Question 1 :
In the question given below, use the following notations: <br>{tex} \mathrm{A}" \mathrm{B} {/tex} means 'add {tex} \mathrm{B} {/tex} to {tex} \mathrm{A} {/tex}.<br> {tex} \mathrm{A}' \mathrm{B} {/tex} means 'subtract {tex}\mathrm B{/tex} from {tex}\mathrm A{/tex}'.<br>{tex}\mathrm{ A @ B}{/tex} means 'divide {tex}\mathrm A{/tex} by {tex}\mathrm B{/tex}'.<br> {tex} \mathrm{A}^{*} \mathrm{B} {/tex} means 'multiply {tex} \mathrm{A} {/tex} by {tex} \mathrm{B} {/tex}'.<br> Now, answer the following question.<br>The time taken by two running trains in crossing each other is calculated by dividing the sum of the lengths of two trains by the total speed of the two trains. If the length of the first train is {tex} L_{1} {/tex}, the length of the second train is {tex} L_{2} {/tex}, the speed of the first train is {tex} \mathrm{V}_{1} {/tex} and the speed of the second trains is {tex} \mathrm{V}_{2} {/tex} which of the following expressions would represent the time taken {tex} ? {/tex}<br>

Question 2 :
Below are given some symbols indicating some relations given against them. Read these symbols carefully and then answer the questions given below. There are four options to each question, of which only one is correct. Find the correct answer.<br />{tex} \begin{array}{ll}\Delta=\text { greater than } ; +=\text { not greater than } \ \\\theta=\text { equal to ; } \phi=\text { not equal to } \\\ x=\text { less than, } \square=\text { not less than }\end{array} {/tex}<br />a {tex} \square {/tex} b {tex} \Delta {/tex} c implies that

Question 3 :
If A + B = 2C and C + D = 2A, then

Question 4 :
If A + B = C + D and A + D > B + C, then which one of the following is definitely wrong >

Question 5 :
If P denotes +, Q denotes –, R denotes × and S denotes ÷, which of the following statements is correct?

Question 6 :
If 3 + 2 = 7, 4 + 3 = 10, 5 + 4 = 13, then 6 + 5 = ?

Question 7 :
In the following question, the symbols, &copy;, {tex}\underline{&copy;}{/tex}, =, * {tex}\underline{*}{/tex}&nbsp;are used with the following meanings <br />{tex}'\mathrm A &copy; \mathrm{B}' {/tex} means 'A is greater than B';<br />'A {tex}\underline{&copy;}{/tex}B' means 'A is greater than or equal to B';<br />'A = B' means 'A is equal to B';<br />'A {tex} ^{*} {/tex} B' means 'A is smaller than B';<br />'A {tex} \mathrm{}_{-}^{*}{/tex} B' means 'A is either smaller than or equal to B'<br />Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.<br />Give answer (1) if only if conclusion I is true; (2) if only conclusion II is true; (3) if either I or II is true; (4) if neither I nor II is true.<br /><strong>Statements :</strong> {tex} \mathrm{S}&nbsp; &copy;\mathrm{T}, \mathrm{M}_{-}^{*} \mathrm{~K}, \mathrm{T}=\mathrm{K} {/tex} <br /><strong>Conclusions:</strong><br />I. {tex}\mathrm{T&nbsp; }&copy;\mathrm M{/tex} <br />II. {tex}\mathrm{T=M}{/tex}

Question 8 :
If + means × . × means –, ÷ means + and – means ÷, then which of the following gives the result of<br> 175 – 25 ÷ 5 ÷ 20 × 3 + 10 ?

Question 9 :
In the following question, the symbols, &copy;, {tex}\underline{&copy;}{/tex}, =, * {tex}\underline{*}{/tex}&nbsp;are used with the following meanings&nbsp;<br />{tex}'\mathrm A &copy; \mathrm{B}' {/tex} means 'A is greater than B';<br />'A {tex}\underline{&copy;}{/tex}B' means 'A is greater than or equal to B';<br />'A = B' means 'A is equal to B';<br />'A {tex} ^{*} {/tex} B' means 'A is smaller than B';<br />'A {tex} \mathrm{}_{-}^{*}{/tex} B' means 'A is either smaller than or equal to B'<br />Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.<br />Give answer (1) if only if conclusion I is true; (2) if only conclusion II is true; (3) if either I or II is true; (4) if neither I nor II is true.<br /><strong>Statements:</strong> {tex}\mathrm E \underline{&copy;}\mathrm U, C * E, C &copy;&nbsp;B{/tex}<br /><strong>Conclusions:</strong><br />I. {tex} \mathrm{U}=\mathrm{C} {/tex}<br />II.{tex}\mathrm{ E &copy; B}{/tex}

Question 10 :
The letters L, M, N, O, P, R, S and T in their order are substituted by nine integers 1 to 9 but not in that order. 4 is assigned to P. The difference between P and T is 5. The difference between N and T is 3. What is the integer assigned to N?

