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If A, B, C are angle of a triangle ABC,...

If `A, B, C` are angle of a triangle `ABC`, then the value of the determinant `|(sin (A/2), sin (B/2), sin (C/2)), (sin(A+B+C), sin(B/2), cos(A/2)), (cos((A+B+C)/2), tan(A+B+C), sin (C/2))|` is less than or equal to

A

`1//2`

B

`1//4`

C

`1//8`

D

none of these

Text Solution

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The correct Answer is:
C
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FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If A+B+C =pi , then the value of determinant |{:(sin^2A,cotA,1),(sin^2...

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  2. For A=a^2+b^2+c^2,B=ab+bc+ca,(a^3,b^3c^3-3abc)^2 is equal to

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  3. If A, B, C are angle of a triangle ABC, then the value of the determi...

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  4. If the expression |{:(x^2+x+3,1,4),(2x^4+x^3+2x+1,2,3),(x^2+x,1,1):}| ...

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  5. The sum of two non integral roots of |{:(x,2,5),(3,x,3),(5,4,x):}|=0 i...

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  6. |[1,1,1] , [(2^x+2^(-x))^2, (3^x+3^(-x))^2, (5^x+5^(-x))^2] , [(2^x-2^...

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  7. There are three points (a,x) ,(b,y) and (c,z) such that the straight l...

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  8. If |{:(overset(n-2)underset(k=0)sum1,n(n-1),n^2),(overset(n)underset(k...

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  9. Delta=|{:(1+a^2+a^4,1+ab+a^2b^2,1+ac+a^2c^2),(1+ab+a^2b^2,1+b^2+b^4,1+...

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  10. If A(x1, y1), B (x2, y2) and C (x3, y3) are the vertices of a DeltaABC...

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  11. The number of distinct real roots of |s in x cos x cos x cos x s in x ...

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  12. If f(x) =("In"x)/x "then" |{:("In"x,x,0),(1//x,1,x),(-1//x^2,0,2):}| i...

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  13. Statement 1: If the system of equation lambdax+(b-a)y+(c-a)z=0,(a-b)x+...

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  14. If Ir^2+mr^2+nr^2=1 where r=1,2,3 and I1I2+m1m2+n1n2=0 …..etc. then ...

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  15. If alpha is a root of x^4 = 1 with negative principal argument then th...

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  16. If a, b gt 0 and Delta (x)|(x,a,a),(b,x,a),(b,b,x)|, then

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  17. If f(x)=|{:(cos(x+alpha),cos(x+beta),cos(x+gamma)),(sin(x+alpha),sin(x...

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  18. The value of f(pi/6) where f(theta)=|{:(cos^2theta,costhetasintheta,-s...

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  19. The system of equation 102x-95y+88z=81,3x+10y+17z=24, 57x+50y+43z=36 h...

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  20. IF ax^3+bx^2+cx+d=|(x^2,(x-1)^2, (x-2)^2),((x-1)^2 (x-2)^2, (x-3)^2), ...

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