Explore topic-wise InterviewSolutions in Current Affairs.

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1.

(1) (9+8i)—(7i+3)

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2.

Ex. 6. नीचे के चित्र में ४ का मान ज्ञात करें ।हुन ।

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answer will be...180-90+70=20 degree

20° is correct answer

correct answer is 20 °

correct answer is 20 °

20° is the correct answer

3.

1. Find the cubes of the following numbers(ii) 16(iii) 21(iv) 30

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8^3=8×8×8=51216^3=16×16×16=409621^3=21×21×21=926130^3=30×30×30=27000

4.

1.Find 'x' in the following figures?6(iv)(111)A30c

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1. i) use angle A + angle B = angle ACDx + 56 = 123x = 123 - 56 = 67°

(ii)ans=125 is the answer by angle sum property sum of all the angles =180

5.

formulae forfrustum of right circular cone?

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6.

Q1. Write the formulae ofArea of parallelogram

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The area of a parallelogram is given by the formula

Area=b×awherebis the length of any baseais the corresponding altitude

7.

Find the formulae of cosA

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8.

(i) 5襾ー2 히(ii) 1+2iき1

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9.

t a LABC in which BC-3.6 crn. AB 5 cm. and AC-54 cm. Draw theperpendicular bisector of the side BC

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10.

a-tib4. If x-w-/--prove that x2 + yz-c2 + d25.Convert the following in the polar form:1+7i1+3i1-2i(2-1)(ii) 3

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11.

1. Express each of the following in the form (a + ib) and find its conjugate:(2-i)(1-2i)(ii) (2+302(iii)(4+3i)()( 02 ( ()21(iv)+301+2i2+1

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12.

23 In what time will 15625 amount to 17576 at 4% per annum compound interest?what timo will1500 yieldき496.50 as compound intorost at 100, nor a

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13.

₹12000 for 18 months at 12%per annum compound ed half year

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P = 12000, R = 12/100, n = 18/12 = 3/2Amount = P(1+R/2)^2 n = 12000(1+.12/2)^3 = 12000(1.06)^3 = 12000(1.19) = 14280

CI = A-P = 14280-12000 = Rs 2280

14.

65. After allowing a discount of 18%, a washingmachine is available for 13489. What is themarked price of the washing machine?

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18 is divided into 13489

15.

17.The value of a machine depreciates every year by 20%. If the present value of the machine be160000, what was its value last year?

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16.

17. The value of a machine depreciates every year by 20%. If the present value of the machine be160000, what was its value last year?

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X= 200000.

17.

factorise formulae

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Vgvxxxvbvv

18.

Why are - and I zeroes of the polynomials p(x) = 4.1 +3.8 - 19

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I don't know the answer

4x^2+3x-1=0; 4(1/4)^2+3(1/4)-1=4/16+3/4-1=1/4+3/4-1=1+3-4/4=4-4/4=0

because when we put that values then p(x) =0

because when we put that values then p(x) =0

19.

Solve the equation foriHOIn given figure Ape and COD are semicircies of diameter 7cm eachand aso are semicireles of diameter 14cm each. Find the perimeter of theshaded region. [ User =17 cmcrn

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sale ye bhi nahi ata

20.

Whand-1 zeroes of the polynomials p(x) =44x2 + 3x-1?y are

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If they are the zeros of the polynomial after putting them we should get a 0so now puttingx= -1(-1)^2*4-3-1= 0now putting X= -1/44*(-1/4)^2+3(-1/4)-14/16-3/4-11/4-1/4= 0hence they are the zeros

21.

2. Verify the division algorithm for the polynomialsp(x) = 2x* - 6x +2r-x+2 and g(x) = x+2.

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22.

Q2) For a material modulus of elasticity is 116 GPa and shear modulus is 45 GPa. Find thevalue of bulk modulus for the material. (M99, 4marks)

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Given E = 116 GPa and shear modules G = 45GPa

so, G = E/2(1+μ)

so, 45=116/2(1+μ) => 90(1+μ) = 116 => 1+μ = 116/90 => μ = 1.2888-1 = 0.28888

now bulk modulus = E/3(1-2μ) = 116/3(1-2*0.2888) = 116/3*0.4222 = 47.89GPa

23.

