Home
Class 11
MATHS
If a , b in [0,2pi] and the equation x^...

If `a , b in [0,2pi]` and the equation `x^2+4+3sin(a x+b)-2x=0` has at least one solution, then the value of `(a+b)` can be (a)`(7pi)/2` (b) `(5pi)/2` (c) `(9pi)/2` (d) none of these

A

`(7pi)/2`

B

`(5pi)/2`

C

`(9pi)/2`

D

none of these

Text Solution

Verified by Experts

`x^(2)+4-2x+3 sin (ax+b)=0`
`(x-1)^(2)+3=-3 sin (ax+b)`
`L.H.S. ge 3` and `R.H.S. le 3`
`rArr L.H.S. = R.H.S.=3`
`(x-1)^(2)+3+3 sin (ax+b)=0`
`rArr x=1, sin (ax+b)=-1`
`rArr sin (a+b)=-1`
`rArr a+b=(4n-1) pi/2, n in I`
`rArr a+b=(7 pi)/2` (from the given options)
Promotional Banner

Similar Questions

Explore conceptually related problems

If f(x)=sin^(-1)cosx , then the value of f(10)+f^(prime)(10) is (a) 11-(7pi)/2 (b) (7pi)/2-11 (c) (5pi)/2-11 (d) none of these

If the equation x^(2)+12+3sin(a+bx)+6x=0 has atleast one real solution, where a, b in [0,2pi] , then the value of a - 3b is (n in Z)

If x , y in [0,2pi]a n dsinx+siny=2, then the value of x+y is pi (b) pi/2 (c) 3pi (d) none of these

The principal value of sin^(-1)(sin((2pi)/3)) is (a) -(2pi)/3 (b) (2pi)/3 (c) (pi)/3 (d) (5pi)/3 (e) none of these

The range of f(x)=sin^(-1)((x^2+1)/(x^2+2)) is [0,pi/2] (b) (0,pi/6) (c) [pi/6,pi/2] (d) none of these

x=tcost ,y=t+sintdot Then (d^(2x))/(dy^2)at t=pi/2 is (a)(pi+4)/2 (b) -(pi+4)/2 (c) -2 (d) none of these

The least and the greatest values of (sin^(-1)x)^3+(cos^(-1)x)^3 are (a) (-pi)/2,pi/2 (b) (-pi^3)/8,(pi^3)/8 (c) (pi^3)/(32),(7pi^3)/8 (d) none of these

If 2|sin2alpha|=|tanbeta+cotbeta|,alpha,beta in (pi/2,pi), then the value of alpha+beta is (a) (3pi)/4 (b) pi (c) (3pi)/2 (d) (5pi)/4

If the equation sin^2 x-a sin x + b = 0 has only one solution in (0, pi) then which of the following statements are correct?

If cos3x+sin(2x-(7pi)/6)=-2 , then x is equal to (k in Z) pi/3(6k+1) (b) pi/3(6k-1) pi/3(2k+1) (d) none of these