Mathematics

Q.

If $\mathrm{y}={\mathrm{x}}^{{\mathrm{x}}^{\mathrm{x}....\infty }},$, then $\frac{\mathrm{dy}}{\mathrm{dx}}$ is equal to

1. ${\mathrm{yx}}^{\mathrm{y}-1}$

2. $\frac{{\mathrm{y}}^2}{\mathrm{x}(1-\mathrm{ylog}\mathrm{x})}$

3. $\frac{\mathrm{y}}{\mathrm{x}\left(1+\mathrm{ylogx}\right)}$

4. None of these

Q.

The number of all possible matrices of order $3\times 3$ with each entry 0 to 1 is
(a)27
(b)18
(c)81
(d)512

Q.

What is the value of $e^{-\infty }$?

Q.

Prove that $6+\surd 2$ is an irrational number.

Q. If $a+b+c=1,ab+bc+ca=2$ and $abc=3$, then the value of $a^4+b^4+c^4$ is equal to

Q.

Find the value of $\sin {75}^{\circ }$.

Q. $P,Q,R,S,T,U,V$ and $W$ are sitting round the circle and are facing the centre :
$1.P$ is second to the right of $T$ who is the neighbour of $R$ and $V.$
$2.S$ is not the neighbour of $P.$
$3.V$ is the neighbour of $U.$
$4.Q$ is not between $S$ and $W.$
$5.W$ is not between $U$ and $S.$
Which two of the following are not neighbours?

1. $RV$
2. $UV$
3. $RP$
4. $SW$

Q.

What is the formula of $\left(a^3+b^3\right)$?

Q.

Count the number of triangles in given figure.

Q.

Find the value of $\frac{1}{c\mathrm{os}C}$

Q.

What is the integral of $sec\left(x\right)$?

Q.

Express $\tan \theta$ in terms of $\sin \theta$.

Q. The rank of the word $SUCCESS$, If all possible permutations of the word $SUCCESS$ are arranged in dictionary order is

1. $341$
2. $331$
3. $351$
4. $361$

Q. The angle between the minute hand and the hour hand of a clock when the time is $7:20\text{a.m.}$ is

1. ${75}^{\circ }$
2. ${90}^{\circ }$
3. ${100}^{\circ }$
4. ${120}^{\circ }$

Q.

Let $R_1$ and $R_2$ be two relations defined as follows:

$R_1=\left\{\left(a,b\right)\in R^2:a^2+b^2\in \mathrm{\mathbb{Q}}\right\}$and

$R_2=\left\{\left(a,b\right)\in R^2:a^2+b^2\notin \mathrm{\mathbb{Q}}\right\}$, where $\mathrm{\mathbb{Q}}$ is the set of all rational numbers. Then :

1. $R_1$ is transitive but $R_2$ is not transitive

2. $R_1$ and $R_2$ are both transitive

3. $R_2$ is transitive but $R_1$ is not transitive

4. Neither $R_1$ nor $R_2$ is transitive

Q.

What are ${}^{n}P_r$ and ${}^{n}C_r$ in math?

Q.

What is the derivative of $\log \left(x\right)$?

Q. x+1/2 log(x+1/2) (x2+ 2x-3/4x2-4x-3)

Q.

A lift can carry up to $8$ persons. At the ground floor$A,B,C$ whose weights are in increasing AP with an average weight of $62kg$ enter the lift. When the lift stops at $3rd$ floor $E,FandG$ whose weights are in an increasing AP enter the lift. The new average weight of people in the lift becomes $66kg$. What is the weight of F?

Q.

${\text{a}}^2{\text{+b}}^2\text{is equal to ?}$

Q.

For real numbers $xandy,$we write$xRy\Rightarrow x–y+\surd 2$ is an irrational number. Then the relation $R$ is

1. Reflexive

2. Symmetric

3. Transitive

4. None of these

Q.

A software engineer creates a LAN game where an $8$ digit code made up of $1,2,3,4,5,6,7,8$ has to be decided on universal code. There is a condition that each number has to be used and no number can be repeated. What is the probability that first $4$ digits of the code are even numbers ?

Q.

For $x\in R,\text{let}\left[x\right]$ denote the greatest integer $\le x,$ then the sum of the series $[-\frac{1}{3}]+[-\frac{1}{3}-\frac{1}{100}]+[-\frac{1}{3}-\frac{2}{100}]+....+[-\frac{1}{3}-\frac{99}{100}]$ is :

1. $-135$
2. $-153$
3. $-131$
4. $-133$

Q. The sum of all the elements in the set $\{n\in \{1,2,...,100\}|\text{H.C.F. of}n\text{and 2040 is 1}\}$ is equal to

Q. The number of real roots of the equation $5+|2^x-1|=2^x(2^x-2)$ is

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

Q.

Let $A=\left\{a,b,c\right\}$ and $B=\left\{1,2,3,4\right\}$. Then the number of elements in the set $C=\left\{f:A\to B|2\in f\left(A\right)\text{and}f\text{is not one-one}\right\}$ is

Q.

A survey shows that $63\%$ of the people in a city read newspaper $A$ whereas $76\%$ read newspaper $B$. If $x\%$ of the people read both the newspapers, then a possible value of $x$ can be:

$37$

$29$

$65$

$55$

Q. Find the value of $\tan \frac{\pi }{8}.$

Q. Find the correctly spelt word.

1. Aberant
2. Abbarant
3. Aberrant
4. Abberant

Q.

Find the sum: $1+2+3+4+5+......+100$.