81279 + Interview Questions in Mathematics QA in Mathematics

1.	:Find two solutions for each of the following equations:(i) 4x+3), 12(ii) 2x + 5y 0(ii) 3y + 4-0
Answer» If you find this solution helpful, Please give it a 👍

Discussion

2.	X.le 4 Find two solutions for each of the following equations:(G) 4x + 3y 12(ii) 2x + 5y 0(ii) 3y + 4 0So (0. 4 is a solution
Answer» i) 4x + 3y = 12 x = (12-3y)/4 y=1 -> x=9/4 y=2 -> x=6/4=3/2 ii) 2x+5y = 0 x = -5y/2 y=1 -> x=-5/2 y=2 -> x=-5 iii) 3y+4 = 0 y = -4/3 If you find this answer helpful then like it.

2.

X.le 4 Find two solutions for each of the following equations:(G) 4x + 3y 12(ii) 2x + 5y 0(ii) 3y + 4 0So (0. 4 is a solution

Answer»

i) 4x + 3y = 12 x = (12-3y)/4 y=1 -> x=9/4 y=2 -> x=6/4=3/2 ii) 2x+5y = 0 x = -5y/2 y=1 -> x=-5/2 y=2 -> x=-5 iii) 3y+4 = 0 y = -4/3

If you find this answer helpful then like it.

Discussion

3.	\frac{\cos ^{2} 22 \frac{1}{2}+\sin ^{2} 22 \frac{1}{2}^{\circ}}{\cos ^{2} 22 \frac{1}{2} \cdot-\sin ^{2} 22 \frac{1}{2}}
Answer»

Discussion

4.	2corresponding value of y is--. So \| I,\|5 )is another solution of 2x + 5y 0.
Answer» 2x + 5y = 0 if we put y = -2/5 2x + 5(-2/5) = 0 2x - 2 = 0 2x = 2 x = 1 so (1,-2/5) is a solution of an equation.

Discussion

5.	(2 4)The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x +2y 16(A) 2x-5y 11 (B)2x +5y-11 (C) 2x+5y+ 11 0 (D)2x-5y- 110IS:
Answer»

Discussion

6.	10. The ratio of the area of the outer circle to theinner circle shown in the diagram is (ABCDis a square).(2) 22:1(b) 22:1(C) 2:1(d) 4:1
Answer» √2:1 is the correct answer

Discussion

7.	\left. \begin{array} { \| c \| c \| c \| } \hline 28 & { 21 } & { 51 } \\ \hline 25 & { 17 } & { 44 } \\ \hline 23 & { 25 } & { ? } \\ \hline \end{array} \right.
Answer» 21+28+2=5125+17+2=4423+25+2=50

Discussion

8.	(1+tan21) (1+ tan24)/(I+tan 22 (1+tan23)
Answer» [(1+ tan 24°)(1+ tan 21°)] /[(1+ tan 23°)(1+ tan 22°) ][1+tan24+tan21+tan24tan21] [1+tan23+tan22+tan23tan22].......(1)tan(45)=1=tan(24+21) = tan(23+22)tan(A+B) = (tanA+tanB)/(1-tanAtanB)tan(24+21) = (tan24+tan21)/(1-tan24tan21)1*(1-tan24tan21)=tan24+tan211=tan24+tan21+tan24tan21....(2)similarly, tan23+tan22+tan23tan22=1......(3)substituting equation 2 & 3 in equation 1[1+1] /[1+1]=1

Discussion

9.	1. 2+2 22+3.23++n.22 (n-1) 2n+1 +2;(nEN)
Answer» thankx

Discussion

10.	22.Geometric mean of 1, 2, 22, 232a is2n+1a) 2nb) 22c) 2 2d) 2 223 The
Answer» Option B is correct.

Discussion

11.	. . oo(11) T+チャ2+1ik(i) 何22-1) , (ii) 24iS. (1
Answer»

Discussion

12.	\frac{23^{10}}{23^{7}}=23^{3}
Answer»

Discussion

13.	The mode and median of the followingdata 21, 23, 25, 23, 21, 24, 22, 20, 23respectively, are(A) 23, 23(C) 25, 21(B) 21, 23(D) 23, 21
Answer»

Discussion

14.	The decimal expansion of 23 52 will terminateafter:2323 x 52
Answer» 23---------2³ ×5² 23----------------25 × 4 ×2 23------------100 ×2 0.23--------- 2 0.115 After three decimal the fraction will terminate. Please hit like if you find my solution useful

14.

