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51.

Statement I The system of linear equations `x+(sin alpha )y+(cos alpha )z=0` `x+(cos alpha ) y+(sin alpha )z=0` `-x+(sin alpha )y-(cos alpha )z=0` has a not trivial solution for only one value of ` alpha ` lying between ` 0 and pi`. Statement II `|{:(sin x, cos x , cos x),( cos x , sin x , cos x) , (cos x , cos x , sin x ):}|=0` has no solution in the interval `-pi//4 lt x lt pi//4 ` .A. Statement I is true , Statement II is true , Statement II is a correct explanation for Statement I.B. Statement I is true , Statement II is true , Statement II is not a correct explanation for Statement II.C. Statement I is true , Statement II is falseD. Statement I is false , Statement II true .

Answer» Correct Answer - B
Discussion
52.

Statement I The number of solution of the equation `|sin x|=|x|` is only one. Statement II `|sin x| ge 0 AA x in R `.A. Statement I is true , Statement II is true , Statement II is a correct explanation for Statement I.B. Statement I is true , Statement II is true , Statement II is not a correct explanation for Statement II.C. Statement I is true , Statement II is falseD. Statement I is false , Statement II true .

Answer» Correct Answer - B
Discussion
53.

Let `theta ,phi in [0,2pi]` be such that `2 cos theta (1-sin phi)=sin^2 theta ((tan)theta/2+(cot)theta/2) cos phi -1, tan(2pi-theta) > 0 and -1 < sin theta < -sqrt3/2.` Then `phi` cannot satisfyA. `0 lt phi lt (pi)/2 `B. `(pi)/2 ltphi lt (4pi)/3`C. `(4pi)/3 lt phi lt (3pi)/2 `D. `(3pi)/2 lt phi lt 2pi `

Answer» Correct Answer - A::C::D
Discussion
54.

If `0 le x le 2pi`, then the number of real values of x, which satisfy the equation `cos x + cos 2x + cos 3x + cos 4x=0`, isA. 3B. 5C. 7D. 9

Answer» Correct Answer - C
Discussion
55.

The number of values of `theta`in the interval `(-pi/2,pi/2)`satisfying the equation `(sqrt(3))^sec^(2theta)=tan^4theta+2tan^2theta`is2 (b)4 (c) 0(d) 1A. 2B. 4C. 0D. 1

Answer» Correct Answer - A
Discussion
56.

Consider a circle , in which a point P is lying inside the circle such that `(PA)(PB)=(PC)(PD)` ( as shown in figure ) . On the basis of above information , answer the questions If `PA=| cos theta + sin theta | and PB=| cos theta - sin theta |`, then maximum value of (PC)(PD) , is equal toA. 1B. `2sqrt(2)`C. `sqrt(2)`D. `2`

Answer» Correct Answer - A
Discussion
57.

Consider a circle , in which a point P is lying inside the circle such that `(PA)(PB)=(PC)(PD)` ( as shown in figure ) . On the basis of above information , answer the questions Let PA=4 , PB=3 cm and CD is diameter of the circle having the length 8. If `PC gt CD` , then `(PC)/(PD) ` is equal toA. 3B. 4C. 5D. 6

Answer» Correct Answer - A
Discussion
58.

PA and PB are two tangents drawn from point P to circle of radius 5 . A line is drawn from point P which cuts at C and D such that PC=5 and PD=15 and ` angleAPB= theta `. On the basis of above information answer the questions .Number of solution(s) of the equation `log_(cos theta )(x+2)=2+3 log_((x+2)) sin""((5 theta )/(2))` is

Answer» Correct Answer - C
Discussion
59.

If `alpha in [-2pi, 2pi]` and `cos.(alpha)/(2)+sin.(alpha)/(2)=sqrt(2)(cos 36^(@)-sin18^(@))`, then a value of `alpha`A. `(7pi)/(6)`B. `(pi)/(6) `C. `-(5pi)/(6)`D. `-(pi)/(6)`

Answer» Correct Answer - A::D
Discussion
60.

The number of solutions of the equation ` cos 4x+6=7 cos 2x ` , when ` x in[315^(@),317^(@)]` is

Answer» Correct Answer - A
Discussion
61.

If ` tan((pi)/(2) sin theta )= cot((pi)/(2) cos theta )`, then ` sin theta + cos theta ` is equal to

Answer» Correct Answer - D
Discussion
62.

The equation `sin x + sin y + sin z = -3` for `0le x le2pi, 0le y le 2pi, 0le z le 2pi` hasA. one solutionB. two sets of solutionsC. four sets of solutionsD. no solutions

Answer» Correct Answer - A
Discussion