Explore topic-wise InterviewSolutions in Current Affairs.

Log ₃(3⁴)=4 it is not irrationalwe can write it as 4/1 so it is rational

No, π is an irrational number. Reason: We can not write it is in form of p/q form.

Note: 22/7 is its approximate value used for calculation.

yes, as x² + (4x^3/2)/x^1/2 simplified as x² + 4x which is a polynomial.

Here is my solution:

Given factor: x2 + 2x + k = 0

Given polynomial: 2x4 + x3 -14x2 + 5x + 6

Divide the polynomial by the factor

x2 + 2x + k ) 2x4 + x3 -14x2 + 5x + 6 ( 2x2 - 3x +(- 8 - 2k)

2x4 + 4x3 +2kx2 ( substract)

------------------------------

- 3x3 +(-14 - 2k)x2 + 5x

- 3x3 - 6x2 - 3kx ( substract)

------------------------------

(- 8 - 2k) x2 +( 5 + 3k)x + 6

(- 8 - 2k) x2 +(-16 - 4k)x + (- 8k - 2k2) ( substract)

-----------------------------------------------------------------

( 21 + 7k)x + (6 + 8k + 2k2)

The remainder is: ( 21 + 7k)x + (6 + 8k + 2k2) = 0

21 + 7k = 0 ⇒ k = -3.

The factors are x2 + 2x - 3 = 0 and 2x2 - 3x - 2 = 0

x2 + 3x - x - 3 = 0 and 2x2 - 4x + x - 2 = 0

x( x + 3 )-1( x + 3) = 0 and 2x (x - 2) + 1(x - 2) = 0

(x - 1)( x + 3) = 0 and (2x + 1)(x - 2) = 0

x = 1 ,3 ,-1 / 2 and 2.

The zeros are 1 ,3 ,-1 / 2 and 2.

1;2;3;-1/2 are zeros of given polynomial.

( x^2+2x+k )

to be a factor of

(2x^4+ x^3- 14x^2+ 5x + 6)

(x+a)=.: x=-a; x^2+px+q=(-a)^2+p(-a)+q=a^2-ap+q=0 ; x=-a^2; (-a)^2+m(-a)+n=a^2-ma+n; a^2-ap+q=a^2-ma+n; -ap+q=-ma+n; am-ap=n-q; a=n-q/m-p

(9t-7)(t+6)=(3t+5)(3t-4)We move all terms to the left:(9t-7)(t+6)-((3t+5)(3t-4))=0We multiply parentheses ..(+9t^2+54t-7t-42)-((3t+5)(3t-4))=0

We calculate terms in parentheses: -((3t+5)(3t-4)), so:(3t+5)(3t-4)We multiply parentheses ..(+9t^2-12t+15t-20)We get rid of parentheses9t^2-12t+15t-20We add all the numbers together, and all the variables9t^2+3t-20Back to the equation:-(9t^2+3t-20)

We get rid of parentheses9t^2-9t^2+54t-7t-3t-42+20=0We add all the numbers together, and all the variables44t-22=0We move all terms containing t to the left, all other terms to the right44t=22t=22/44t=1/2

5t-3=3t-55t-3t=-5+22t=-2t=-1

Euler's formula tells us that

V - E + F = 2;

or, in words: the number of vertices, minus the number of edges, plus the number of faces, is equal to two.

2x + 5 = 02x = -5x = -5/2

2x+5=02x=-5X=-5/2so (b) is ryt option

Answer: b)Rs 3500Given:Amount = 3605 rs; rate=5% per annum; time= 219 days=219/365 yrsLet priciple be xFormula:SI=PRT/100=x*5*(219/365)/100=3x/1003x/100+x=3605x=3500

p(x)=3x4+6x3-2x2-10x-5

as we have given that two of its zeroes are √(5/3) and -√(5/3). so their factors are;

(x-√(5/3)) and (x+√(5/3)). the product of the factors ;

(x-√5/3) (x+√5/3)=x^2-5/3

=3x^2-5/3=1/3(3x^2-5)

where k=1/3

now g(x)=3x^2-5

dividing p(x) by g(x) we get

q(x)=x^2+2x+1

by division algorithm;

p(x)=g(x)*q(x)+r(x)

=(3x^2-5)(x^2+2x+1)

=(3x^2-5)(x^2+x+x+1)

=(3x^2-5)(x(x+1)+1(x+1)

(3x^2-5)(x+1)(x+1)

the other two zeroes are -1 and-1

thanks it is correct

96=2 x 48

96=2 x 2 x 24

96=2 x 2 x 2 x 12

96=2 x 2 x 2 x 2 x 6

96=2 x 2 x 2 x 2 x 2 x 3

96= 2^5 x 3

96=2×48 2×2×24 2×2×2×12 2×2×2×2×6 2×2×2×2×2×3

96=2x2x24=2x2x2x12=2x2x2x2x6=2x2x2x2x2x3Answer

LHS = √(1 + sin∅)/√(1 - sin∅)= √(1 + sin∅) × √(1 + sin∅)/√(1 -sin∅)×√(1 +sin∅)= √(1 + sin∅)²/√(1 -sin²∅)= (1 + sin∅)/√cos²∅= (1 + sin∅)/cos∅= 1/cos∅ + sin∅/cos∅= sec∅ + tan∅ = RHS

Like my answer if you find it useful!

