prove that
Question: If $\frac{15}{8}-7 x=9$, then $-7 x=9+\frac{15}{8}$ Solution: False Given,$\frac{15}{8}-7 x=9$ $\Rightarrow$ $-7 x=9-\frac{15}{8}$ $\left[\right.$ transposing $\frac{15}{8}$ to RHS $]$...
Read More →In the equation 2x = 4 – x,
Question: In the equation 2x = 4 x, transposing x to LHS, we get x = 4. Solution: False Given, 2x = 4-x = 2x + x = 4 [transposing -x to LHS] = 3x = 4...
Read More →In the equation 3x – 3 = 9,
Question: In the equation 3x 3 = 9, transposing 3 to RHS, we get 3x = 9. Solution: FalseGiven, 3x 3 = 9 = 3x = 9 + 3 [transposing -3 to RHS] = 3x = 12...
Read More →Two different equations can never
Question: Two different equations can never have the same answer. Solution: False Two different equations may have the same answer. e.g. $2 x+1=2$ and $2 x-5=-4$ are the two linear equations whose solution is $\frac{1}{2}$...
Read More →A and B are together 90 years old.
Question: A and B are together 90 years old. Five years ago, A was thrice as old as B was. Hence, the ages of A and B five years back would be (x 5) years and (85 x) years, respectively. Solution: True Let the age of A be x yr. Then, age of S = (90 x) yr Five years ago, the age of A = (x- 5) yr The age of B= 90-x-5 = (85-x)yr Hence, the ages of A and 8 five years back would be (x 5) yr and (85 x) yr, respectively....
Read More →The number of boys and girls in a class
Question: The number of boys and girls in a class are in the ratio 5 : 4. If the number of boys is 9 more than the number of girls, then number of boys is 9. Solution: False Let the number of boys be 5x and the number of girls be 4x. According to the question, 5x 4x = 9 = x = 9 Hence, number of boys = 5 x 9 = 45...
Read More →Sum of the ages of Anju and her mother
Question: Sum of the ages of Anju and her mother is 65 years. If Anjus present age is y years, then her mothers age before 5 years is (60 y) years. Solution: True Given, Anjus present age = y yr Then, Anjus mother age = (65 y)yr Before 5 yr, Anjus mother age = 65 y 5 = (60 y)yr...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability that the drawn card is a black 6? (a) $\frac{3}{26}$ (b) $\frac{1}{26}$ (c) $\frac{1}{13}$ (d) $\frac{1}{52}$ Solution: (b) $\frac{1}{26}$ Total number of cards $=52$ Total number of black 6 cards $=2$ (6 of spades, 6 of cloves) Now, $\mathrm{P}_{(\text {black } 6)}=\frac{2}{52}=\frac{1}{26}$...
Read More →In a 2-digit number,
Question: In a 2-digit number, the units place digit is x. If the sum of digits be 9, then the number is (10x 9). Solution: False Given, units digit = x and sum of digits = 9 Tens digit = 9 x Hence, the number = 10 (9 -x)+x = 90 -10x + x = 90 9x...
Read More →Shikha’s present age is p years.
Question: Shikhas present age is p years. Reemus present age is 4 times the present age of Shikha. After 5 years, Reemus age will be 15p years. Solution: False Given, Shikhas present age = pyr Then, Reemus present age = 4 x (Shikhas present age) = 4pyr After 5 yr, Reemus age = (4p+5)yr...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: From a well-shuffled deck of 52 cards, one card is drawn at random. What is the probability that the drawn card is a queen? (a) $\frac{1}{4}$ (b) $\frac{1}{52}$ (c) $\frac{1}{13}$ (d) $\frac{1}{26}$ Solution: (c) $\frac{1}{13}$ Total number of cards $=52$ Number of queens $=4$ (i.e., queen of hearts, queen of diamonds, queen of cloves and queen of spades) Now, $\mathrm{P}_{(\text {queen })}=\frac{4}{52}=\frac{1}{13}$...
Read More →3 years ago, the age of boy was y years.
Question: 3 years ago, the age of boy was y years. His age 2 years ago was (y 2) years. Solution: False Given, 3 yr ago, age of boy = y yr Then, present age of boy = (y + 3)yr 2 yr ago, age of boy = y + 3-2 = (y + 1)yr...
Read More →The sum of two consecutive multiples
Question: The sum of two consecutive multiples of 10 is 210. The smaller multiple is-. Solution: 100 Let the two consecutive multiples of 10 be $10 x$ and $10 x+10$. According to the question, $10 x+10 x+10=210$ $\Rightarrow \quad 20 x+10=210$ $\Rightarrow$ $20 x=210-10$ [transposing 10 to RHS] $\Rightarrow$ $20 x=200$ $\Rightarrow$ $\frac{20 x}{20}=\frac{200}{20}$ [dividing both sides by 20] $\therefore$ $x=10$ Hence, the smaller multiple is $10 \times 10$, i.e. 100 ....
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: A die is thrown. What is the probability of getting an even number? (a) $\frac{1}{2}$ (b) $\frac{2}{3}$ (c) $\frac{5}{6}$ (d) $\frac{1}{6}$ Solution: (a) $\frac{1}{2}$ Total number of outcomes $=6$ (Numbers: $1,2,3,4,5$ and 6 ) The even numbers are 2, 4, and 6 . Number of favourable outcomes $=3$ Now, $\mathrm{P}_{(\text {even number })}=\frac{3}{6}=\frac{1}{2}$...