5.52ELEMENTS OF MATHEMATICSAXEXERCISE 5.41. Find the modulusand principal argument of the following complex numbersthem in modulus amplitude form :3ii)) 2i

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i) 1+√-3 = 1+ √3i , so modulus is √(1)²+(√3)² = √4 = 2. and argument is ∅ = tan^-1(√3/1) = π/3

ii) 1+i = modulus is √1²+1² = √2. and argument is ∅ = tan^-1(1/1) = π/4

iii) -2i , modulus is 2. and argument is -π/2.

24.

7.The area of a rectangular field is 3400 m2 and its length is 68 m. Find(i) its breadth《 the distance covered by a man in going 5 times around the field.

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Area of a rectangular field is equal to length into breadth. Area =lb 3400=68×b b= 50 m.So the breadth of field is 50 m.

For travelling one time completely around the field, distance covered= Perimeterdistance covered in one round =2(l+b) =2(68+50) = 2(118) = 236m So in 5 rounds he travels 236×5 =1180 m.

25.

The modulus of _-is

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26.

The area of a square garden is 8,464 m2. A man takes 3 rounds of this garden. Find the distancecovered by him.

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Area = 8464 m²The side of square field = √8464 = 92 mDistance covered in making three rounds = 3 × Perimeter of the square field = 3 × 4 × 92 = 1104 m

27.

EXERCISE 5.4I. Find the modulus and principal argument of the following complex numbers and ethem in modulus amplitude form :ii) 2i-1620zu1-(1-i2

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iv) -16/1+i√3.

on rationalizing it with 1-√3i we get. -16*(1-√3i)/(1)²+(√3)² = 16(√3i-1)/4 = 4√3i -4.

so, the module is √(4√3)² +(4)² =√48+16 = 8.

and principal argument is ∅ = tan^-1(-√3) = -π/3.

28.

9. If Sagar takes 3 rounds of a square park of side 70m, then what is thedistance travelled by him?

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29.

The length of rectangular field is twice its breath . A girl jogged around it 4 time and covered a distance of 4.5km What is length of field ?

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Length of field = xBreadth of field = x/2

Given4*Perimeter = 4.5 km4*(2*(length + breadth)) = 4.58(x + x/2) = 4.58(3x/2) = 4.5x = 1.5/4 = 1500/4 = 375 m

Length of field = 375 m

30.

the length of a rectangular field is twice its breath . a girl joked around it 4 times and covered a distance of 4.5 km. What is the length of the field ?

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31.

Through a rectangular field of sides 120 m x 30 m, two roads are constructed which areparallel to the sides and cut each other at right angles through the centre of the field. Ifthe width of the road is 3 m, find the total area covered by the two roads.

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32.

13. The length of a rectangular field is twice its breadth. If theperimeter of the field is 288 m, find the dimensions of the field.

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33.

A set of data has a normal distribution with a mean of50 and a standarddeviation of 8. Find the percent of data within each interval.15. from 42 to 5816. greater than 3417. less than 50

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greater than 34

34.

24. Prove that (x-2), (x + 3) and (x -4) are the factors of the polynomials P(x)x^{3}-3 x^{2}-10 x+24

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for proving this we will put x= 2,(-3),4 in the equation if the answer comes as zero so that means these are the factors of the polynomialso put x= 28-12-20+24=0so this is a factor just like this we will keep doing the same thing and at the end these all three are the factors after putting x= (-3)p(-3) = 0p(4) = 0 as well

35.

Find the mode of the following data.Height (In cm) Above 30 Above 40 Above 50 Above 60 Above 70 Above&No. of plants25.3430 219

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36.

Find the period of tan 3π

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The period of the tangent function isπ. Therefore, the period oftan(3x)isπ/3(3xwill increase byπunits anytimexincreases byπ/3units).

