Related InterviewSolutions

• Find the number of solution of `theta in [0,2pi]`satisfying the equation `((log)_(sqrt(3))tantheta(sqrt((log)_(tantheta)3+(log)_(sqrt(3))3sqrt(3)=-1)`A. `theta =(pi)/(6)`B. `(pi)/(3),(5pi)/(3)`C. has sum `(4pi)/(3)`D. `gt 2 `
• If `xsina+ysin2a+zsin3a=sin4a``xsinb+ysin2b+zsin3b=sin4b``xsinc+ysin2c+zsin3c=sin4c`then the roots of the equation `t^3-(z/2)t^2-((y+2)/4)t+((z-x)/8)=0,a , b , c ,!=npi,`are`sina ,sinb ,sinc`(b) `cosa ,cosb ,cosc``sin2a ,sin2b ,sin2c`(d) `cos2a ,cos2bcos2c`A. sin a , sin b , sin cB. cos a, cos b , cos cC. sin 2a , sin 2b , sin 2cD. cos 2a , cos 2b , cos 2c
• Let `n`be a positive integer such that `sinpi/(2n)+cospi/(2n)=(sqrt(n))/2dot`Then`6lt=nlt=8`(b) `4A. `6 le n le 8`B. `4 lt n le 8`C. `6 lt n lt 8`D. `4 lt n lt 8`
• Let `log_(a)N=alpha + beta` where ` alpha ` is integer and ` beta =[0,1)`. Then , On the basis of above information , answer the following questions. If `N_1` is number of integers when a=2 and `alpha=2` and `N_2` is number of integers when ` alpha=1 and a=3` , then the minimum value of `(N_1 sec^(2) theta +N_(2) "cosec"^2 theta )A. `10+4sqrt(6)`B. `10+sqrt(6)`C. `10`D. 100
• In the interval `[-pi/2,pi/2] `the equation `log_(sin theta)(cos 2 theta)=2` hasA. no solutionB. a unique solutionC. two solutionD. infinitely many solution
• If the equation `sin^4x-(k+2)s in^2x-(k+3)=0`has a solution then `k`must lie in the interval`(-4,-2)`(b) `[-3,2)``(-4,-3)`(d) `[-3,-2]`A. ` k gt -3 `B. `k lt -2 `C. `-3 le k le -2 `D. `k ` is any (+ve) value
• The solution of the equation ` sin 2x + sin 4x = 2 sin 3x ` isA. `x=(npi)/3`B. `x=npi `C. `x=2npi `D. None of the above
• The general solution of ` 4sin^(4) x + cos^(4) x=1 ` isA. `(2n+1)""(pi)/(2)`B. `npi`C. `npi pm sin^(-1)sqrt((2)/(5))`D. None of these
• General solution of `tan theta+tan 4 theta+tan 7 theta=tan theta tan 4 theta tan 7 theta` isA. `theta =(n pi )/4`B. `theta =(n pi )/(12) `C. `theta=(n pi )/12`D. None of these
• If number of solution and sum of solution of the equation ` 3sin^(2)x-7sinx +2=0, x in [0,2pi]` are respectively N and S and ` f_(n)(theta)=sin^(n)theta +cos^(n) theta`. On the basis of above information , answer the following questions. If ` alpha ` is solution of equation ` 3sin^(2)x-7sinx+2=0, x in [0,2pi]`, then the value of `f_(4)(alpha)` isA. `(97)/(81)`B. `(57)/(81)`C. `(65)/(81)`D. 0