Prime factorisation of 1947:1947=3 x 11 x 59

7429 as a product of its prime factors...17×19×23=7429

1000008000 this is the answer

Solution

Referrence

this is wrong solution try again

r1= 1 cm,r2= 2.5 cm,h= 6 cml = √h² + (r2-r1)²= √(6)² + (2.5-1)² cm= √36 + 2.25 cm= √38.25 cm= 6.18cmSo,External Surface area = (curved surface area of frustum) + (curved surface area of hemisphere)= 22/7(r1+r2)l +2.22/7.r1= 22/7 [(1+2.5)6.18 + 2×(1)²] cm²= 22/7 (3.5 × 6.18 +2) cm²= 22/7 (21.63+2) cm²= 22/7 × 23.63 cm²= 519.86/7 cm²= 74.26 cm²

Given:r1= 1 cm,r2= 2.5 cm,h= 6 cml = √h² + (r2-r1)²= √(6)² + (2.5-1)² cm= √36 + 2.25 cm= √38.25 cm= 6.18cmSo,External Surface area = (curved surface area of frustum) + (curved surface area of hemisphere)= 22/7(r1+r2)l +2.22/7.r1= 22/7 [(1+2.5)6.18 + 2×(1)²] cm²= 22/7 (3.5 × 6.18 +2) cm²= 22/7 (21.63+2) cm²= 22/7 × 23.63 cm²= 519.86/7 cm²

sint = 7/25 cost = √(1-49/625) = √(576/625) = 24/25 tant = sint/cost = (7/25)/(24/25) = 7/24

= 1 cm,r2= 2.5 cm,h= 6 cml = √h² + (r2-r1)²= √(6)² + (2.5-1)² cm= √36 + 2.25 cm= √38.25 cm= 6.18cmSo,External Surface area = (curved surface area of frustum) + (curved surface area of hemisphere)= 22/7(r1+r2)l +2.22/7.r1= 22/7 [(1+2.5)6.18 + 2×(1)²] cm²= 22/7 (3.5 × 6.18 +2) cm²= 22/7 (21.63+2) cm²= 22/7 × 23.63 cm²= 519.86/7 cm²= 74.26 cm²

hit like if you find it useful

LHS = (cos∅ - sin∅ + 1)/(cos∅ + sin∅-1) dividing sin∅ both Numerator and denominator. = (cos∅/sin∅ - sin∅/sin∅ + 1/sin∅)/(cos∅/sin∅ + sin∅/sin∅ - 1/sin∅)= (cot∅ - 1 + cosec∅)/(cot∅ + 1 - cosec∅)

now, put 1 = cosec²∅ - cot²∅ in numerator

= {cot∅ + cosec∅ - (cosec²∅-cot²∅)}/(cot∅-cosec∅ +1)= (cosec∅+cot∅)(1 - cosec∅ + cot∅)/(cot∅-cosec∅+1)= cosec∅ + cot∅ = RHS

Hence proved

Other than this value all are having a lower value as sin (60)= √3/2and cos(60)= 1/2so√3/2(1+1/2)√3/2(3/2)3√3/4

sinθ(1+tanθ)+cosθ(1+cotθ)=secθ+cosecθ

soling LHS

sinθ+sin²θ/cosθ + cosθ + cos²θ/sinθ=(sinθ+cos²θ/sinθ)+(cosθ+sin²θ/cosθ)=1/sinθ + 1/cosθ=cosecθ + secθ

2(sin⁶θ+cos⁶θ)-3(sin⁴θ+cos⁴θ)+1= 2{(sin²θ)³+(cos²θ)³}-3{(sin²θ)²+(cos²θ)²}+1= 2{(sin²θ+cos²θ)³-3sin²θcos²θ(sin²θ+cos²θ)}-3{(sin²θ+cos²θ)²-2sin²θcos²θ}+1=2(1-3sin²θcos²θ)-3(1-2sin²θcos²θ)+1=2-6sin²θcos²θ-3+6sin²θcos²θ+1=-1+1=0 (Proved)