Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

Point T is in the interior of rectangle PQRS prove that TS + TQ = TP + TR

Answer»

Answer:

(TS+TQ)= (TP+TR).... PROVED

Step-by-step explanation:

LET us assume that any rectangle PQRS(a×b) is placed on the coordinate PLANE in such a way that the coordinates of P(0,0), Q(a,0), R(a,b) and S(0,b) respectively. (See the diagram)

Also assume an interior point T(h,k) to the rectangle on the coordinate plane.

Then, we can have

TS=\sqrt{h^{2}+(k-b)^{2}} ...... (1)

TQ=\sqrt{(h-a)^{2}+k^{2}} ...... (2)

TP=\sqrt{h^{2}+k^{2}} ...... (3)

and, TR=\sqrt{(h-a)^{2}+(k-b)^{2}} ..... (4)

We have to prove that, TS+TQ= TP+TR

Now, (TS+TQ)^{2}=(\sqrt{h^{2}+(k-b)^{2}}+\sqrt{(h-a)^{2}+k^{2}})^{2}

⇒(TS+TQ)^{2}= h^{2}+k^{2}+(h-a)^{2}+(k-b)^{2}+2\sqrt{(h^{2}+(k-b)^{2})((h-a)^{2}+k^{2}  )  }

⇒(TS+TQ)^{2} =h^{2}+k^{2}+(h-a)^{2}+(k-b)^{2}+2\sqrt{h^{2}(h-a^{2})+h^{2}k^{2}+k^{2}(k-b)^{2}+(h-a)^{2}(k-b)^{2}} .... (5)

Similarly, (TP+TR)^{2}=(\sqrt{h^{2}+k^{2}}+\sqrt{(h-a)^{2}+(k-b)^{2}})^{2}

⇒(TP+TR)^{2}=h^{2}+k^{2}+(h-a)^{2}+(k-b)^{2}+2\sqrt{h^{2}(h-a^{2})+h^{2}k^{2}+k^{2}(k-b)^{2}+(h-a)^{2}(k-b)^{2}} .... (6)

So, from (5) and (6) it is CLEAR that,

(TS+TQ)^{2}=(TP+TR)^{2}

⇒(TS+TQ)= ±(TP+TR)

⇒(TS+TQ)= (TP+TR) {Since sum of two lengths can not be negative}

Hence, proved.

2.

How long will a man take to walk 600 metres if he walk at the rate of 4 km per hour?

Answer»

Time = distance / speed
600m= 0.600km
Time= 0.600/4
time= 0.15 hours or 9 minutes (0.15*60)


PLZ mark my answer brainliest

3.

Ram and Shyam appeared for the examination Ram secure 24 marks more than Shyam and the marks of Ram was 65% of the sum of marks obtained by both of them the marks obtained by Ram and Shyam are

Answer»

Let MARK is obtained by SHYAM = x
∴ mark is obtained by Ram = x + 24

ALSO mark of Ram 65% of the SUM of marks obtained by them.
∴ 65 % = Ram's mark/(Ram's mark + Shyam's mark) × 100
⇒65 = (x + 24)/(x + 24 + x) × 100
⇒65 = (x + 24)/(2x + 24) × 100
⇒13(2x + 24) = 20(x + 24)
⇒26x + 312 = 20x + 480
⇒26x - 20x = 480 - 312
⇒6x = 168
⇒x = 28

Hence, mark is obtained by Shyam = x = 28
Make is obtained by Ram = x + 24 = 28 + 24 = 52

4.

If 18.5 kg is the weight of 1 tin then how many tins will weigh 462.5 kg

Answer»

No of TINS = 462.5/18.5
                = 25

5.

The sum of two number is 84 and ratio is 5 ratio 7 find the number

Answer» LET the no. be 5x and 7x.
5x + 7x= 84
12X = 84
X = 7
Hope it helped
-Ad.
6.

