33 + Interview Questions in RATIONAL-NUMBERS IN GENERAL AWARENESS Page 1 InterviewSolution

1.	Amit purchases a motorcycle, having marked price Rs 46000 at a discount of 5%. If VAT is charged at the rate of 10%, find the amount Amit has paid to purchase the motorcycle.
Answer» Selling price of motorcycle after `5%` discount ` = 46000(100-5)/100 = 4600095/100=43700` Rs Amount that Amit has to pay after paying `10%` VAT ` = 43700(100+10)/100 = 43700110/100 = 48070` Rs

Discussion

2.	Three gold cubes each of 3cm length are melted and gold cuboid is formed from it.The area of the base of the cuboid is `27cm^2`. What is the height of the cuboid?
Answer» `a=3cm` volume of cube`a^3=3^3=27cm^3 ` volume of 3 cubes `=3xx 27cm^3` `LxxB=27cm^3` `volume of cuboid =(LxxBxxH)` cuboid=cube`` `3xx27=27xxH` `H=3cm`

Discussion

3.	Write.(i) The rational number that does not have a reciprocal.(ii) The rational numbers that are equal to their reciprocals.(iii) The rational number that is equal to its negative.
Answer» (i) If we try to find the reciprocal of `0` then, we get infinity. As, `1/0 = `Not a number So, we can say that `0` does not have a reciprocal. (ii)Only numbers that are equal to their reciprocals are `1` and `-1`. As, `1/1 = 1` and `1/-1 = -1` (iii)The rational number that is equal to its negative is `0`. As, `-(0) = 0`

Discussion

4.	Divide the sum of `8/3` and `4/7` by the product of `-3/7` and `14/9`
Answer» Sum of `8/3` and `4/7 = 8/3+4/7 = (56+12)/21 = 68/21` Product of `-3/7` and `14/9 = -3/7 xx14/9 = -2/3` Now, `(68/21)/(-2/3) = 68/21 xx -3/2 = -34/7`, which is the required solution.

Discussion

5.	Find the values of `sqrt(3.1428) and sqrt(0.31428)`
Answer» Below are the steps that needs to be followed to find the square root of a number that have numbers after decimal point : 1. Place a suitable number of pair of zeros after the decimal point. 2. Now find the square root of the number using long division method. Please refer to video to see the long division method to find the square root. 3. After that round off the quotient. With these steps, `sqrt3.1428 = 1.772` `sqrt0.31428 = 0.560`

Discussion

6.	Evaluate `sqrt(441/961)`
Answer» `sqrt(441/961)` `sqrt(21^2/31^2)` `21/31`.

Discussion

7.	Evaluate useing properties `[-9/10] xx [-3/5]-13/15+[-9/10] xx 3/20`
Answer» `[-9/10][-3/5]-13/15+[-9/10]3/20` `27/50-13/15-27/200` `27/50-(1340-81)/(2003)` `27/50-439/600` `-115/600`.

Discussion

8.	`sqrt(170.0416)`
Answer» `sqrt170.0416` after taking root `1304*10^-2` `13.04`.

Discussion

9.	7L of an acid solution was mixed with 3L of a 15% acid solution to make a 29% acid solution. Find the percent concentration of the first solution.
Answer» Let 7L acid solution concentration=x% According to question `(7x+3*15)/10=29` `7x+45=290` `x=35%`.

Discussion

10.	The HCF of `2/3, 8/9, 64/81` and `10/27` is...
Answer» `HCF` of fractions is given by, `HCF` of a fraction `= HCF` of numerators of fractions `/ LCM` of denominators of fractions `HCF` of the numerators of given `4` numbers is `2`. `LCM` of denominators of given `4` numbers is `81`. So, `HCF` of the given 4 fractions will be `2/81`.

Discussion

11.	The sum of two rational number is `-1/2`. If one of the number is `-14/5`, find the other number.
Answer» Let the other number =x `-14/5+x=-1/2` `x=14/5-1/2=23/10` `x=23/10`.

Discussion

12.	In a right triangle ABC `/_B=90^@` if AC=10 cm, BC=8 cm then find the length AB
Answer» Let AB=x cm `AB^2+BC^2=AC^2` `AB^2=AC^2-BC^2` `=100-64=36` AB=6 cm.