Read More →The denominator of a rational number
Question: The denominator of a rational number is greater than the numerator by 10. If the numerator is increased by 1 and the denominator is decreased by 1, then expression for new denominator is. Solution: $x+9$ Let numerator be $x$. Then, denominator $=x+10$ $\therefore$ Rational number $=\frac{x}{x+10}$ According to the question, New rational number $=\frac{\text { Numerator }+1}{\text { Denominator }-1}=\frac{x+1}{x+10-1}=\frac{x+1}{x+9}$ Hence, the new denominator is $x+9$....
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: A die is thrown. What is the probability of getting $6 ?$ (a) 1 (b) $\frac{1}{6}$ (c) $\frac{6}{1}$ (d) none of these Solution: (b) $\frac{1}{6}$ The possible outcomes are $1,2,3,4,5$ and 6 . Total number of outcomes $=6$ Now, $\mathrm{P}_{\text {(getting 6) }}=\frac{1}{6}$...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: A bag contains 3 white and 2 red balls. One ball is drawn at random. What is the probability that the ball drawn is red? (a) $\frac{1}{2}$ (b) $\frac{2}{3}$ (C) $\frac{1}{5}$ (d) $\frac{2}{5}$ Solution: (d) $\frac{2}{5}$ Total number of outcomes $=5$ Number of red balls $=2$ Now, $\mathrm{P}_{(\text {red ball })}=\frac{2}{5}$...
Read More →Convert the statement ‘adding 15
Question: Convert the statement adding 15 to 4 times x is 39 into an equation Solution: 4x+ 15=39 To convert the given statement into an equation, first x is multiplied by 4 and then 15 is added to get the result 39. i.e. 4x + 15=39...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: Two coins are tossed simultaneously. What is the probability of getting one head and one tail? (a) $\frac{1}{4}$ (b) $\frac{1}{2}$ (c) $\frac{3}{4}$ (d) $\frac{2}{3}$ Solution: (b) $\frac{1}{2}$ When two coins are tossed, the possible outcomes are HH, HT, TH and TT. Total number of outcomes $=4$ Number of outcomes with one head and one tail $=2$ Now, $\mathrm{P}_{\text {(one head and one tail) }}=\frac{2}{4}=\frac{1}{2}$...
Read More →Solve the following systems of linear in equations:
Question: Solve the following systems of linear in equations: $\frac{7 x-1}{2}-3, \frac{3 x+8}{5}+110$ Solution: When $\frac{7 x-1}{2}-3$ Multiplying both the sides by 2 $\left(\frac{7 x-1}{2}\right)(2)-3(2)$ $7 x-1-6$ Adding 6 to both the sides in above equation $7 x-1+6-6+6$ $7 x+50$ Subtracting 5 from both the sides in above equation $7 x+5-50-5$ $7 x-5$ Dividing both the sides by 7 in above equation $\frac{7 x}{7}\frac{-5}{7}$ Therefore $x\frac{-5}{7}$ Now when, $\frac{3 x+8}{5}+110$ Subtrac...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: 8 cards are numbered as 1, 2, 3, 4, 5, 6, 7, 8 respectively. They are kept in a box and mixed thoroughly. One card is chosen at random. What is the probability of getting a number less than 4? (a) $\frac{1}{2}$ (b) $\frac{3}{4}$ (c) $\frac{3}{8}$ (d) $\frac{3}{5}$ Solution: (C) $\frac{3}{8}$ Total number of cards $=8$ Number of cards with numbers less than $4=3$ (cards with numbers 1,2 and 3 ) Now, $\mathrm{P}_{\text {(getting a number less than 4) }}=\frac...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: In a spinning wheel, there are 3 white and 5 green sectors. It is spinned. What is the probability of getting a green sector? (a) $\frac{5}{3}$ (b) $\frac{5}{8}$ (C) $\frac{1}{5}$ (d) $\frac{3}{8}$ Solution: (d) $\frac{3}{8}$ The wheel has a total of $5+3=8$ sectors. Number of green sectors $=5$ Now, $\mathrm{P}_{\text {(getting a green sector) }}=\frac{5}{8}$...
Read More →Solve the following systems of linear in equations:
Question: Solve the following systems of linear in equations: $3 x-xx+\frac{4-x}{3}3$ Solution: $3 x-xx+\frac{4-x}{3}$ and $x+\frac{4-x}{3}3$ When, $3 x-xx+\frac{4-x}{3}$ $2 xx+\frac{4-x}{3}$ Subtracting x from both the sides in above equation $2 x-xx+\frac{4-x}{3}-x$ $x\frac{4-x}{3}$ Multiplying both the sides by 3 in the above equation $3 x3^{\left(\frac{4-x}{3}\right)}$ $3 x4-x$ Adding x on both the sides in above equation $3 x+x4-x+x$ $4 x4$ Dividing both the sides by 4 in above equation $\f...
Read More →One card is drawn at random from a well-shuffled deck of 52 cards.
Question: One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a 4 (ii) a queen (iii) a black card. Solution: Total number of possible outcomes $=52$ (i) There are 4 cards of with the number 4 (4 of hearts, 4 of diamonds, 4 of spades and 4 of cloves) $\therefore \mathrm{P}_{(4 \text { card })}=\frac{4}{52}=\frac{1}{13}$ (ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves)...
Read More →One card is drawn at random from a well-shuffled deck of 52 cards.
Question: One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is (i) a king (ii) a spade (iii) a red queen (iv) a black 8. Solution: Total number of possible outcomes $=52$ (i) There are 4 kings cards (king of hearts, king of diamonds, king of spades and king of cloves) Number of kings $=4$ $\therefore \mathrm{P}_{(\text {king })}=\frac{4}{52}=\frac{1}{13}$ (ii) There is a total of 13 spades cards. Number of spades $=13$ $\therefore \mathrm...
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