What is the square root of 6.875 correct to two decimal places

Answer»

GIVEN :  6.875

To Find : square root of 6.875 correct to two decimal places using division method

Solution:

   

                     2.622

                 ________

                    6.875000

          2        4

                 __________

                   287

      46         276

                __________

                     1150

     522         1044

                 _______

                       10600

    5242           10484

                     ________

                            116

√6.875 = 2.622

= 2.62  upto 2 decimal places

Learn More:

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7.

An A.P consist of 37 terms. the sum of three middle most term is 225 and the sum of last 3 term is 429. find AP?

Answer»

The middlemost term is (37 + 1) /2 = 19.
Therefore
The THREE middle most TERMS are a18 , a19 and a20.
=> a18 + a19 + a20 = 225.
=> a + 17d + a + 18d + a + 19d = 225
=> 3a + 54d = 225
=> a + 18d = 75 ---------eq.1


Last three terms are a35 , a36 and a37.
Therefore
a + 34d + a + 35d + a + 36d = 429.
=> 3a + 105d = 429
=> a + 35d = 143 ----------eq.2


Solving EQUATIONS 1 and 2
We get
a = 3
d = 4

The AP is 3,7,11,15.........

8.

1/x-1/x-2=3. Solve by factorisation

Answer»

X-2-x/x^2-2x=3
-2=3x^2-6x
3x^2-6x+2=0

x= -B +-√(b^2-4ac)/2a

here a=3 b=-6, c=2 PUT VALUE and GET ANS....

9.

Find the zeros of the polynomial 4 x square - 12 x + 9

Answer» HEYA!

=4x^2-12x+9
=4x^2-6x-6x+9
=2x(2x-3)-3(2x-3)
=(2x-3)(2x-3)=0
=x=3/2,3/2

hope this HELPS you ☺
10.

there are 11 apples and oranges in the basket. If the number of apples are 20% more than the oranges. Find the number of apple and oranges in the basket

Answer»

Hey there
let the no of oranges be X
no of APPLES x(1+20/100)
x(1+20/100) +x = 11
x(1+1/5)+x = 11
6/5x +x = 11
11x/5 = 11
x = 11*5/11
x = 5
no of oranges = 5
no of apples = 6

11.

If 14% of a number is 315 ,find the number

Answer»

Here is your ANSWER



please MARK me as BRAINLIST if you LIKED my answer

12.

Find the sum of 7/12 +11/16 +9/24

Answer» ANSWER for the above EXPRESSION is 79/48
13.

If the quadratic equation (1 + m2)x2 + 2 mcx + c2 - a2 = 0 has equal roots, prove that c2 = a2 (1 + m2).

Answer»

D=b^2-4ac=0
(2MC)^2-4(1+m^2)(c^2-a^2)=0
4m^2c^2-4(c^2+m^2c^2-a^2-a^2m^2)=0
4m^2c^2-4c^2-4m^2c^2+4a^2+4m^2a^2=0
-4c^2+4a^2+4m^2a^2=0
-c^2+a^2+m^2a^2=0
-c^2+a^2(1+m^2)=0
C^2=a^2(1+m^2)

14.

Find the value of x,y and z if( 2^x)(3^y)(5^z)=9000

Answer»

I HOPE this ANSWER HELP you

15.

Is zero (0) a rational number? justify your answer

Answer»

Yes zero is a RATIONAL number
because rational number MEANS a number that can be EXPRESS ED in the FORM of p/q
so zero can be express ed in the form of p/q
0/m

16.

How many days are between children's day and republic day?

Answer» 62 DAYS between CHILDREN's DAY and REPUBLIC day
17.

If a ray stands on a line then the sum of the adjacent angle so formed is ???

Answer»

The answer is given below :

When a ray stands on a LINE, TWO adjacent ANGLES are formed.

We KNOW that the angle lying on a straight line is 180°.

The two angles being adjacent, make a total angle of 180° on the straight line.

Another way, we can see since the ray stands on the straight line, we can consider it is a perpendicular line.

Thus, the two adjacent angles are RIGHT angles.

So, the total angle

= 90° + 90°

= 180°

(Referred to the given attachment.)

Thank you for your question.

18.

Find the measure of each exterior angle of a regular 10 sided polygon

Answer» MEASURE Of each EXTERIOR Angle=360°/number of sides
So,
MESURE Of Each Exterior Angle=360°/10=36°
19.