Discussion

13.	If `sintheta +cos theta =m` and `sec theta + cosec theta =n` then `n(m+1)(m-1)` equals
Answer» Here, `sintheta+costheta = m` `sectheta+cosectheta = n` `:. n(m+1)(m-1) = n(m^2-1)` `= (sectheta+cosectheta)((sintheta+costheta)^2-1)` `= (1/costheta+1/sintheta)(sin^2theta+cos^2theta+2sinthetacostheta-1)` `= ((sin theta+costheta)/(sinthetacostheta))(1+2sinthetacostheta-1)` `=(2(sintheta+costheta)sinthetacostheta)/(sinthetacostheta)` `=(2(sintheta+costheta)` `=2m` `:. n(m+1)(m-1) = 2m`

Discussion

14.	Write five rational numbers greater than -2
Answer» Five rational numbers greater than -2 are 0,1,2,3,4.

Discussion

15.	Find the HCF of 1365, 1560 and 1755
Answer» `1365 = 13573` `1560 = 352^313` `1755 = 53^313` `HCF` will be the common factors of these numbers. `:. HCF` of these three numbers `= 3513 = 495`.

Discussion

16.	Find five rational numbers between `1/4` and `3/5`.
Answer» Difference between two given rational numbers `(b-a) = 3/5-1/4 = 7/20` So, we will take `5` numbers with difference ,`(b-a)/(n+1) = 7/(20(5+1)) = 7/120`. `:.` First number will be ` = 1/4+7/120 = 37/120` So, `5` rational numbers between `1/4` and `3/5` using mean method are, `37/120,44/120,51/120,58/120,65/120.`

Discussion

17.	Find two rational numbers between -2 and 2.
Answer» `(2-(-2))/(1+2)` `(2+2)/3=4/3` adding and subtracting from them `-2,-2+4/3,-2+2*4/33,2` `-2,-2/3,2/3,2`.

Discussion

18.	Represent these numbers on the number line. (i) `7/4` (ii) `(−5)/6`
Answer» (i) `7/4 = (4+3)/4 = 1+3/4` So, this number will lie between `1` and `2` on number line. Please refer to video to see this number on number line. (ii)`-5/6 = (-6+1)/6 = -1+1/6` So, this number will lie between `-1` and `0` on number line. Please refer to video to see this number on number line.

Discussion

19.	If `\|z^2-1\|=\|z\|^2+1`, then `z` lies on(a) a circle(b) the imaginary axis(c) the real axis(d) an ellipse
Answer» `\|Z^2-1\|=\|Z^2\|-1` `\|(Z^2-1)^2\|=(\|Z^2\|-1)^2` `(Z^2-1)(Z^2-1)=(1+ZZ)^2` `-(Z^2-2^2)=2ZZ` Re(Z)=0 Z lies on the imaginary axis.

Discussion

20.	Find (i) `7/24-17/36` (ii) `5/63-((-6)/21)` (iii) `(-6)/13-7/11` (v) `-2/9 -6`
Answer» (i)`7/24 -17/36 = (73)/(243) - (172)/(362)` `=21/72 - 34/72 = (21-34)/72 = -13/72` (ii)`5/63 - (-6/21) = 5/63+6/21 = (5+63)/63 ` `(5+18)/63 = 23/63` (iii) `-6/13 -7/11 = (-611-713)/143` `(-66-91)/143 = -157/143` (iv)`(-2) 1/9 - 6 = -19/9 - 6 = (-19-69)/6` `(-19-54)/6 = -73/6`

Discussion

21.	List five rational numbers between: (i) `-1 and 0` (ii) `-2 and -1` (iii) `(-4)/5 and (-2)/3` (iv) `- 1/2 and 2/3`
Answer» (i) `-1 and 0` `-1/2, -2/3,-3/4 , -5/7 , -9/13` (ii) `-2 and -1` `-20/10 and -10/10` `-19/10, -18/10, -16/10, -14/10, -12/10` (iii) `-4/5 and -2/3` `(-4 xx 6)/(5 xx 6) = -24/30 ` `(-2 xx 10)/(3 xx 10) = -20/30` `-21/30 , -22/30 , -23/30, -45/60 , -43/60` (iv) `-1/2 and 2/3` `= -1/2 xx 3/3 = -3/6` `2/3 xx 2/2 = 4/6` `-2/6, -1/6 , 1/6 , 2/6 ,3/6` answer

