(i) `(a^(p+q))^(p-q) (a^(q+r))^(q-r)(a^(r+p))^(r-p)` (ii) `[(a/b)^(sqrt(p)+sqrt(q))]^(sqrt(p)-sqrt(q))[(a/b)^(sqrt(q)+sqrt(r))]^(sqrt(q)-sqrt(r))` `[(a/b)^(sqrt(r)+sqrt(p))]^(sqrt(r)-sqrt(p))`
1 Answers
Talk Doctor Online in Bissoy App
If `sin^(-1)x_i in [0,1]AAi=1,2,3, .28` then find the maximum value of `sqrt(sin^(-1)x_1)sqrt(cos^(-1)x_2)+sqrt(sin^(-1)x_2)sqrt(cos^(-1)x_3)+` `sqrt(
`E = sqrt(sin^(-1)x_(1)) sqrt(cos^(-1) x_(2)) + sqrt(sin^(-1) x_(2)) sqrt(cos^(-1) x_(3)) + sqrt(sin^(-1) x_(3)) sqrt(cos^(-1) x_(4)) +...+ sqrt(sin^(-1) x_(28)) sqrt(cos^(-1) x_(1))` `x_(i) in [0,1] AA i = 1, 2, 3, ..,...
2 Answers 1 views
The value of `sin^(-1)[xsqrt(1-x)-sqrt(x)sqrt(1-x^2)]` is equal to `sin^(-1)x+sin^(-1)sqrt(x)` `sin^(-1)x-sin^(-1)sqrt(x)` `sin^(-1)sqrt(x)-sin^(-1)x`
Correct Answer - B Let `x = sin theta and sqrtx = sin phi, " where " x in [0, 1]` `rArr theta, phi in [0, pi//2]` `rArr theta - phi...
2 Answers 1 views
If ` A(3/sqrt(2), sqrt(2))`, `B(-3/sqrt(2), sqrt(2)), C(-3/sqrt(2), -sqrt(2))` and `D(3 cos theta , 2 sin theta)` are four points . If the area of the
Area of qudrilateral AbCD is maximum when area of ACD is maximum. Area of triangle ACD. `Delta_1=(1)/(2)||{:(3/sqrt2,,sqrt2,,),(3/sqrt2,,-sqrt2,,),(3sintheta,,2costheta,,),(3/sqrt2,,sqrt2,,):}||` `=|-3sqrt(2)costheta+3sqrt(2)sintheta|` `therefore Delta_1("max")=6`, when`theta=(7pi)/(4)` (as `theta epsilon(3pi//2,2pi`)) Maximum area is 12 sq.units (as...
2 Answers 1 views
If `y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x)),t h e n(dy)/(dx)i se q u a lto` `(a y)/(xsqrt(a^2-x^2))` (b) `(a y)/(sqrt(a^2-x^2))` `(a y)/(xsqrt(a
`y=(sqrt(a+x)-sqrt(a-x))/(sqrt(a+x)+sqrt(a-x))` `=((sqrt(a+x)-sqrt(a-x))^(2))/((a+x)-(a-x))` `=((a+x)+(a-x)-2(sqrt(a^(2)-x^(2))))/(2x)` `=(2a-2sqrt(a^(2)-x^(2)))/(2x)=(a-sqrt(a^(2)-x^(2)))/(x)" (1)"` Differentiating w.r.t. x, we get `(dy)/(dx)=(x[-(1)/(2sqrt(a^(2)-x^(2)))(-2x)]-(a-sqrt(a^(2)-x^(2))))/(x^(2))` `=(x^(2)-asqrt(a^(2)-x^(2)+a^(2)-x^(2)))/(x^(2)sqrt(a^(2)-x^(2)))=(a(a-sqrt(a^(2)-x^(2))))/(x^(2)sqrt(a^(2)-x^(2)))` `(a)/(xsqrt(a^(2)-x^(2)))[(a-sqrt(a^(2)-x^(2)))/(x)]=(ay)/(xsqrt(a^(2)-x^(2)))" [by (1)]"`
2 Answers 1 views
If `y=e^(sqrt(x))+e^(-sqrt(x))` , then `(dy)/(dx)i se q u a lto` `(e^(sqrt(x)))/(2sqrt(x))` (b) `(e^(sqrt(x))-e^(-sqrt(x)))/(2x)` `1/(2sqrt(x))sqrt(y^
`(dy)/(dx)=(e^(sqrt(x)))/(2sqrt(x))-(e^(-sqrt(x)))/(2sqrt(x))=(e^(sqrt(x)-)e^(-sqrt(x)))/(2sqrt(x))` `=(sqrt((e^(sqrt(x))+e^(-sqrt(x)))^(2))-4)/(2sqrt(x))` `=(sqrt(y^(2)-4))/(2sqrt(x))`
2 Answers 1 views
If `sqrt(2)=1.414, sqrt(3)=1.732` and `sqrt(5)=2.236`, find the values of the following. (i) `sqrt(98)` (ii) `sqrt(300)` (iii) `sqrt(128)+sqrt(48)` (i
Correct Answer - (i) 9.898 (ii) 17.32 (iii) 18.24 (iv) 6.928
2 Answers 1 views
Given `sqrt(2)=1.414, sqrt(3)=1.732, sqrt(5)=2.236`, find the value, correct to three decimals of the following `(1-sqrt(3))/(sqrt(5)-sqrt(2))`
Correct Answer - `-0.891`
2 Answers 1 views
Simplify :- (i)`(6)/(sqrt(2))` (ii)`(sqrt(3))/(3)` (iii)`sqrt((3)/(4))` (iv)`(6)/(sqrt(2))` (v)`(sqrt(5))/(10)` (vi)`sqrt((16)/(2))`
Correct Answer - (i)`sqrt(2)` (ii)`(1)/(sqrt(3))` (iii)`(sqrt(3))/(2)` (iv)`3sqrt(2)` (v)`(1)/(2sqrt(5))` (vi)`2sqrt(2)`
2 Answers 1 views
निम्नलिखित व्यंजको में से प्रत्येक व्यंजक को सरल कीजिए : (i) `(3+sqrt(3)) (2+sqrt(2))` (ii) `(3+sqrt(3))(3-sqrt(3))` (iii) `(sqrt(5)+sqrt(2))^(2)` (iv
Correct Answer - (i) `6+3sqrt(2) +2sqrt(3)+sqrt(6)" "`(ii) 6`" "` (iii) `7+2sqrt(10) " "` (iv) 3
2 Answers 1 views
निम्नलिखित के हरो का परिमेयकरण कीजिए : (i) `(1)/(sqrt(7))` `(ii) (1)/(sqrt(7)-sqrt(6))` (iii) `(1)/(sqrt(5)+sqrt(2))` (iv) `(1)/(sqrt(7)-2)`
Correct Answer - (i) `(sqrt(7))/(7)" "` (ii) `sqrt(7)+sqrt(6) " " ` (iii) `(sqrt(5)-sqrt(2))/(3) " " ` (iv) ` (sqrt(7)+2)/(3)`
2 Answers 1 views