If `alt=3cosx+5sin(x-pi/6)lt=b` for all `x` then `(a , b)` is (a)`(-sqrt(19),sqrt(19))` (b) `(-17 ,17)` (c) `(-sqrt(21),sqrt(21))` (b) none of these

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The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(2) (d) none of these

Which of the following is the value of sin 27^0-cos 27^0? (a) -(sqrt(3-sqrt(5)))/2 (b) (sqrt(5-sqrt(5)))/2 (c) -(sqrt(5)-1)/(2sqrt(2)) (d) none of these

If a<0,b>0, then sqrt(a)sqrt(b) is equal to (a) -sqrt(|a|b) (b) sqrt(|a|b)i (c) sqrt(|a|b) (d) none of these

The value of ("lim")_(xto2)(sqrt(1+sqrt(2+x))-sqrt(3))/(x-2)i s (a) 1/(8sqrt(3)) (b) 1/(4sqrt(3)) (c) 0 (d) none of these

If the vertices of a triangle are (sqrt(5,)0) , ( sqrt(3),sqrt(2)) , and (2,1) , then the orthocentre of the triangle is (sqrt(5),0) (b) (0,0) (c) (sqrt(5)+sqrt(3)+2,sqrt(2)+1) (d) none of these

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If cos28^0+sin28^0=k^3, t h e ncos17^0 is equal to (a) (k^3)/(sqrt(2)) (b) -(k^3)/(sqrt(2)) (c) +-(k^3)/(sqrt(2)) (d) none of these

The equation sin^4x-2cos^2x+a^2=0 can be solved if (a) -sqrt(3)lt=alt=sqrt(3) (b) sqrt(2)lt=alt=""sqrt(2) (c) -""1lt=alt=a (d) none of these