Discussion

22.	Write any three rational numbers between `-2 a n d 0.`
Answer» There are infinite rational numbers between two rational numbers. if a and b are the two rational numbers then rational numbers between them can be `(a+b)/2, (a+(a+b)/2)/2, (b+(a+b)/2)/2`. here a=`-2 and b=0` the three rational numbers are - `-1,-1.5,-0.5`

Discussion

23.	Write five rational numbers which are smaller than 2.
Answer» Five rational numbers which are smaller than 2 can be, `1/2,2/3,3/2,4/5,5/4`

Discussion

24.	The area of a square plot is `800 m^2`.Find the estimated length of the side of the plot.
Answer» Let side of the square plot is `x` metre in length. Then, `x^2 = 800` `x = sqrt800 = 20sqrt2m` `:.` Length of side of the plot is `20sqrt2`m.

Discussion

25.	Arrange the followingrational numbers in descending order:`4/9, (-5)/6, (-7)/(-12),(11)/(-24)`
Answer» Rational numbers are`4/9,-5/6,7/12,11/-24` >arranged in descending order=>`7/12>4/9>(-11)/24>(-5)/6`

Discussion

26.	How to find the equation of tangents drawn to a parabola `y^2 = 4x` from a point (-8,0) ?
Answer» Equation of tangents of a parabola is given by, `y = mx+a/m->(1)` In the given parabola, `a =1` So, equations of tangents will be, `y = mx+1/m` Now, tangents are passing through `(-8,0)`. `:. 0 = -8m+1/m` `=>8m^2 = 1=> m = +-1/(2sqrt2)` So, equation otangents will be, For `m = 1/(2sqrt2)` `y = x/(2sqrt2)+2sqrt2` For `m = -1/(2sqrt2)` `y = -x/(2sqrt2)-2sqrt2`

Discussion

27.	The difference between the circumference and radius of a circle is 37 cm. Find the area of the circle.
Answer» Let `r` is the radius of circle. The difference between the circumference and radius of a circle is 37 cm. `:. 2pir-r = 37` `=>r(2pi-1) = 37` `=>r = 37/(2pi-1)` `=>r = (377)/(222-7) = 7cm` `:.` Area of circle`(A) = pir^2 = 22/777 = 154cm^2`

Discussion

28.	A parallelogram has sides of 15 cm and 12 If the distance between the 15 cm sides is 6 cm, find the distance between 12 cm sides.
Answer» With the given details, we can create a diagram. Please refer to video for the diagram. Here, we are given, `AB = CD = 12` cm `BC = AD = 15` cm Now, in `Delta ABE and Delta CBF` `/_BAE = /_BCF ` (opposite angles of parallelogram are equal) `/_AEB = /_BFC = 90^@` So, `Delta ABE ~ Delta CBF` `:. (AB)/(BE) = (CB)/(BF)` `=> 12/6 = 15/(BF) => BF = 15/2` `=>BF = 7.5` cm So, distance between `12` cm sides is `7.5cm`.

Discussion

29.	Ashok completed `1/2` of his task in the morning and `1/3` of the task in evening. How much task was done and how much task was left?
Answer» Task done=`1/2+1/3=(3+2)/6=5/6` Completed task=5/6 task left=`1-5/6=1/6`.

Discussion

30.	Factorrise the expressions `10ab+4a+5b+2`
Answer» `4a+2+5b+10ab` `2(2a+1)+5b(1+2a)` `(2a+1)(2+5b)`.

Discussion

31.	The speed of a sub marine over sea surface is 30 knot per hour and below sea surface is 20 knots per hour. What is the average speed of the submarine if it is below water surface for 3/4th of her time of journey What is the average speed of the submarine if it is under water surface for 3/4th of the total distance covered by him.
Answer» 1)`V_(avg)`=(total distance/total distance) `=(30T/4+203T/4)/T=45/2` 2)Total distance=d `T_1=(3/4d)/20` `T_2=(1/4d)/30` `V_(avg)`=Total distance/total time `=D/((3/4D)/20+(1/4d)/30)` `=240/11` .