Question 11 :
In the following questions, three statements of numbers following same rules are given. Find the rule and accordingly find the value of the number?<br>If 7*3 = 52; 9*5 = 86; 3*4 = 13, then 5*7 = ?

Question 12 :
In the following questions, the symbols @ {tex} \mathrm{C} $ \% {/tex} and {tex} \# {/tex} are used with the following meanings as illustrated below :&nbsp;<br />'A {tex} \${/tex} B' means' A is not smaller than B'&nbsp;<br />'A # B' means 'A' is not smaller than B'<br />'A @ B' means 'A is neither smaller than nor equal to B'&nbsp;<br />'A{tex}C {/tex}B' means 'A is equal to B'&nbsp;<br />'A % B' means 'A' is neither greater than nor equal to B'<br />Now in each of the following questions, assuming the given statement to be true, find which of the three conclusions. I, II and III given below then is {tex} / {/tex} are definitely true and give your answer accordingly. Clearly, we have&nbsp;<br />A $ B {tex}\Rightarrow{/tex}&nbsp;A &lt; B {tex}\Rightarrow{/tex} A {tex}\geq{/tex}&nbsp;B<br />A # B {tex}\Rightarrow{/tex} A &gt; B {tex}\Rightarrow{/tex} A {tex}\leq{/tex}&nbsp;B.&nbsp;<br />A @ B {tex}\Rightarrow{/tex} A &lt; B and A # B {tex}\Rightarrow{/tex}&nbsp;A &gt; B,&nbsp;<br />A {tex}C {/tex} B {tex}\Rightarrow{/tex} A &gt; B and A # B {tex}\Rightarrow{/tex} A &lt; B<br /><strong><strong><strong><strong>Statements:</strong> M @ J, J $ T, T C N<br /><strong>Conclusion:</strong><br />I. N#J<br />II. T% M <br />III. M @ N</strong></strong></strong>

Question 13 :
Below are given some symbols indicating some relations given against them. Read these symbols carefully and then answer the questions given below. There are four options to each question, of which only one is correct. Find the correct answer.<br />{tex} \begin{array}{ll}\Delta=\text { greater than } ; +=\text { not greater than } \ \\\theta=\text { equal to ; } \phi=\text { not equal to } \\\ x=\text { less than, } \square=\text { not less than }\end{array} {/tex}<br />a {tex} \Delta {/tex} b {tex} \Delta {/tex} c does not imply

Question 14 :
If × stands for’ addition’, < for ‘substraction’, + stands for ‘division’, > for ‘multiplication’, –, stands for ‘equal to’, ÷ for ‘greater than’ and = stands for ‘less than’, state which of the following is true ?

Question 15 :
Which of the following conclusions is correct according to the given expression and symbols ?<br><img style='object-fit:contain' src="https://s3.ap-south-1.amazonaws.com/me-p/5fb4e7ea16d7e6154e4692a3.jpg" /><br> Expression (qEq) and (qEr)

Question 16 :
In the following question, the symbols, &copy;, {tex}\underline{&copy;}{/tex}, =, * {tex}\underline{*}{/tex}&nbsp;are used with the following meanings&nbsp;<br />{tex}'\mathrm A &copy; \mathrm{B}' {/tex} means 'A is greater than B';<br />'A {tex}\underline{&copy;}{/tex}B' means 'A is greater than or equal to B';<br />'A = B' means 'A is equal to B';<br />'A {tex} ^{*} {/tex} B' means 'A is smaller than B';<br />'A {tex} \mathrm{}_{-}^{*}{/tex} B' means 'A is either smaller than or equal to B'<br />Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.<br />Give answer (1) if only if conclusion I is true; (2) if only conclusion II is true; (3) if either I or II is true; (4) if neither I nor II is true.<br /><strong>Statements</strong> {tex} : \mathrm{U}=\mathrm{V}, \mathrm{V}^{*} \mathrm{N}, \mathrm{R}_{-}^* \mathrm{U} {/tex}<br /><strong> Conclusions : </strong><br />I. {tex}\mathrm{R}^{*} \mathrm{N} {/tex} <br />II. U {tex} \underline{&copy;} {/tex} N

Question 17 :
Below are given some symbols indicating some relations given against them. Read these symbols carefully and then answer the questions given below. There are four options to each question, of which only one is correct. Find the correct answer.<br>{tex} \begin{array}{ll}\Delta=\text { greater than } ; & +=\text { not greater than } \ \\\theta=\text { equal to ; } & \phi=\text { not equal to } \\\ x=\text { less than, } & \square=\text { not less than }\end{array} {/tex}<br>{tex} \mathrm{a} \times \mathrm{b} \theta \mathrm{c} {/tex} implies that

Question 18 :
In the following questions which one of the four interchanges in signs and numbers would make the given equation correct ? <br>(3 ÷ 4) + 2 = 2

Question 19 :
If 3 + 8 = 17; 5 – 2 = 23; 6 × 2 = 72, then 8 ÷ 4 = ?