The decimal expansion of 23 52 will terminateafter:2323 x 52

Answer»

23---------2³ ×5²

23----------------25 × 4 ×2

23------------100 ×2

0.23--------- 2

0.115

After three decimal the fraction will terminate.

Please hit like if you find my solution useful

Discussion

15.	. Determine the values of p and q for whichgiven system of equations has infinitely manyolutionsx+3y67, (p+q) x + (2p-q) y =21.
Answer»

Discussion

16.	sible to write a given system of equbove can also be written in the formuations in the form of statements.(iti) xty 5ty 6Wha
Answer»

Discussion

17.	For the given system of equations 3x-4y 5 and5x+by-c to be inconsistent, one pair of values of b and ccan be
Answer»

Discussion

18.	in 60 words describe the temba childhood and his feelings for the mountains
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19.	avea Com.bae rD Vee.
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20.	an article was sold for rs 250 with a profit of 5%. what was its cost price.
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Discussion

21.	Yash spent 60% of his money and was leftwith 120. How much money did Yash haveinitially?
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Discussion

22.	Kate bought a bus pass that had an initial value of$90. For every bus ride Kate takes, $1.80, the cost ofone bus ride, is subtracted from the value of the pass.What percent of the initial value of Kate's bus pass isthe cost of one bus ride?
Answer»

Discussion

23.	को हि =Z+Jz mb=
Answer» Rationalize(4+√2)(2-√2)/(4-2)(8-2√2-2)/26-2√2/2=3-√2 a=3b=2

23.

को हि =Z+Jz mb=

Answer»

Rationalize(4+√2)(2-√2)/(4-2)(8-2√2-2)/26-2√2/2=3-√2

a=3b=2

Discussion

24.	2. 942 people rode the new ride at Mountain ofMagic Amusement Park on Thursday. On Friday,879 people rode the same ride. ABOUT how manypeople rode the new ride altogether?
Answer» Total = 942 + 879 = 1,821 people

Discussion

25.	13817. Ip 2008, the cost of an oven was3500. I2010, it rose to 4900. What is the per centincrease in price ?(a) 50%(b) 40%(c)35%(d) 45%
Answer»

Discussion

26.	11. Salim wishes to visit his grandparents' village during school holidays. He plans to travelE rd of the distance by train. 4 th by bus and the remaining 50 km by a taxi. What isHoTs]hol haa is 7 80 more than twice the cost of a tiffin box. Find the costthe distance to be covered?
Answer»

Discussion

27.	6.You are at an elevation 380 m above sea level as you start a motor ride. During theride, your elevation changes by the following metres: 540 m, -268 m, 116 m, -152m, 490 m, -844 m, 94 m. What is your elevation relative to the sea level at the endof the ride?
Answer» 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1

Discussion

28.	11. Raju has four times as much money as Rohit.Together, their money sums to Rs 250. How muchmoney does each of them have?
Answer» let x be the money of rohitraju has 4x of money now x+4x=250 5x=250 x=50so rohit have rupees 50 and raju have 50×4= 200.

Discussion

29.	कर के. 1 4= x— 17— -1 [८ . jZ
Answer»

Discussion

30.	D n+t Jz(0 (रू) G
Answer»

Discussion

31.	6. Joni had thrice as much money as Glen at first. They each spent $45 on aAnswer:haversack bag. In the end, Joni had 8 times as much money left as Glen Howmuch money did they have altogether in the end?
Answer» This is a wonderful question

Discussion

32.	YXRar-+jz oe4-D094-Yदे1का$i{Ve7
Answer» Let,x/b-c = y/c-a = z/a-b = kSo, x =(b-c)k, y=(c-a)k, z=(a-b)k Now,L.H.S = ax+by+cz= a(b-c)k + b(c-a)k + c(a-b)k= abk-ack + bck-abk + ack-bck= 0

32.

YXRar-+jz oe4-D094-Yदे1का$i{Ve7

Answer»

Let,x/b-c = y/c-a = z/a-b = kSo, x =(b-c)k, y=(c-a)k, z=(a-b)k

Now,L.H.S = ax+by+cz= a(b-c)k + b(c-a)k + c(a-b)k= abk-ack + bck-abk + ack-bck= 0

Discussion

33.	Sandeep has twice as much money as Sonia. Together they haveHow much money does Sonia have?
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Discussion

34.	Ashish and Suresh together have R700in total. Suresh has three times as muchmoney as Ashish. How much money doeeach of them have?
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Discussion

