$
3. $Q$
4. $T$

Q. Complete the given series
$25,245,2545,25455,.........$

1. $254545$
2. $25555$
3. $254555$
4. $255454$