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.

g N o 'T"FQW‘W«” LD"‘WW’W‘_W“% ’—T%‘D—'WWW o WO T oymvg“’frmw7 i mvzm‘;pfif

Answer»

Given, Distance between person and church = 80 mAngle of elevation = 45°Height of church H =?

We know,tan x = P/B

tan 45° = H/801 = H/80H = 80

Therefore, height of church is 80 m

2.

51. If 3x - 4 (64 - x) = 10, then x = ?

Answer»
3.

10. Factorise 8 x^{3}+\sqrt{64 y^{3}}

Answer»

8x³ + √64y³= 8x³ + 8y³= (2x)³ + (2y)³= 2³ ( x³ + y³)= 8 ( x+y)(x²+y²-xy)

4.

then find the values of x, y, z and w.[Ans : x = 1,) If2x-y32+w/-L013

Answer»

x-y = -1 and 2x-y =0y = x+1 putting the value of y in 2nd equation2x - x -1 =0 , x - 1 = 0, x=1and y = 1+1 = 2

2x + z = 5and 3z + w = 13 2[1] + z =5, z = 5 -2 =3 3[3] + w =13 , w = 13 - 9 = 4

5.

15. If a+ b+ c 0, show that axb bx c cxa.

Answer»

ifa + b + c = 0then

a x (a+b+c) = a x a + a x b + a x c = a x 0 = 0a x b + a x c = 0a x b - c x a = 0soa x b = c x a

b x (a+b+c) = b x a + b x b + b x c = b x 0 = 0b x c = a x b

c x (a+b+c) = c x a + c x b + c x c = c x 0 = 0c x a = b x c

putting it all together, a x b = b x c = c x a

6.

Verify the property a x(b-c) = axb-axcby taking a =

Answer»

ax(b-c)=1/2*(-3/4-(-2/3)=1/2*(-3/4+2/3)=-1/2*(1/12)=-1/24anda*b-a*c=1/2*-3/4-1/2*-2/3=-3/8+1/3=-1/24hence proved

7.

(3xC)1) (BnS)x c=()ii) AXCB-C) = (AXB) - CARTA={1,2,3,4,5,6,73B={2,3,5,73|C=523ney

Answer»

(AI-IB=[1,2,3,4,5,6,7]; (AI-I)×c=[1,2,3,4,5,6,7]x(2)=(2,4,6,8,10,12,14); (AxB)=(2,3,4,6,8,9,10,12 ,14 16,18,20,21,24,25,26,28,30)(Axc)=(2,4,6,8,10,12,14); (AI-IB)-(BI-IC)=(3,15, 16 18,20,21 ,24,26,28,30)

2) AX(B-C)=(AxB)-(AxC); Ax(3,5,7)=(1,2,3,4,5,6,7)×(3,5,7)=(3,6,9,12,15,18,21,5,10,20,30,35,14,28,35,42,49);

8.

2-3sin dx20.cos x

Answer»

Seperate2/cos^2x-3sinx/cos^2x=integral(sec^2x)-integral(3secx*tanx)dxnow1/2log(secx+tanx)-3secx+C

9.

289= 17x*1/5

Answer»

17x17= 17^(x/5)17^2= 17^(x/5)( आधार समान है इसलिए घाते भी समान होगी2= x/5x= 10please like the solution 👍 ✔️

and check previous Answer as well

10.

24x^2-17x + 3=0

Answer»

javab

11.

22. If a,b,c are three non-zero vectors suchthat axb č and bxč- à, prove thata,b,c are mutually perpendicular andI) | 1 and | c |

Answer»
12.

3. यदि a.b = 0 हो तो axb] निम्न में सेकिसके बराबर है ?(A) शून्य (B) |ab](C) इकाई (D) JEET

Answer»

AxB =ABsin theta.So whenAxB=0 then theta is also 0° as

AxB= 0

=> ABsin theta =0

=> Sin theta = 0

=> theta = 0°now A.B = 0cos theeta = 0sin 90= 1so answer 1

second part

B is correct answer

1 is the right answer

(b) is a good answer

13.

Find the quadratic polynomial whose zeroes are(5+213) and (5-213)

Answer»

sum of zeroes= 5+2√3+5-2√3 = 10product of zeroes=(5+2√3)(5-2√3){since (a+b)(a-b)=a^2 - b^2) = (5)^2-(2√3)^2 = 25-4×3 = 25-12 = 13polynomial=x^2-x(sum of zeroes)+(product of zeroes)x^2-x(10)+(13)x^2-10x+13

14.

increase 213 by 623

Answer»

Increasing 213 by 623 means (213+623)=836

15.