Question 20 :
If L denotes ×, M denotes ÷ , P denotes + and Q denotes –, than 8 P 36 M 6 Q 6 M 2 L 3 = ?

Question 21 :
If the given interchanges namely : signs + and ÷ and numbers 2 and 4 are made in signs and numbers, which one of the following four equations would be correct ?

Question 22 :
In the following question, different alphabets stand for various symbols as indicated below: Addition : O<br> Subtraction : M <br>Multiplication : A <br>Division : Q <br>Equal to : X<br> Greater than : Y <br>Less than : Z <br>Out of the four alternatives given in these question, only one is correct.

Question 23 :
If A + D > C + E, C + D = 2B and B + E > C + D, it necessarily follows that

Question 24 :
If × means ÷, – means × , ÷ means + and + means – then (3 – 15 ÷ 19) × 8 + 6 = ?

Question 25 :
In the following questions, three statements of numbers following same rules are given. Find the rule and accordingly find the value of the number?<br>If 3 + 9 = 31; 15 + 12 = 45; 18 + 9 = 36, then 12 + 27 = ?

Question 26 :
Below are given some symbols indicating some relations given against them. Read these symbols carefully and then answer the questions given below. There are four options to each question, of which only one is correct. Find the correct answer.<br />{tex} \begin{array}{ll}\Delta=\text { greater than } ; +=\text { not greater than } \ \\\theta=\text { equal to ; } \phi=\text { not equal to } \\\ x=\text { less than, } \square=\text { not less than }\end{array} {/tex}<br />{tex} a \times b \theta {/tex} c does not mean

Question 27 :
If 24 + 35 = 28; 15 + 42 = 24; 84 + 57 = 48, then 69 + 37 = ?

Question 28 :
If 20 – 10 means 200, 8 ÷ 4 means 12, 6 × 2 means 4 then 100 – 10 × 1000 ÷ 1000 + 100 × 10 = ?

Question 29 :
If 'x' Stands for ' addition' 'z' for subtraction' '+' for division' > for multiplication' '–' for equal to' '+' for ' greater than' and '=' for ' less than' state which of the following is true. ?

Question 30 :
If ÷ means +, – means ÷, × means – and + means ×, then {tex}\frac{(36 \times 4)-8 \times 4}{4+8 \times 2 + 16 \div 1}=?{/tex}

Question 31 :
Find the correct inference according to given premises and symbols :<br> A : Not greater than <br>B : Greater than <br>C : Equal to <br>E : Not less than <br>F : Less than<br> Premise : (pCm) and (pAm)

Question 32 :
In the following questions, three statements of numbers following same rules are given. Find the rule and accordingly find the volume of the number?<br> If 84 {tex}\bigoplus{/tex} 72 = 45; 63 {tex}\bigoplus{/tex} 41 = 33, 25 {tex}\bigoplus{/tex} 52 = 33, then 94 {tex}\bigoplus{/tex} 82 = ?

Question 33 :
Below are given some symbols indicating some relations given against them. Read these symbols carefully and then answer the questions given below. There are four options to each question, of which only one is correct. Find the correct answer.<br />{tex} \begin{array}{ll}\Delta=\text { greater than } ; +=\text { not greater than } \ \\\theta=\text { equal to ; } \phi=\text { not equal to } \\\ x=\text { less than, } \square=\text { not less than }\end{array} {/tex}<br />{tex} \mathrm{c}+\mathrm{b} \times {/tex} a means

Question 34 :
If + means ÷ ,– means ×, ÷ means + and × means –, then 36 × 8 + 4 ÷ 6 +2 –3 = ?

Question 35 :
If 3 + 5 = 16 ; 7 + 9 = 64 ; 10 + 12 = 121, then 11 + 3 = ?

Question 36 :
If {tex}\rightarrow{/tex} stands for 'addition'; {tex}\leftarrow{/tex} stands for 'subtraction' ; {tex}\uparrow{/tex}­ stands for 'division '; {tex}\downarrow{/tex} stands for 'multiplication' ;{tex}\nearrow{/tex} stands for equal to', then which of the following alternatives is correct ?

Question 37 :
Find the correct inference according to given premises and symbols.<br> (A) Not greater than <br>(B) Greater than <br>(C) Not equal to<br> (D) Equal to <br>(E) Not less than<br> (F) Less than <br>Premises : (lCm) and (lAm)

Question 38 :
If 3 × 4 = 14; 5 × 6 = 33; 7 × 8 = 60, then 8 × 9 = ?