37.

हा r bपक -3 LT Wi TR |

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38.

5S + 3(S )(S2s+5) (Imp.)

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39.

malaPetherefield. Some are pigs and some are ducks. There are 54 legs in all Howmany of each animal are in the field?

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40.

Theor gle between the straight lines x2 + 4 y + y®wi(A) 30°1S-(B) 45°60°r

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thanks

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41.

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42.

11. In each of the following numbers, replace * by the smallest number(1) 27*4(ii) 53 46(iii) 8*711

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43.

If 'd' is the diameter of a sphere, then its volume i.24RC3td324

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Ans :- Option (b) is correct.

44.

15. Assertion (A) : Median of the given data 34,31,42,43,46,25,39,45,32, is 39.Reason (R) : When the number of observations (n) is even arrange the numbers in the ascendingorder then the median is the mean of the and | n+1 | observations.2a) Both A and R are correct, R is the correct explanation of A.b) Both A and R are correct, R is the not correct explanation of A.c) A is correct, R is wrongd) A is wrong, R is correct

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For given question option b is correct

As for finding median first we need to arrange observations in ascending order for both odd and even no. Of observations

Thus both Assertion and reason is correct, but R is not correct explanation of A

45.

LIDAY HOMEWORKATECT : MataTEST: MATHEMATICSCLASS. 8TH A'TEACHER: PANKAT KMwhat is the catione counter 20Eocnicis the followung in standard laim.is the catione Launbei? Gece rocamplesQ24Ecpress - 2 as cleational number having denominaAssange the following sational number inascending in des-0:5Find additive Invesse -is (11-15 i 3 Cine4-6 what should be subtracted lon ge037 The sumotwo sational numbelinyLOL them us 5. Find the otherthe otherenuh literatue doll hous, akidawuch time did the scende studi058_ Radhika readhouse and did nendemathematics forHy hoursEind multiplicative investegcinal numbe Wi-thotelmu

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46.

radius I0LThe circumference of a circle is 616 m. Find its radius and area.rce is 2826 sq. cm. Find its radius. (Take π = 3.14)

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Circumference=2πr616 m = 2 × (22/7) × rr= 98mArea = πr^2 = (22/7)(98)^2 m^2 = 30184 m^2

47.

11. Find the 18th and 23rd terms of the A.P., 1,5, 11, ,...

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48.

IN11. Find ten rational numbers between

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49.

719° Girl! Out of a group of swans ,-times the square root cf the number are paying on the shore of a tank.The two remaining ones are playing, with amorous fight, in the water. What is the total number of swans?

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Let the total no. of swans = xNo. of swans playing on the shore = 7/2 √xRemaining swans = 2A/Q x=7/2 √x+2x-2 = 7/2 √x2(x-2) = 7√x4(x-2)² = 49x4(x²-4x+4) = 49x4x²-65+16 = 0(x-16) (4x -1) = 0x-16 = 0 or 4x-1 = 0x = 16 or x = 1/4Since, the no. of swans cannot be 1/4∴ x = 16The total no.of swans = 16

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50.

The radius of a circle is greater than the radius of othercircle by 3 m. The sum of their areas is 89Tt m2. Find theradius of each circie.76

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Area of circle with radius r is given by,

Area of circle, A = πr²

Let 'r' be the radius of smaller circle, then radius of large circle = r+3

It is given that sum of areas = 89π m^2

To find r

Sum of areas = πr² + π(r +3)² = 89π m^2

⇒ π[r² + (r +3)²] = 89π

⇒ r² + (r +3)² = 89

⇒ r² + r² + 6r + 9 = 89

⇒ 2r² + 6r + 9 - 89 = 0

⇒ 2r² + 6r - 80 = 0

⇒ r² + 3r - 40 = 0 ----(1)

eq(1) is a quadratic equation.

Solving we get

r = 5 and r = -8

we take +ve values, so r = 5

Therefore radius of smaller circle = 5m

And radius of larger circle = r + 3 = 5 = 3 = 8m