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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The length of an are of a circle is given by the formula `l=(x)/(360^(@))xx2pir`. Make r as the subject of the formula.A. `r=(720^(@)pix)/(l)`B. `r=(180^(@)l)/(pix)`C. `r=(720^(@)l)/(pix)`D. `r=(180^(@)l)/(x)` |
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Answer» Correct Answer - B Given: `l=(x)/(360^(@))xx2pir` `rArr lxx360^(@)=x xx 2pir` `rArr(360^(@)l)/(2pix)=r` `rArr r=(180^(@))/(pix)` Hence, the correct option is ((b). |
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| 2. |
The number of aubiliar formulae that can be divided from `S=((100-l))/(100)r` is_A. 4B. 3C. 2D. 1 |
| Answer» Correct Answer - C | |
| 3. |
If `A=2(lb+bh+lh)`, then which of the following is/are true?A. `l=(A-2bh)/(2(b+h))`B. `b=(A-2h)/(2(l+b))`C. `h=(A-2lb)/(2(l+b))`D. None of these |
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Answer» Correct Answer - D Given `a=2(lb+1h)`. Making 1 as the subject of the formula. `A=2(lb+bh+2lh)` `rArr A=2(lb=lh)+2bh` Subtracting wbh from both the sides, we get `A-2bh=2l(b+h)`. Dividing both the sides with 2(b+h), we get `(A-2bh)/(2(b+h))=1rArrl=(A-2bh)/(2(b+h))` Similarly, we get `therefore b=(A-2lh)/(2(l+h))` and `h=(A-2lb)/(2(l+b))` Hence, the correct option is (d). |
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| 4. |
If `M=a+(b)/(c)`, then b=______A. `Mc-a`B. `M-ac`C. `((M-a))/(c)`D. `(M-a)c` |
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Answer» Correct Answer - D Given `M=a+b//c`. `rArrM-a=b//c`. `rArr (M-a)c=b` `rArr b=(M-a)c` |
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| 5. |
Write the formula for finding the circumference S of a circle. Make r the subject in this formula and find r when S=154cm. |
| Answer» The formula for finding the circumference S of a circle of radius r is `S=2pir`. Hence, `r=(S)/(2pi)`. Substituting S=154 cm and `pi=(22)/(7)` in above equation, we get `r=24.5cm` | |
| 6. |
If `V=lbh`, then h=__A. `(v)/(lb)`B. `(v)/(bh)`C. `(v)/(lh)`D. `(lb)/(v)` |
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Answer» Correct Answer - A Given V=lbh. Dividing on both the sides with lb, we get `rArr (V)/(lb)=(lbh)/(lb)rArrh=(V)/(lb)`. |
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| 7. |
If V=lbh, then b=______A. `(v)/(lh)`B. `(l)/(vh)`C. `(h)/(vl)`D. `lvh` |
| Answer» Correct Answer - A | |
| 8. |
Using the formula `S=2(lb+bh+lh)`, find S when l=12cm, b=8cm,and h=4 cm. |
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Answer» Given `S=2(lb+bh+lh)` and l=-12,b=8, and h=4. Substituting the given values, We get `S=(12xx8+8xx4+12xx4)=2(96+32+48)=352`. `therefore S=352cm^(2)`. |
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| 9. |
Write the formula for finding the circumference (C) of a circle with radius r units. What is the subject in this formula? |
| Answer» We know that the circumtancence (C) of a circle of radius r is given by C=`2pir`. In this formula the subject is C. | |
| 10. |
The number of variables in the formula `T=2pisqrt((l)/(g))` is _____A. 4B. 5C. 3D. 2 |
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Answer» Correct Answer - C T,l,g The number of variables =3 |
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| 11. |
Make f as the subject of the formula |
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Answer» Given `(1)/(f)=(1)/(u)+(1)/(v)rArr(1)/(f)=(v+u)/(uv)` `rArr f=(uv)/(v+u)` (`because` Reciprocal form) |
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| 12. |
Make h the subject of the formula, where V=lbh, and find h, when `V=960cm^(3),l=20cm`, and b=12cm. |
| Answer» V=lbh, on dividing both the sides with lb, we get `(V)/(lb)=h`. Hence, `h=(V)/(lxxb)`. | |
| 13. |
If `(a+b)/(x+y)=(z+t)/(c+d)`, then make d as the subject of the formula.A. `d=((z+t)(x+y))/(a+b)`B. `d=((z+t)(x+y)-ac-bc)/((a+b))`C. `d=((z+t)(x+y)-ac-bc)/(a+b)`D. `d=((a+b)(x+)-az-at)/(z+t)` |
