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If f(x)=|{:(x,cosx,e^(x^2)),(1,2 cosx,1)...

If `f(x)=|{:(x,cosx,e^(x^2)),(1,2 cosx,1),(0,1,2 cosx):}|` then the value of `overset(pi//2)underset(-pi//2)int` f(x) dx is equal to

A

0

B

1

C

2

D

none of these

Text Solution

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The correct Answer is:
A
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FIITJEE-DETERMINANT-ASSIGNMENT PROBLEMS (OBJECTIVE) LEVEL-I
  1. If a,b,c are even natural numbers, then |{:(a-1,a,a+1),(b-1,b,b+1),(c-...

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  2. If f(x) =|{:(cosx,1,0),(1,2 cosx,1),(0,1,2 cosx):}|, "then" |overset(p...

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  3. If f(x)=|{:(x,cosx,e^(x^2)),(1,2 cosx,1),(0,1,2 cosx):}| then the valu...

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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 determinant Delta=|{:(a,b,aalpha+c),(b,c,balpha+c),(aalpha+b,balph...

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  6. If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then th...

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  7. The number of values of k for which the system of the equations (k+1)x...

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  8. The determinant Delta =|(a^2(1+x),ab,ac),(ab,b^2(1+x),bc), (ac,bc,c^2(...

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  9. If alpha , beta and gamma the roots of the equation x^2(px + q) = r(x...

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  10. If the system of equations x+a y=0,a z+y=0 and a x+z=0 has infinite so...

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  11. If A+B+C =pi , then the value of determinant |{:(sin^2A,cotA,1),(sin^2...

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

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

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

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

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

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