Find the smallest natural number which when added to diffrence of squares of 17and13 gives a perfect square?

Answer»

The ANSWER is 1. 17^2-13^2=289-169=120.So 11^2=121 which is 1 more than 120.

20.

Find the value of k if the roots of x²+kx+12=0 are in the ratio of 1:3.

Answer» HEY Mate ☺

Here is your solution :-

___________________________


LET the two roots be α and β
Given α : β = 1 : 3
That is α / β = 1 / 3
β = 3 α
Given quadratic EQUATION is x^2+kx+12=0
Sum of roots (α + β) = -b/a = - k
That is (α + 3 α) = - k
Hence α = - k/4 ---- (1)
Product of roots, (αβ) = c/a = 12/1
That is (3α^2) = 12
α^2 = 4
α = ± 2
Equation (1) becomes,
2 = - k/4
Hence k = -8
If α = - 2
k = 8

_________________________


Hope it helps ☺
21.

find the values of A and B so that f of x is equal to X square + 3 X + a ,x less than and equal one,and another function is a bx+2,x>1, is differentiable at X=1

Answer» HEY Friend..... :-)

don't DEPEND on brainly always

Go to www.cymath.com

for your question.

you can VIEW all the STEPS and DETAILED solution there with every formula.

Hope it helps

Thanks :D
22.

Find the five rational numbers between 3/4 and 5/6

Answer»

Heya ✋

Let see your answer !!!

Let x = 3/4 ; y = 5/6

y > x ; n = 5

d = y - x/n + 1

= (5/6 - 3/4)/5 + 1

= (10 - 9/12)/6

= (1/12)/6

= 1/12 ÷ 6

= 1/12 × 1/6

= 1/72

1st rational NUMBER = x + d

= 3/4 + 1/72

= 54 + 1/72

= 55/72

2nd rational number = x + 2D

= 3/4 + 2 × 1/72

= 3/4 + 2/72

= 54 + 2/72

= 56/72

3rd rational number = x + 3d

= 3/4 + 3 × 1/72

= 3/4 + 3/72

= 54 + 3/72

= 57/72

4th rational number = x + 4d

= 3/4 + 4 × 1/72

= 3/4 + 4/72

= 54 + 4/72

= 58/72

5th rational number = x + 5d

= 3/4 + 5 × 1/72

= 3/4 + 5/72

= 54 + 5/72

= 59/72





Thanks :))))


23.

Determine Ap whose 3rd term is 5 and 7th term is 9

Answer»

Hii friend,

THIRD term of an AP = 5

a+2d = 5

a = 5-2d.....(1)

Again,

SEVENTH term of an AP = 9

a+6d = 9.......(2)


Putting the value of A in equation (2)

a+6d = 9

5-2d +6d = 9

4d = 9-5

4d = 4

D = 4/4

d = 1.

Putting the value of D In equation (1)

a = 5-2d

a = 5-2 × 1 = 5-2 = 3

Therefore,

First term of an AP = 3

Second term = a+d = 3+1 = 4

Third term = a+2d = 3 +2 × 1 = 3+2 = 5

Four term = a+3d = 3 + 3 × 1 = 3+3 = 6

AP = a , a+d , a+2d , a+3d.....


=> 3 , 4 , 5 , 6......


HOPE IT WILL HELP YOU.... :-)


24.

Prove that tan72=tan18+2tan54

Answer» SOLUTION:-

LET,
tan54 = TAN(72-18)

= tan54 =( tan72-tan18)/1+tan72.tan18

= tan54 = ( tan72-tan18)/1+tan(90-18).tan18

= tan54 =( tan72-tan18)/1+cot18.tan18

= tan54 =( tan72-tan18)/2

= tan72-tan18 = 2tan54

=(tan72 = tan18+2tan54)PROVED


25.

Using suitable identities evaluate the following(i)6.1^2 (ii)20.5 × 19.5(iii)9.6^2

Answer»

I HOPE this will HELP U...

26.