Question 39 :
It being given that x denotes ' greater than', {tex}\phi{/tex} denote 'equal to', < denotes 'not less than', ^ denotes 'not equal to, D denotes 'less than' and + denotes ' not greater than', choose the correct statement from the following<br> If a x b {tex}\Delta{/tex} c, it follows that

Question 40 :
If P denotes ÷, Q denotes ×, R denotes + and S denotes –, then the value of 18 Q 12 P 4 R 5 S 6 when simplified gives

Question 41 :
In the following questions, three statements of numbers following same rules are given. Find the rule and accordingly find the value of the number?<br>If 43 = 158; 35 = 824; 42 = 153; then 32 = ?

Question 42 :
If 36 × 92 = 9623 ; 25 × 82 = 8522; 68 × 75 = 7856, then 47 × 52 = ?

Question 43 :
In the following question, the symbols, &copy;, {tex}\underline{&copy;}{/tex}, =, * {tex}\underline{*}{/tex}&nbsp;are used with the following meanings&nbsp;<br />{tex}'\mathrm A &copy; \mathrm{B}' {/tex} means 'A is greater than B';<br />'A {tex}\underline{&copy;}{/tex}B' means 'A is greater than or equal to B';<br />'A = B' means 'A is equal to B';<br />'A {tex} ^{*} {/tex} B' means 'A is smaller than B';<br />'A {tex} \mathrm{}_{-}^{*}{/tex} B' means 'A is either smaller than or equal to B'<br />Now in each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.<br />Give answer (1) if only if conclusion I is true; (2) if only conclusion II is true; (3) if either I or II is true; (4) if neither I nor II is true.<br /><strong>Statements :</strong>{tex} \mathrm{S}^{*} \mathrm{M}, \mathrm{M} &copy;\mathrm{L}, \mathrm{L} {\underline&copy;} \mathrm{P} {/tex}<br /><strong> Conclusions :</strong><br />I. {tex} \mathrm{S}=\mathrm{P} {/tex}<br />II. {tex} \mathrm{S}_{-}^{*} \mathrm{~L} {/tex}

Question 44 :
If A stands for +, B stands for –, C stands for x, then what is the value of (10 C4) + (4 C 4) B 6 ?

Question 45 :
In the following questions, three statements of numbers following same rules are given. Find the rule and accordingly find the value of the number?<br>If 213 = 419; 322 = 924; 415 = 16125, then 215 = ?

Question 46 :
If 3 + 5 = 16 ; 7 + 9 = 64 ; 10 + 12 = 121, then 11 + 3 = ?

Question 47 :
Which one of the four interchanges in signs and numbers would make the given equation correct ? 3 + 5 – 2= 0

Question 48 :
If 4 × 8 = 42; 6 × 4 = 23; 8 × 6 = 34, then 2 × 4 = ?

Question 49 :
If ' + ' means ' divided by', '–' means ' added to', 'x' means 'subtracted from' and ÷ means 'multiplied by', then what is the value of 24 ÷ 12 – 18 + 9 ?

Question 50 :
In the following questions, the symbols @ {tex} \mathrm{C} $ \% {/tex} and {tex} \# {/tex} are used with the following meanings as illustrated below : <br />'A {tex} \${/tex} B' means' A is not smaller than B' <br />'A # B' means 'A' is not smaller than B'<br />'A @ B' means 'A is neither smaller than nor equal to B' <br />'A{tex}C {/tex}B' means 'A is equal to B' <br />'A % B' means 'A' is neither greater than nor equal to B'<br />Now in each of the following questions, assuming the given statement to be true, find which of the three conclusions. I, II and III given below then is {tex} / {/tex} are definitely true and give your answer accordingly. Clearly, we have <br />A $ B {tex}\Rightarrow{/tex}&nbsp;A &lt; B {tex}\Rightarrow{/tex} A {tex}\geq{/tex}&nbsp;B<br />A # B {tex}\Rightarrow{/tex} A &gt; B {tex}\Rightarrow{/tex} A {tex}\leq{/tex}&nbsp;B. <br />A @ B {tex}\Rightarrow{/tex} A &lt; B and A # B {tex}\Rightarrow{/tex}&nbsp;A &gt; B, <br />A {tex}C {/tex}&nbsp;B {tex}\Rightarrow{/tex} A &gt; B and A # B {tex}\Rightarrow{/tex}&nbsp;A &lt; B<br /><strong><strong><strong>Statements :&nbsp;</strong></strong></strong>H % J,J {tex}C {/tex}&nbsp;N, N @ R<strong><strong><strong><br /><strong>Conclusions: </strong><br />I. {tex} R \% J {/tex}<br />II. H {tex} @ {/tex} J <br />III. N @ H</strong></strong></strong>