35.	11. Priyanka had 50. He spent 25 on stationary and 12 on books. How much money did shespend in all? How much money is left with her?
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36.	Suresh spent Rs. 560 in the market if the money he spent was 40 % of the money he had, how much money did he have?
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Discussion

37.	stive times money as that of Bunny. After givingHow much money did John have in the beginning ?25 to Bunny, John has double the money Bunny
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Discussion

38.	If one-seventh of my money is 35, then how much money do I have
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Discussion

39.	9. Rashmi found a bag of money. She decided to give 1 of the money to her best frieof the money to her sister, of the money to her brother and of the moneyher dad. The amount of money left was 125. How much money was in the bag w164[Hoshe found it?
Answer»

Discussion

40.	\left. \begin{array} { l } { x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } + \frac { 3 } { 4 } x + \frac { 1 } { 8 } } \\ { ( x + 3 ) ^ { 2 } + p ^ { 2 } + 2 p ( x + 3 ) } \\ { 2 x ^ { 2 } + 11 x - 21 } \\ { \frac { 1 } { 2 } y ^ { 2 } - 3 y + 4 } \end{array} \right.
Answer»

Discussion

41.	opt 4x (sin 5x + sin 3x)=cot x (sin 5x - sin 3x)
Answer»

Discussion

42.	2 ^ { - 2 } - \{ - 2 ^ { - 3 } - ( 2 ^ { - 2 } - 3 ^ { - 2 } ) \}
Answer» this is wrong answer... plz solve one more time ...

Discussion

43.	cot 4x (sin 5x + sin 3x) = cot x (sin 5x-sin 3x)
Answer» LHS=cot4x (sin5x+sin3x)=cot4x.2sin4x.cosx=2(cos4x/sin4x)sin4x. cosx=2co4x.cosx=2cos4x. sinx.cotx=cotx(2sinx.cos4x)=cotx(sin5x-sin3x)=RHS

Discussion

44.	jzcot 4r (sin 5x + sin 3x) = cot x (sin 5x-sin 3x)
Answer»

Discussion

45.	8. If the length of a side of a rhombus is 13 cm and one of its diagonals is of length 24 cm, then find thearea of the rhombus.
Answer» If you find this solution helpful, Please like it.

Discussion

46.	Graphically, find whether the following pair of equations has no solutioExample 5:unique solution or infinitely many solutions:5x-8), + 1 = 024 3
Answer»

Discussion

47.	to that of the squarer8. If the length of a side of a rhombus is 13 cm and one of ts diagonals is of length 24 cm, then find thearea of the rhombus
Answer» According to question

Discussion

48.	1. Find whether the following pair of equations hasno solution, unique solution or infinitely manysolutions.5x - 8y + 1 = 0;24 3V+3
Answer» 5x-8y+1=03x-24y/5+3/5=0 5x-8y+1=0---------------(1)3x-24y/5+3/5=0×515x-24y+3=0-----------(2) equation 1 and 25x-8y+1=015x-24y+3=0now,a1/a2=5/15 =1/3b1/b2=-8/-24 =1/3c1/c2=1/3therefore, it has infinite many solution. 5x-8y+1=0; 3x-24y/5+3/5=0; 15x-24y+3_______(2); 5x-8y+1=0;; 15x-24y+3=0; a1/a2=5/15=1/3; a1=8/-24=1/3; c1/ c2=1/3; it is infinite

48.

1. Find whether the following pair of equations hasno solution, unique solution or infinitely manysolutions.5x - 8y + 1 = 0;24 3V+3

Answer»

5x-8y+1=03x-24y/5+3/5=0

5x-8y+1=0---------------(1)3x-24y/5+3/5=0×515x-24y+3=0-----------(2)

equation 1 and 25x-8y+1=015x-24y+3=0now,a1/a2=5/15 =1/3b1/b2=-8/-24 =1/3c1/c2=1/3therefore, it has infinite many solution.

5x-8y+1=0; 3x-24y/5+3/5=0; 15x-24y+3_______(2); 5x-8y+1=0;; 15x-24y+3=0; a1/a2=5/15=1/3; a1=8/-24=1/3; c1/ c2=1/3; it is infinite

Discussion

49.	A)2. The system of linear equations 5x + my 10 and4x ny 8 have infinitely many solutions, where mand n are positive integers. Then, the minimumpossible value of (m n) is equal to
Answer»