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Answer» Correct Answer - C (i) Apply transposition. (ii) Cross multiply and then bring (a+b) to RHS. (iii) Then bring c to RHS. |
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| 14. |
(a) In the formula `S_(n)=(n)/(2){2a+(n-1)d}`, make d as the subject. (b) Find the value of d, when `S_(n)=240,n=10,` and `a=6`. |
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Answer» (a) Given formula is `S_(n)=(n)/(2){2a+(n-1)d}`. `rArr(n)/(2){2a+(n-1)d}=S_(n)` `rArr 2a+(n-1)d=(2S_(n))/(n)` `rArr (n-1)d=(2S_(n))/(n)-2a` `rArr d=(2)/(n-1)[(S_(n))/(n)-a]` (b) Substituting the values `S_(n)=240,n=10`, and a=6, we get. `d=(2)/((10-1))[(240)/(10)-6]=(2)/(9)xx18=4` `therefore d=4`. |
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| 15. |
If `(p+q)/(r+s)=(t+u)/(v+w)`. Express v in terms of p,q,r,s and w. |
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Answer» `(p+q)/(r+s)=(t+u)/(v+w)` `implies(p+q)(v+w)=(t+u)(r+s)` `impliesv(p+q)=(t+u)(r+s)-w(p+q)` `impliesv=((t+u)(r+s)-(p+q)w)/(p+q)` |
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| 16. |
In the formula `S=(n)/(2)[2a+(n-1)d]`, make a as the subject of the formula. |
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Answer» Given `S=(n)/(2)[2a+(n-1)d]` `implies(2S)/(n)=2a+(n-1)d` `implies2a=(2S)/(n)-(n-1)d` `impliesa=(S)/(n)-(n-1)(d)/(2)` |
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| 17. |
the relation between two or more variables is called a _____ |
| Answer» Correct Answer - Formula | |
| 18. |
In `c=(22a+9b)/(3a+2b),c=6 and a=3`, find b.A. 6B. 2C. 4D. 8 |
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Answer» Correct Answer - C `c=(22a+9b)/(3a+2b)` `c=6 and a=3` `therefore6=(66+9b)/(9+2b)` `implies54+12b=66+9b` `impliesb=4` |
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| 19. |
If `S=(a)/(1-r)`, then make r as the subject of the formula.A. `r=(a)/(S)+1`B. `r=1+(S)/(a)`C. `r=1-(S)/(a)`D. `r=1-(a)/(S)` |
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Answer» Correct Answer - D Apply transposition. |
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| 20. |
In `y=mx+c`, make c as the subject. |
| Answer» Correct Answer - `c=y-mx` | |
| 21. |
The following figure has a network of rectangles. Two rows and three columns. (A) Totally how many rectangles are there in the figure? (B) If there are x rectangles in each row and y rectangles in each column, totally how many rectangles will be there in the network, in terms of x and y. |
| Answer» Correct Answer - `(x(x+1))/(2)xx(y(y+1))/(2)` | |
| 22. |
If the curved surface area of a closed cylinder is `2pirh` ad base area is `pir^(2)`, then total surface area of that cylinder A is ______ |
| Answer» Correct Answer - `2pir(r+h)` | |
| 23. |
A formula is based on the equlity property. True or False? |
| Answer» Correct Answer - 1 | |
| 24. |
if pressure P is inversely proportional to volume (V) at constant temperature, then PV is constant (True/False) |
| Answer» Correct Answer - 1 | |
| 25. |
If `x^(2)+y^(2)=r^(2)`, then x is equal to |
| Answer» Correct Answer - `sqrt(r^(2)-y^(2))` | |
| 26. |
If the area of an equilateral tirangle is `A=12sqrt(3)cm^(2)`, then the length of its altitude h is? |
| Answer» Correct Answer - 6cm | |
| 27. |
The area of an equilateral triangle is `A=(h^(2))/(sqrt(3))`, where h is the length of the altitude. Write the formula making h as the subjectA. `h=sqrt(3)A`B. `h=sqrt(sqrt(3)A)`C. `h=sqrt(sqrt(3)A)`D. `h=3A^(2)` |
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Answer» Correct Answer - B (i) apply transposition (ii) First make `h^(2)` as subject. (iii) Apply square root on both the sides. |
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| 28. |
Make b as the subject the formula `f=(a+b)/(a)`A. `b=af+a`B. `b=af-a`C. `b=(a+f)/(a)`D. `b=(a+f)/(f)` |
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Answer» Correct Answer - B `f=(a+b)/(a)impliesf.a=a+b` `impliesb=a(f-1)` |
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| 29. |
