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cos^-1(cos 13pi/6)

= cos^-1(cos 2pi + pi/6)

= cos^-1(cos pi/6)[cos (2pi + x) = cos x[

= pi/6

As pi/6 £ (0, pi)

it is middle term splitting so x =2/13

b) √7 is irrational.

Reason : √7 can't be written as p/q form

³√121׳√297 = ³√121×297 = ³√35937 = 33

n term sum = 3n²/2 + 13n/2as we know that nth term = (Sum of nth term ) -( sum of (n-1)th term)method 1so25th term = (sum of 25terms) - ( sum of 24 terms) =(3×(25)²/2 +(13×25)/2) - ( 3×(24)²/2 + (13×24)/2) = 1100 - 1020 =80method 21st term = 8sum of 2 terms = 192nd term = 19 - 8= 11so. difference = 11- 8 = 325th term = (8 + (25 -1)×3) = 80

Comes under conditional probabaility{H,T} {T,H} {H,H} {T,T}

So given atleast one head occurs

~{H,T} {T,H} {H,H}

P(E) = n(E)/n(S) = 1/4

s = 24 + 32 + 40 = 96From heron’s formula,A = √s (s-a)(s-b)(s-c)here, a= 24, b=32, c= 40Putting all the values

A = √ 96*72*64*56A = √24*4*24*3* 64*4*14A = 24*4*8 √42Answer is 768√42

(4x+5y)2+(4x-5y)2=8x+10y+8x-10y=16x

use identity (a+b)² = a²+b² + 2abso (4x+5y)² = 16x² + 25y² + 40xy

When calcium chloride and Sodium sulphate react, they form equal amount of sodium chloride and calcium sulphate.

Hence the law of conservation of matter is verified

i) 90-34 = 56

ii) 90-89 = 1

iii) 90-25 = 65

iv) 90-90/3 = 90-60 = 30

1.562.013.754.60these are the complement of the above angles in the question.complement means the sum two angles should be 90 degree

56÷57÷34×534+66.982÷34×534+66.0288×534+6614.95+6680.95

good

Let Nisha's age is x years Aisha's age = (x² + 2) years

Now, A/C to question , when Nisha grows to her mother present age .means Nisha's grows = Aisha's present age - Nisha's present age = x² + 2 - x Then, this time Aisha's age = Aisha's present age + growing time = x² + 2 + x² + 2 - x = 2x² - x + 4

Now, question said , Aisha's age = 10× times of Nisha's age -1 2x² - x + 4 = 10x -1 2x² - 11x + 5 = 0 2x² -10x - x + 5 = 0x = 5 and 1/2 x ≠ 1/2 because age doesn't in moths

Hence , Nisha's present age = 5 years Aisha's present age = (5)² + 2 = 27 years

2y^2-5y+10=02y^2-5y=-10y^2=-10/2+5yy=√5+√5yy=5√y

y=5√y is a right answer

d=55 is the correct answer h

2y^2-5y+10=02y^2-5y=-10

y=5 is the right answer of this question

y=5√y is correct answer

Y=5√y is a correct answer

3y² - 20 = 160 - 2y²

3y² + 2y² = 160 + 20

5y² = 180

y² = 180/5

y² = 36

y = √(36)

y = + or - 6

Put in X=4hence3(4)-5=12-5=7hence proved it's a solution.

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answer is 20

Given:11⁴x × 11-³= 11× 121⁴

11⁴x × 11-³= 11× (11²)⁴

11⁴x × 11-³= 11× 11^8

11⁴x=11^9/11-³11⁴x=11^(9+3)11⁴x=11^12since base are equal4x=12x=12/4

=3

equation has two equal rootsso b^2-4ac=0k^2-4(2)(k)=0k^2-8k=0k(k-8)=0so k=0 or k=8