Discussion

50.	Who discovered electron, proton and neutron?
Answer» Experiments by J.J. Thomson in 1897 led to the discovery of a fundamental building block of matter one hundred years ago, the British physicist J.J. Thomson was venturing into the interior of the atom. t took more experimental work by Thomson and others to sort out the confusion. He found out that the rays are made up of electrons: very small, negatively charged particles that are indeed fundamental parts of every atom. In 1911 Ernest Rutherford who performed many experiments to explore radioactivity did an experiment in which he discovered that the atom must have a concentrated positive center charge that contains most of the atom's mass. He suggested that the nucleus contained a particle with a positive charge the proton. Atoms of different elements have different numbers of protons giving their nuclei different charges. That meant the hydrogen nucleus (it has one proton) was an elementary particle. Rutherford named it the proton, from the Greek word "protos," meaning first. In 1932, James Chadwick, an English physicist who had worked with Rutherford, detected neutrons and measured their mass in an invisible game of billiards. He fired the neutrons at a block of paraffin wax, which has a high concentration of hydrogen and is therefore rich in protons. Some of the neutrons collided with protons in the wax and knocked them out.

50.

Who discovered electron, proton and neutron?

Answer»

Experiments by J.J. Thomson in 1897 led to the discovery of a fundamental building block of matter one hundred years ago, the British physicist J.J. Thomson was venturing into the interior of the atom. t took more experimental work by Thomson and others to sort out the confusion. He found out that the rays are made up of electrons: very small, negatively charged particles that are indeed fundamental parts of every atom.

In 1911 Ernest Rutherford who performed many experiments to explore radioactivity did an experiment in which he discovered that the atom must have a concentrated positive center charge that contains most of the atom's mass. He suggested that the nucleus contained a particle with a positive charge the proton. Atoms of different elements have different numbers of protons giving their nuclei different charges. That meant the hydrogen nucleus (it has one proton) was an elementary particle. Rutherford named it the proton, from the Greek word "protos," meaning first.

In 1932, James Chadwick, an English physicist who had worked with Rutherford, detected neutrons and measured their mass in an invisible game of billiards. He fired the neutrons at a block of paraffin wax, which has a high concentration of hydrogen and is therefore rich in protons. Some of the neutrons collided with protons in the wax and knocked them out.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

:Find two solutions for each of the following equations:(i) 4x+3), 12(ii) 2x + 5y 0(ii) 3y + 4-0

X.le 4 Find two solutions for each of the following equations:(G) 4x + 3y 12(ii) 2x + 5y 0(ii) 3y + 4 0So (0. 4 is a solution

\frac{\cos ^{2} 22 \frac{1}{2}+\sin ^{2} 22 \frac{1}{2}^{\circ}}{\cos ^{2} 22 \frac{1}{2} \cdot-\sin ^{2} 22 \frac{1}{2}}

2corresponding value of y is--. So | I,|5 )is another solution of 2x + 5y 0.

(2 4)The locus of the centers of the circles such that the point (2,3) is the mid point of the chord 5x +2y 16(A) 2x-5y 11 (B)2x +5y-11 (C) 2x+5y+ 11 0 (D)2x-5y- 110IS:

10. The ratio of the area of the outer circle to theinner circle shown in the diagram is (ABCDis a square).(2) 22:1(b) 22:1(C) 2:1(d) 4:1

\left. \begin{array} { | c | c | c | } \hline 28 &amp; { 21 } &amp; { 51 } \\ \hline 25 &amp; { 17 } &amp; { 44 } \\ \hline 23 &amp; { 25 } &amp; { ? } \\ \hline \end{array} \right.

(1+tan21) (1+ tan24)/(I+tan 22 (1+tan23)

1. 2+2 22+3.23++n.22 (n-1) 2n+1 +2;(nEN)

22.Geometric mean of 1, 2, 22, 232a is2n+1a) 2nb) 22c) 2 2d) 2 223 The

. . oo(11) T+チャ2+1ik(i) 何22-1) , (ii) 24iS. (1

\frac{23^{10}}{23^{7}}=23^{3}

The mode and median of the followingdata 21, 23, 25, 23, 21, 24, 22, 20, 23respectively, are(A) 23, 23(C) 25, 21(B) 21, 23(D) 23, 21

The decimal expansion of 23 52 will terminateafter:2323 x 52

. Determine the values of p and q for whichgiven system of equations has infinitely manyolutionsx+3y67, (p+q) x + (2p-q) y =21.

sible to write a given system of equbove can also be written in the formuations in the form of statements.(iti) xty 5ty 6Wha

For the given system of equations 3x-4y 5 and5x+by-c to be inconsistent, one pair of values of b and ccan be

in 60 words describe the temba childhood and his feelings for the mountains

avea Com.bae rD Vee.

an article was sold for rs 250 with a profit of 5%. what was its cost price.

