Basics of Inequalities and Intervals

In each of the following questions, two equations are given. You have to solve both the equation and find out the values of $x$ and $y$ and give the answer:

$\mathrm{I}$. $3x^2+13x+14=0$

$\mathrm{II}$. $y^2+7y+12=0$

The equation is solved on the basis of a certain system. Find out the correct answer for the unsolved equation on that basis.
98 – 64 --> 12,
86 – 32 --> 21,
42 – 11 --> ?

In the following questions, the symbols %, δ, *, + and / are used with the following meaning as illustrated below;

'B%C' means 'B is neither greater than nor equal to C'.
'BδC' means 'B is neither smaller than nor equal to C'.
'B*C' means 'B is not greater than C'.
'B+C' means 'B is not smaller than C'.
'B/C' means 'B is neither smaller than nor greater than C'.
In the following questions statements showing, relationship between different elements has been given, which are followed by two conclusions I and II.

Statements : M + L * J + Y, L δ U δ V δ S, N * G * V δ A

Conclusions : I. M % S II. M δ S

In the following question two equations numbered $I$ and $II$ are given. You have to solve both the equation and give answer.
$$\begin{gathered} 1. if x > y \\ 2. if x \ge y \\ 3. if x < y \\ 4. if x \le y \end{gathered}$$
$5. if x = y or the relationship cannot be established.$

$$\begin{gathered} I. x^2-2\sqrt{3}x-24=0 \\ II. y^2+7\sqrt{3}y+30=0 \end{gathered}$$

The following equations follow a common property. Find out the correct value to complete D:

A= 51 (714) 14;
B= 61 (915) 15;
C = 71 (1136) 16;
D= 81 (?) 17

What value will come in place of question mark $\left(?\right)$ in the question given below:

$4897÷59+{\left(7\right)}^2=?$

Which of the following statement is true for pair of linear equation?
$$\begin{gathered} \mathrm{I}. 7\mathrm{x}+3\mathrm{y}=8 \\ \mathrm{II}.3\mathrm{x}+2\mathrm{y}=12 \end{gathered}$$

1. $y>x$
2. $x>y$
3.$x\ge y$
4. $x=y$

What value will come in place of question mark $\left(?\right)$ in the questions given below:

$0.09-?-6.8=1.1016$

If + means ÷, - means x, ÷ means -, x means +, what will be the value of
$8 + 6 ÷ 4 - 7 \times 3 ?$

$\frac{\sqrt{7}}{\sqrt{16+6\sqrt{7}}-\sqrt{16-6\sqrt{7}}}$ is equal to _____.

In the following question, two equations numbered I and II are given. You have to solve both the equation and give answer.

A. If $x>y$

B. If $x\ge y$

C. If $x<y$

D. If $x\le y$

E. If $x=y$ or the relationship cannot be established.

$$\begin{gathered} \mathrm{I}. 10x+11y=19 \\ \mathrm{II}. 4x+2y=\frac{298}{55} \end{gathered}$$

If FOR = 6 and BOAT = 24 then MEANS = ?

In the following questions, the symbols %, δ, *, + and / are used with the following meaning as illustrated below;

'B%C' means 'B is neither greater than nor equal to C'.
'BδC' means 'B is neither smaller than nor equal to C'.
'B*C' means 'B is not greater than C'.
'B+C' means 'B is not smaller than C'.
'B/C' means 'B is neither smaller than nor greater than C'.
In the following questions statements showing, relationship between different elements has been given, which are followed by two conclusions I and II.

Statements : M + L * J + Y, L δ U δ V δ S, N * G * V δ A

Conclusions : I. Y + V II. V δ Y

A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in two classes of alphabets as in two matrices given below. The columns and rows of Matrix-I are numbered from $0 \mathrm{to} 4$ and that of Matrix-II are numbered from $5 \mathrm{to} 9$. A letter from these matrices can be represented first by its row and next by its column e.g., 'P' can be represented by $12, 24,$ etc., and 'O' can be represented by $57, 69,$ etc. Similarly, you have to identify the set for the word given in the question.

WARD

Matrix — I

If + stands for 'division', x stands for 'addition', - stands for 'multiplication' and ÷ stands for 'subtraction', then which of the following equations is correct ?

In a solid cube made up of 27 small cubes two opposite sides are painted red, two opposite sides are yellow, and two other sides are white. How many small cubes have the colours yellow and white alone in them?

If $x,y,z$ are real and unequal numbers, such that, $2016x^2+2016y^2+6z^2>2\left(mxy+3yz+3zx\right)$ then the sum of digits of $m$ is

Find the solution of $ax\le 1$.

Write the set of values of $x$ satisfying the inequation $\sqrt[3]{(x-4)\left(x-7\right)}\ge 2^{\frac{2}{3}}$.