6.If a and bare any two positive integers then HCF (a, b) x LCM (a, b) isequal to(A)a+b(B)a-b(c) axb(D)a= b

Answer»

option: C (a×b) hcf×lcf=product of the numbershcf(a, b) ×lcf(a,b) =ab

option c a×b hcf×lcf=product of the Number hcf(a,b)×lcf(a,b)=ab

16.

0.25 ( 4 p - 3 ) = 005 ( 10 p - 9 )

Answer»
17.

48(5a — 2b)? — 75(2a — 5b)?

Answer»
18.

U Q. 10. Factorize:27 p^{3}-\frac{1}{216}-\frac{9}{2} p^{2}+\frac{1}{4} p

Answer»
19.

Prove that √3sin x+3cosx has a maximum value atx=π/6.

Answer»
20.

2-3sin x dx/2Cos² x

Answer»
21.

find the max.value of sin^2 x - 3sin x + 2

Answer»

2 sin^2 (x) - 3 sinx + 2.

Let y = 2 sin^2 (x) - 3 sinx + 2

For y to be minimum or maximum,dy/dx = 0

Or, 4 sinx cosx - 3 cosx = 0Or, cosx (4 sinx - 3) = 0

cosx = 0, sinx = 3/4x = 90°, 48.59°.

d^2 y / dx^2= 4 (cos^2 (x) - sin^2 (x)) + 3 sinx= 4 cos (2x) + 3 sinx

When x = 90°, d^2 y / dx^2 = -1 < 0So, y is maximum when x = 90°

When x = 48.59°, d^2 y / dx^2 = 1.75 > 0So, y is minimum when x = 48.59°

y (max) = 2 sin^2 (90°) - 3 sin (90°) + 2= 1

22.

) 187 S -- BSIF® +GEA0 = 1-3Sinke. G

Answer»

Using the binomial theorem,(a+b)^3=a^3+3a^2b+3ab^2+b^3

⇒a^3+b^3=(a+b)^3−3a^2b−3ab^2=(a+b)^3−3(a+b)ab

Substitutinga=sin^2(x)aandb=cos^2(x), we have:

sin^6(x)+cos^6(x)=(sin^2(x)+cos^2(x))3−3(sin^2(x)+cos^2(x))sin^2(x)cos^2(x)

Using the trigonometric identitycos^2(x)+sin^2(x)=1 our expression simplifies to:

sin^6(x)+cos^6(x) =1−3sin^2(x)cos^2(x)

23.

\left. \begin{array} { l } { \text { If } x = \operatorname { log } _ { 12 } 6 , y = \operatorname { log } _ { 18 } 12 \text { and } z = \operatorname { log } _ { 24 } 18 } \\ { \text { that } 1 + x y z = 2 y z } \end{array} \right.

Answer»
24.

Ex. 16. Evaluate : 213 x 213 + 187 187.

Answer»
25.

17x 18)(17z+187)

Answer»

(a+b)²=a²+2ab+b²

(17x+18y)²=(17x)²+2*17x*18y+(18y)²=289x²+612xy+324y²

26.

Q.6 What number must be added toso that the sum is 187

Answer»

Your correct answer is 76/5

The correct answer is 76/5

27.

.5-Find the additive inverse of:lat?2015(4) 01872(0) 118719

Answer»

2/3, 7/19, 5,0, 1, 1/9, 7/5 is the correct answer of the given question

28.

the total surface area of a cuboid is 184m find the length of the cuboid if it breath is 6m and height is 2m

Answer»
29.

10. Priya earns 22% of her investment. If she earns 187, then how much did she invest?DIYbycot D

Answer»
30.

12*z - 4*y - 6*x %2B z^2 %2B x^2 %2B y^2 - 36=0

Answer»
31.

breadth of a rectangular park are in the ratio 5: 3 and its perimeter is128 m. Find the area of the park.

Answer»
32.

1) The square of a diagonal of a square is 128 cm. Find the side of a square.

Answer»
33.

n^2 %2B 20*n %2B 75

Answer»

give me answer

x^2 + 20x + 75 = 0x^2 + 15x + 5x + 75 = 0x(x + 15) + 5(x + 15) = 0(x + 5)(x + 15) = 0x = - 5, - 15

34.