Yash spent 60% of his money and was leftwith 120. How much money did Yash haveinitially?

Kate bought a bus pass that had an initial value of$90. For every bus ride Kate takes, $1.80, the cost ofone bus ride, is subtracted from the value of the pass.What percent of the initial value of Kate's bus pass isthe cost of one bus ride?

को हि =Z+Jz mb=

2. 942 people rode the new ride at Mountain ofMagic Amusement Park on Thursday. On Friday,879 people rode the same ride. ABOUT how manypeople rode the new ride altogether?

13817. Ip 2008, the cost of an oven was3500. I2010, it rose to 4900. What is the per centincrease in price ?(a) 50%(b) 40%(c)35%(d) 45%

11. Salim wishes to visit his grandparents' village during school holidays. He plans to travelE rd of the distance by train. 4 th by bus and the remaining 50 km by a taxi. What isHoTs]hol haa is 7 80 more than twice the cost of a tiffin box. Find the costthe distance to be covered?

6.You are at an elevation 380 m above sea level as you start a motor ride. During theride, your elevation changes by the following metres: 540 m, -268 m, 116 m, -152m, 490 m, -844 m, 94 m. What is your elevation relative to the sea level at the endof the ride?

11. Raju has four times as much money as Rohit.Together, their money sums to Rs 250. How muchmoney does each of them have?

कर के. 1 4= x— 17— -1 [८ . jZ

D n+t Jz(0 (रू) G

6. Joni had thrice as much money as Glen at first. They each spent $45 on aAnswer:haversack bag. In the end, Joni had 8 times as much money left as Glen Howmuch money did they have altogether in the end?

YXRar-+jz oe4-D094-Yदे1का$i{Ve7

Sandeep has twice as much money as Sonia. Together they haveHow much money does Sonia have?

Ashish and Suresh together have R700in total. Suresh has three times as muchmoney as Ashish. How much money doeeach of them have?

11. Priyanka had 50. He spent 25 on stationary and 12 on books. How much money did shespend in all? How much money is left with her?

Suresh spent Rs. 560 in the market if the money he spent was 40 % of the money he had, how much money did he have?

stive times money as that of Bunny. After givingHow much money did John have in the beginning ?25 to Bunny, John has double the money Bunny

If one-seventh of my money is 35, then how much money do I have

9. Rashmi found a bag of money. She decided to give 1 of the money to her best frieof the money to her sister, of the money to her brother and of the moneyher dad. The amount of money left was 125. How much money was in the bag w164[Hoshe found it?

\left. \begin{array} { l } { x ^ { 3 } + \frac { 3 } { 2 } x ^ { 2 } + \frac { 3 } { 4 } x + \frac { 1 } { 8 } } \\ { ( x + 3 ) ^ { 2 } + p ^ { 2 } + 2 p ( x + 3 ) } \\ { 2 x ^ { 2 } + 11 x - 21 } \\ { \frac { 1 } { 2 } y ^ { 2 } - 3 y + 4 } \end{array} \right.

opt 4x (sin 5x + sin 3x)=cot x (sin 5x - sin 3x)

2 ^ { - 2 } - \{ - 2 ^ { - 3 } - ( 2 ^ { - 2 } - 3 ^ { - 2 } ) \}

cot 4x (sin 5x + sin 3x) = cot x (sin 5x-sin 3x)

jzcot 4r (sin 5x + sin 3x) = cot x (sin 5x-sin 3x)

8. If the length of a side of a rhombus is 13 cm and one of its diagonals is of length 24 cm, then find thearea of the rhombus.

Graphically, find whether the following pair of equations has no solutioExample 5:unique solution or infinitely many solutions:5x-8), + 1 = 024 3

to that of the squarer8. If the length of a side of a rhombus is 13 cm and one of ts diagonals is of length 24 cm, then find thearea of the rhombus

1. Find whether the following pair of equations hasno solution, unique solution or infinitely manysolutions.5x - 8y + 1 = 0;24 3V+3

A)2. The system of linear equations 5x + my 10 and4x ny 8 have infinitely many solutions, where mand n are positive integers. Then, the minimumpossible value of (m n) is equal to

Who discovered electron, proton and neutron?

\left. \begin{array} { | c | c | c | } \hline 28 & { 21 } & { 51 } \\ \hline 25 & { 17 } & { 44 } \\ \hline 23 & { 25 } & { ? } \\ \hline \end{array} \right.