Hamming distance between 001111 and 010011 is

Answer»

The CORRECT answer should be - 3

In information technology studies, the Hamming DISTANCE in between two strings which are of equal length is DEFINED by the number of positions at which their CORRESPONDING symbols are different.

The Hamming distance is associated with the counting up of which SET of corresponding places or digits are the same, and which are different.

27.

If several frequency distributions are constructed from the same data set, the distribution with the widest class width will have the

Answer»

The answer is FEWEST classes.


If SEVERAL frequency DISTRIBUTIONS areconstructed from the same data SET, the distribution with the widest classwidth will have the fewest classes.


Afrequency distribution refers to a graph, table or list, which highlights thefrequency of different outcomes in a SAMPLE.
28.

How to find inverse of matrix using simplex method

Answer»

First CALCULATE ADJ(A) then divide it by determinantof A. The Matrix you GET is inverse of matrix A.

29.

- A vendor buys bananas at 12 for Rs 50 and sells at 5 for Rs 40. What will be the gain (in %)?

Answer»

C.P. of 12 bananas = Rs.50
C.P. of 1 banana = 50/12 = Rs. 4.16 APPROX
S.P. of 5 bananas = Rs. 40
S.P. of 1 banana = 40/5 = Rs. 8
Gain (in RUPEES) = 8 - 4.16 = Rs. 3.84 approx
Gain (%) = (Gain/C.P.)×100
= (3.84/4.16)×100
= (0.92307)×100
= 92.307 approx

30.

Three pipes A,B and C are attached to a cistern .A and B can fill it in 20 and 30 minutes respectively, while C can empty it in 15 minutes .If A,B and C be kept open successively for 1 minute each,how soon will the cistern be filled?

Answer»

1/6 TIMES FASTER than

31.

What is the next term in the series 18,36,72,132,222,?

Answer»

18,36,72,132,222,342

32.

Odd man out 57,67,77,87

Answer»

77is the ODD ONE from the above

33.

Express 4.32 in the form of p/q where bar is only on 2

Answer»

4.32 BAR in 2 will be ANSWER is 39/3 I THINK

34.

How many triangles are there in the following figure???

Answer»

There are TOTAL 15 triangles in the GIVEN figure

hope this helps you

35.

Write the formula of sodium sulphate with steps

Answer» FORMULA of SODIUM=Na.
valency of sodium=1.

Formula of SULPHATE=SO4.
Valency of sulphate= 2.

Hence, formula of Sodium sulphate=Na2SO4.


hope it is HELPFUL for you:)
36.

External dimensions of a wooden cuboid box are 30 cm × 25 cm × 20 cm. If the thickness of the wood is 2 cm all around, what is the capacity of the box? Find the volume of the wood contained in the cuboid formed.

Answer»

Hey!!!! dear your ANSWER is here....
it is very easy question and you try in home......
I help you to make this question but you try in notebook how to solve this

Given that external volume=30×25×20cm³
=15000cm³
internal dimensions------
(30-4)CM × (25-4)cm ×( 20-4)
26cm*21cm*16cm
8736 cm
therefore capacity= 8736cm 1

again ,
Volume of wood= external volume - internal. volume
=15000-8736
=6264 cm

hey REPLY me

37.

(125)^-1/3[(125)^1/3-(125)^2/3

Answer» HI ,

( 125)-⅓ [ ( 125 )⅓ - ( 125 )⅔ ]

= 1/ ( 125)⅓ [ ( 125 )⅓ - [ ( 125 )⅓]² ]

= { ( 125 )⅓ [ 1 - ( 125 )⅓ } / ( 125 )⅓

after cancellation ,

= 1 - ( 125 )⅓

= 1 - ( 5³ )⅓

= 1 - 5

= - 4

I HOPE this HELPS you.

: )
38.

If the mean of 6,4,7,p and 10 is 8. Find the value of p.

Answer» MEAN = sum/total
8 = 6+4+7+p+10/5
8 × 5 = 27+p
40 = 27 + p
p = 40 - 27
p = 13
39.

the mean weight of a class if 32 students is 40.5 kg. if the weight of the teacher be included the mean rises by 500 g. the weight of the teacher is

Answer» 41 KG is a WEIGHT of TEACHER
40.