If `H=(2b)/(a+b)`, then make b as the subject of the formula.A. `b=(2+H)/(Ha)`B. `b=(Ha)/(2a-H)`C. `b=(2a-H)/(Ha)`D. `b=(Ha)/(2a+H)` |
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Answer» Correct Answer - B (i) Apply transposition. (ii) Cross multiply and then write the terms involving b on LHS and the remaining terms on RHS. |
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| 30. |
In `y=(a+b)/(a-b)`, make b as the subject of the formula.A. `b=(a(y-1))/(1+y)`B. `b=(a(1+y))/(y-1)`C. `b=(a(y+1))/(1-y)`D. `b=(a(1-y))/(1+y)` |
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Answer» Correct Answer - A (i) Apply transposition. (ii) Cross multiply and write the terms involving b on LHS and write the reamaining terms on RHS. |
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| 31. |
In `(x)/(a)+(x)/(b)=1`, make b as the subject of the formula.A. `b=((x)/(a)-1)y`B. `b=(ay)/(x+a)`C. `b=(ay)/(a-x)`D. `b=(a-x)/(ay)` |
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Answer» Correct Answer - C (i) Apply tranposition. (ii) First of all bring `(x)/(a)` to RHS. (iii) Simplify the RHS. (iv). Then write in it reciprocal form. (v) Then bring y to RHS. |
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| 32. |
The sum of the digits of a two-digit number is 11. if 9 is subtracted from the number, then the digits interchagne their places. Find the number. The following steps are involved in solving the above problem. Arrange them in sequential order (A) Let the units digit be x. therefore , the tens digit is (11-x). `therefore` The number is `10(11-x)+x=110-9x`. (B) Given that `110-9x-9=9x+11rArrx=5`. (C) Units digit is S and tens digit is 6 and the required number is 65. (D) The number formed by interchanging the digits is `10x+(11-x)=9x+11`.A. ADBCB. ABDCC. ABCDD. BADC |
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Answer» Correct Answer - A A,D,B,and C is the required sequential order. |
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| 33. |
If one third ofa number is subtracted from three times the number, then the result is 800, find the number.A. 300B. 400C. 200D. 600 |
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Answer» Correct Answer - A Let the number be x. `therefore 3x-(x)/(3)=800` `rArr (9x-x)/(3)=800rArr(8x)/(3)=800` `rArr x=800xx(3)/(8)rArr x=300` |
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| 34. |
Which of the following is a solution of `(2x -5)/(3) gt (3x + 3)/(4)` ?A. x=-5B. x=-2C. Both a and bD. Neither a nor b |
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Answer» Correct Answer - D `(2x-5)/(3)gt(3x+3)/(4)` Put `x=-5rArr-5gt-3`, which is false Put `x=-2rArr-3ge(-3)/(4)`, which is false. |
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| 35. |
Make b the subject for the formula `f=(a+b)/(a)`. |
| Answer» Correct Answer - `b=a(f-1)` | |
| 36. |
In the formula `T=2pisqrt((l)/(g)),T` is ____proportional to `sqrt(l)`. |
| Answer» Correct Answer - Directly | |
| 37. |
If `A=c(a^(2)+b^(2))`, then which of the following is/are true?A. `c=(A)/(a^(2)-b^(2))`B. `a=sqrt((A)/(c)+b^(2))`C. Both a and bD. None of these. |
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Answer» Correct Answer - D Given `A=c(a^(2)+b^(2))` Option (a) `rArr(A)/(a^(2)+b^(2))=c` `rArr c=(A)/(a^(2)+b^(2))` `therefore` Choice (a) is false. Option (b): `(A)/(c)=a^(2)+b^(2)`. `rArr (A)/(c)-b^(2)=a^(2)` `rArr a=sqrt((A)/(c)-b^(2))` `therefore` Choice b is false. |
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| 38. |
The following table shows the relation between a and b. `{:(a,1,2,3,4,5),(b,2,5,12,20,30):}` Express the relation between a and b with b as the subject.A. `b=2a`B. `b=3a`C. `b=(a+b)^(2)`D. `b=a(a+1)` |
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Answer» Correct Answer - D From the given table, `brArr 2=1(1+1)` `rArr 6=2(2+1)` `rArr 12=3(3+1)` . . . . . . . `therefore b=a(a+1)` Hence, the correct option is (d). |
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| 39. |