Discussion

32.	One man and 2 boys can do a piece of work in 12 days. The same work can also be done by 3 men and 1 boy in 6 days. How long it would take for one man alone to complete the work?
Answer» Let man be m Let boy be b `1m+2b=1/12-(1)` `3m+b=1/6-(2)` from equation 1 and 2 `5m=1/2-1/3=1/4` `m=1/20` 1 man take 20 days to complete the work on time.

Discussion

33.	8 pumps to to fill a tank in 1 hour 30 minutes. How long will it take, if only 6 pumps ?
Answer» `1/(83/2)=1/(6t)` `1/12=1/(6t)` `t=2hour` 8 pumps fill in 3/2 hours=1tanks 1 pump fill in 1 hours=`1/(83/2)=1/12` 6 pump fill in 1 hour=`1/126=1/2` t=2hours.

Discussion

Explore topic-wise InterviewSolutions in .

Amit purchases a motorcycle, having marked price Rs 46000 at a discount of 5%. If VAT is charged at the rate of 10%, find the amount Amit has paid to purchase the motorcycle.

Three gold cubes each of 3cm length are melted and gold cuboid is formed from it.The area of the base of the cuboid is `27cm^2`. What is the height of the cuboid?

Write.(i) The rational number that does not have a reciprocal.(ii) The rational numbers that are equal to their reciprocals.(iii) The rational number that is equal to its negative.

Divide the sum of `8/3` and `4/7` by the product of `-3/7` and `14/9`

Find the values of `sqrt(3.1428) and sqrt(0.31428)`

Evaluate `sqrt(441/961)`

Evaluate useing properties `[-9/10] xx [-3/5]-13/15+[-9/10] xx 3/20`

`sqrt(170.0416)`

7L of an acid solution was mixed with 3L of a 15% acid solution to make a 29% acid solution. Find the percent concentration of the first solution.

The HCF of `2/3, 8/9, 64/81` and `10/27` is...

The sum of two rational number is `-1/2`. If one of the number is `-14/5`, find the other number.

In a right triangle ABC `/_B=90^@` if AC=10 cm, BC=8 cm then find the length AB

If `sintheta +cos theta =m` and `sec theta + cosec theta =n` then `n(m+1)(m-1)` equals

Write five rational numbers greater than -2

Find the HCF of 1365, 1560 and 1755

Find five rational numbers between `1/4` and `3/5`.

Find two rational numbers between -2 and 2.

Represent these numbers on the number line. (i) `7/4` (ii) `(−5)/6`

If `|z^2-1|=|z|^2+1`, then `z` lies on(a) a circle(b) the imaginary axis(c) the real axis(d) an ellipse

Find (i) `7/24-17/36` (ii) `5/63-((-6)/21)` (iii) `(-6)/13-7/11` (v) `-2/9 -6`

List five rational numbers between: (i) `-1 and 0` (ii) `-2 and -1` (iii) `(-4)/5 and (-2)/3` (iv) `- 1/2 and 2/3`

Write any three rational numbers between `-2 a n d 0.`

Write five rational numbers which are smaller than 2.

The area of a square plot is `800 m^2`.Find the estimated length of the side of the plot.

Arrange the followingrational numbers in descending order:`4/9, (-5)/6, (-7)/(-12),(11)/(-24)`

How to find the equation of tangents drawn to a parabola `y^2 = 4x` from a point (-8,0) ?

The difference between the circumference and radius of a circle is 37 cm. Find the area of the circle.

A parallelogram has sides of 15 cm and 12 If the distance between the 15 cm sides is 6 cm, find the distance between 12 cm sides.

Ashok completed `1/2` of his task in the morning and `1/3` of the task in evening. How much task was done and how much task was left?

Factorrise the expressions `10ab+4a+5b+2`

One man and 2 boys can do a piece of work in 12 days. The same work can also be done by 3 men and 1 boy in 6 days. How long it would take for one man alone to complete the work?

8 pumps to to fill a tank in 1 hour 30 minutes. How long will it take, if only 6 pumps ?