Letters for Digits

Q.

A student multiplied $7236$ by $65$ instead of multiplying by $56.$ By how much was his answer greater than the correct answer?

Q.

Let $A=\left\{2,3,4,5,..,30\right\}$ and $\cong$ be an equivalence relation $A\times A$, defined by $\left(a,b\right)\cong \left(c,d\right)$, if and only if $ad=bc$. Then the number of ordered pair $\left(4,3\right)$ is equal to:

1. $7$

2. $5$

3. $6$

4. $8$

Q.

How do you multiply a $3\times 3$ matrix$?$

Q.

Fill in the numbers from 1 to 6 without repetition, so that each side of the triangle adds up to 12.

Q.

Which one of the following sums up the story best?

1. A bird in hand is worth two in the bush

2. One is known by the company one keeps

3. A friend in need is friend indeed

Q.

Question 66

A three-digits number 2a3 is added to the number 326 to give a three-digits number 5b9 which is divisible by9. Find the value of b - a.

Q. Reema types 540 words during half an hour. How many words would she type in 6 minutes ?

Q.

A two-digit number is seven times the sum of its digits and also equal to $12$ less than three times the product of its digits. Find the number.

Q.

Find the number of ways in which $16$ identical things can be distributed among $4$ persons, if each person gets at least $3$ things.

1. $15$

2. $25$

3. $35$

4. $40$

Q.

Let a relation $R$ be defined by $R=\left\{(4,5),(1,4),(4,6),(7,6),(3,7)\right\}$ then $R^{-1}oR$ is:

1. $\left\{(1,1),(4,4),(4,7),(7,4),(7,7),(3,3)\right\}$

2. $\left\{(1,1),(4,4),(7,7),(3,3)\right\}$

3. $\left\{(1,5),(1,6),(3,6)\right\}$

4. None of these

Q.

Find Q in the addition
$\begin{array}{c}31Q\\ +1Q3\\ 501\end{array}$

1. 4

2. 1

3. 5

4. 8

Q.

Question 6
Find the value of the following letters.

$AB$
$\underset{–}{\times 5}$
$\underset{–}{CAB}$

Q.

Find the difference between the smallest whole number and smallest natural number.

Q.

A matrix of certain characters is given. These characters follow a certain trend, row-wise or column-wise. Find out this trend and choose the missing character accordingly.

$28$	$60$	$48$
$5$	$6$	$7$
$17$	$30$	$7$
$7$	$?$	$16$

Q.

Find the numerical value of the letters given below (a) DE×3=FDE

Q. If $\frac{2x+1}{3x-2}=\frac{9}{10}$, then the value of 'x' is: [2 MARKS]

Q. Find M and Y such that M $\ne$ Y in the addition Y + Y + Y = MY.

1. M = 2, Y = 5
2. M = 1, Y = 5
3. M = 5, Y = 1
4. M = 3, Y = 5

Q.

If $5A\times A=399$, then the value of $A$ is

1. $3$

2. $6$

3. $7$

4. $9$

Q.

Question 5
Find the values of the letters in the following and give reasons for the steps involved.
$AB$
$\underset{–}{\times 3}$
$\underset{–}{CAB}$

Q. If $ME\times YE=TTT$, then find the value of $Y+M+E+T$.

1. 21
2. 33
3. 41
4. 56

Q.

A three digit number is 297 more than its reversed number. How many such numbers are possible?

1. 60

2. 27

3. 36

4. 6

Q.

Question 47

If 1AB + CCA = 697 and there is no carry - over in addition, find the value of A + B + C.

Q.

Find the values of A, B and C from the given options, if

A B

x 6
_____

C 8 8

1. A = 5, B = 8, C = 1
2. A = 4, B = 7, C = 2
3. A = 4, B = 8, C = 2
4. A = 3, B = 9, C = 2

Q. Make the greatest and the smallest 4 digit numbers by using any one digit twice:
(i) 6, 3, 2
(ii) 1, 0, 6

Q.

Find the value of the letter in the following and give reasons for the steps involved.

Q.

Find the sum of the digits of (111111111)².

Q.

Write an equivalent fraction of $\frac{3}{4}$ with numerator as $36.$

Q.

Solve each of the following cryptarithms.
$\begin{array}{cc}3& 7\\ +A& B\\ 9& A\end{array}$

Q.

Question 61

If 2A7 $÷$ A = 33, then find the value of A.

Q.

Question 4
Find the values of the letters in the following and give reasons for the steps involved.
$AB$
$\underset{–}{+37}$
$\underset{–}{6A}$