If `(x+y)/(z)=(a+b)/(c)`, then y=______A. `((a+b)z)/(c)-x`B. `((a+b)z-x)/(c)`C. `((a+b)z)/(c)+x`D. `((a+b)z+x)/(c)` |
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Answer» Correct Answer - A Given `(x+y)/(z)=(a+b)/(c)` `rArr x+y=((a+b)z)/(c)` `rArr y=((a+b)z)/(c)=x` Hence, the correct option is (a). |
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| 40. |
In the formula `angleA+angleB+angleC=180^(@)`, if `angleA=90^(@)` and `angle B=55^(@)`, then `angleC=`_______A. `45^(@)`B. `45^(@)`C. `25^(@)`D. `35^(@)` |
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Answer» Correct Answer - D Given `angleA+angleB+angle+angleC=180^(@)` `rArr angle C=180^(@)-(angleA+angleB) ` `rARr angleC=180^(@)-(90^(@)+55^(@))` (given) `rArr angleC=35^(@)`. |
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| 41. |
An equation which is used frequendy to solve problems is called a formula. |
| Answer» Correct Answer - 1 | |
| 42. |
Relation P,S,C where P is the profit S is the price, and C is the cost price. |
| Answer» Correct Answer - Profit is equal to the difference of selling price and cowst price. | |
| 43. |
The cost price C is given by the formula C=`(100s)/(100+g)`, where S=selling price and g=gain in %. Make S the subject of the formula . Find S, if `C=rs800` and g=20. The following steps are involved in solving the above problem. Arrange them in sequential order. (A) `rArr100S=C(100+g)` (B) `S=((100+g)C)/(100)` (C) Given `C=(100S)/(100+g)` (D) `therefore S=((100+20)xx800)/(100)=rs960`A. ABCDB. BCADC. CADBD. CABD |
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Answer» Correct Answer - D C,A,B, and D is the required sequential order. |
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| 44. |
One-fifth of a number is 5 more than one-tenth of the number. Find the numberA. 50B. 75C. 25D. 100 |
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Answer» Correct Answer - A Let the number be x. `therefore (x)/(5)=(x)/(10)+5` `rArr (x)/(5)-(x)/(10)=5` `therefore (2x-x)/(10)=5rArrx=50` Hence, the correct option is (a). |
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| 45. |
Which of the following is a solution of `2x-5gt4x-3`? |
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Answer» Correct Answer - D `2x-5gt4x-3` `rArr 2x-4xgt-3+5` `rArr -2xgt2rArr-xgt1` `rArr x=lt-1` `therefore` Choice (d) follows `(because x=-2 "and" -2lt-1)` |
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| 46. |
If `A=S^(2)` and `A=324cm^(2)`, then find the value of S(in cm).A. 162B. `(324)^(2)`C. `18`D. 16 |
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Answer» Correct Answer - C Given `A=S^(2)` and `A=324`. `A=S^(2)rArrsqrt(A)=sqrt(S^(2))` `rArr S=sqrt(A)` `rARr S=sqrt(324)` `rArr S=18cm`. |
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| 47. |
If the cost of two pens is rsx, then the cost of three pens is ______. |
| Answer» Correct Answer - rs(3x/2) | |
| 48. |
If twice a number is added to half the number, then the result is 250. Find one-tenth of the number.A. 20B. 10C. 50D. 25 |
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Answer» Correct Answer - B Let the number be x. `therefore 2x+(x)/(2)=250` `rArr (4x+x)/(2)=250` `rArr 5x=500rArr x=100` `therefore` one -tenth of the number `=(x)/(10)=(100)/(10)=10`. |
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| 49. |
If `h^(2)=a^(2)+b^(2)`, then b`=sqrt(h^(2)-a^(2))`. |
| Answer» Correct Answer - 1 | |
| 50. |
The compound interest on a certain sum is given by `C.I.=P(1+(R)/(100))^(n)-P`. Find C.I. when `P=rs1000,R=10%` P.a., and n=2. The following steps are involved in solving the above problem. Arrange them in sequential order. (A) `therefore C.I.=rs210` (B) `1000((11)/(10))((11)/(10))-1000=1210-100` (C) Given `Cl=P(1+(R)/(100))^(n)-P,P=rs1000`, R=10% p.a., and n=2 (D) C.I. =`1000+(1+(10)/(100))^(2)-1000`A. BCDAB. DCBAC. CDBAD. BDCA |
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Answer» Correct Answer - C C,D,B, and A is the required sequential order |
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