The difference of two natural number is 3 and the difference of their reciprocal is 3/28. Find the numbers.

Answer» HI ,

Let x , x - 3 are TWO numbers .

according to the problem given ,

1/( x - 3 ) - 1/x = 3/28

[ x - ( x - 3 )]/[ ( x - 3 ) x ] = 3/28

( x - x + 3 )/(x² - 3x ) = 3/28

3/(x² - 3x ) = 3/28

( x² - 3x ) /3 = 28/3

x² - 3x = 28

x² - 3x - 28 = 0

x² - 7x + 4x - 28 = 0

x( x - 7 ) + 4(x - 7 ) = 0

( x - 7 ) ( x + 4 ) = 0

Therefore ,

x - 7 = 0 or x + 4 = 0

x = 7 or x = - 4

Required numbers are;,

1 ) if x = 7 ,

x - 3 = 7 - 3 = 4

( 7 , 4 )

2 ) if x = - 4 ,

x - 3 = -4 - 3 = -7

( - 4 , - 7 )

I hope this HELPS you.

: )



41.

the area of a square garden is 8464 m2 . a man takes 3 rounds of this garden. find the distance covered by him

Answer»

Hii friend,

Area of square garden = 8464 m².

Side² = 8464

Side => ✓8464 = 92 m

DISTANCE covered by MAN in one round = Perimeter of square = 4 × side = 4 × 92 = 368 m

Therefore,

Distance covered by man in three rounds = 3 × Perimeter of square = 3 × 368 = 1104 m.


HOPE IT WILL HELP YOU...... :-)

42.

When the polynomial P(x) = x3+ 3x2 – 2Ax + 3,where A is constant, is divided by x2 + 1 andremainder is –5x, then A is

Answer»

The VALUE of A = 2.

43.

Hey! Can anyone tell the laws of exponents? For class 8

Answer»

Hey mate here is UR answer and if it helps u then PLS MARK it as BRAINLIEST

44.

the arthemetic mean of a set of 20 observations is 15:8. the arthemetic mean increases by 0.4 when a new observation is added to the set. the new observaon is:

Answer»

Number of OBSERVATIONS = 20
Mean = 15.8
Sum of 20 observations = 20 * 15.8
= 316
When arithmetic mean increased by 0.4
New mean = 15.8 + 0.4
= 16.2
No.of observations now =21
Mean of 21 observations = 16.2
Sum of 21 observations = 21*16.2
= 340.2
New OBSERVATION = 340.2 - 316
= 24.2

45.

find the cost of fencing a rectangular park of 120m length and 80m breadth at the rate of Rs.2 per meter.

Answer» PERIMETER of rectangular park = 2(length+breadth)

___________________

Perimeter of rectangular park = 2(120+80)

Perimeter of rectangular park =2×200

Perimeter of rectangular park= 400 m



Cost of fencing = 2×400

Cost of fencing = Rs 800



I HOPE this will HELP you


-by ABHAY
46.

divide ₹ 1870 into three parts so that half of the first part one third of second part and one sixth of the third part are equal

Answer» LET the three PARTS be x,y and z
so,x+y+z=1870(given).............1eq
(x/2)=(y/3)=(z/6)=k(let)
then we can SAY,
x=2k,y=3k and z=6k
putting the values in 1eq we get,
2k+3k+6k=1870
11k=1870
k=170


so,
x=2k=340
similarly,
y=510
z=1020
47.

Express the magnitude of vector aÃvector b in terms of scalar product.

Answer»

In the ATTACHMENT I have ANSWERED this problem.

I HOPE this ANSWER HELP you

48.

Six subtracted from a no. Is equal to one fourth of the sum of the And 45

Answer»

(x-6)=1/4(x +45)
4X -24 =x+45
3x= 45 +24
3x= 69
x = 29

49.

(x)2-32x-105. class9

Answer» SEE it and COMMENT if there is any PROBLEM.
50.

99 square using algebraic identity

Answer» 0