MBD EXAMINATION GUIDIf 7 sin2 θ + 3 cos2 θ4, then sec θ + cosec θ s equal to -(a)俩蘩衣2(a)22V3(b)+2The line x =(a) Perpend(b) Parallel(c) Neithe(d) Nothi3, then 5 sin θ-3 cos θ.is equal to-1f5cot®4sin θ +3 cos θ(a) 1811 (b) 29(c)(d) 229(a) 8(c) 12

Answer»

7sin square theta +3cos square theta =4

4 sin square theta + 3sin square theta + 3cos square theta =4

4 sin square theta+3(sin square theta +cos square theta)=4

4sin squre theta=1

sin theta=1/2cos theta= √3/2

tan theta =1/√3sec theta = 2/√3

sec theta + cosec theta = 2 + 2/√3

35.

tan 75°_cot75° = 4sin 600

Answer»

tan75°=tan(30°+45°)

=(tan30°+tan45°)/(1-tan30°tan45°)

={(1/√3)+1}/{1-(1/√3)(1)}

=(√3+1)/(√3-1)

So,cot75°=1/tan75°

=(√3-1)/(√3+1)

Then,tan75°+cot75°={(√3+1)2+(√3-1)2}/{(√3)2-(1)2}

=(3+1+2√3+3+1-2√3)/(3-1)

=4.

36.

(2cos x - 3sin x)/(6cos x +4sin x)

Answer»
37.

2cos x-3sin x/(6cos x + 4sin x)

Answer»
38.

The length and the breadth of a rectangular park are in the ratio 5 : 3 and its perimeter is128 m. Find the area of the park.

Answer»
39.

3. The length and the breadth of a rectangular field are in the ratio 5 : 3. If its perimeter is128 m, find the dimensions of the field.

Answer»

Thanks

40.

Subtract 4 p q-5 a^{2}-3 p^{2} \text { from } 5 p^{2}+3 q^{2}-p q

Answer»

5p^2+3q^2-pq-(4pq-5q^2-3p^2)8p^2+8q^2-5pq

41.

9. The length and the breadth of a rectangular park are in the ratio 5: 3 and its perimeter is128 m. Find the area of the park.

Answer»
42.

शव 55 2 W 4 4 ‘4 x 5%

Answer»

square root is 1/2 power(3^2)^1/2*(4^4)^1/2*(5^2)^1/2=3*4^2*5=15*16=240

43.

What is heat energy

Answer»

Heat energyis the result of the movement of tiny particles called atoms, molecules or ions in solids, liquids and gases.Heat energycan be transferred from one object to another. Thetransferor flow due to the difference in temperature between the two objects is calledheat

44.

(C)1450व:580 में POQएक सरल रखा है।। का मान है।__40X3xचित्र 5.601) 20° (B)25°N (C) 30त्र 5.61 में OP| RS. ZOPQ = 110° और /

Answer»

40 + 4x+ 3x = 1807x + 40. = 180 7x. = 180-40 7x. = 140 x = 140/7 x = 20

40+4x+3x=1807x=180-40x=140/7x=20

7x+40°=180x=140/7x=20°

40+4x+3x=180°7x=180-407x=140X=20° answer

X=20° is the right answer

45.

7 ( 4 w + x + 2 y ) - 5 ( w - x + 3 y )

Answer»

28w + 7x + 14y - 5w + 5x - 15y23w + 12x - y

46.

x*(a*(r*(r*(o*(w*((x - 4)/(x^2 - 3*x - 4)))))))

Answer»

So herex^2-3x-4= x^2+x-4x-4= 0x(x+1)-4(x+1)= 0(x-4)(x+1)nowit will be changed tolim x tends to 4 (1/(x+1)that will be 1/(4+1)= 1/5

47.

\frac{3}{13} \div\left(\frac{-4}{65}\right)

Answer»
48.

Solve: \frac { 2 x + 3 } { 5 } &gt; \frac { 4 x - 1 } { 2 } , x \in W

Answer»

4x+6>20x-511>16xso x<11/16

Give full answer

49.

the cost of a book is one third the cost of a pen. Write a linear equation in two variables to represent this statement

Answer»
50.

Juul (1) BABC (c) abc (d) 4abc17. The number of ordered 4-tuples (x, y, z, w) wherex,y,z, w € [0, 10] which satisfy the inequality2sin? x x 3cosạy x 4sin? 2 x 5cos? w &gt; 120, is(a) 81 (b) 144 (c) O (d) infiniteCalifla1da-1-pi

Answer»

a yghyygfffhkj hhfdzjmf

All the world's a stage" is the phrase that begins a monologue from William Shakespeare's pastoral comedy As You Like It, spoken by the melancholy Jaques in Act II Scene VII Line 138.