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Let f(x)=|cosx x 1 2sinx x2xsinx x x| , ...

Let `f(x)=|cosx x 1 2sinx x2xsinx x x|` , then `(lim)_(x->0)(f(x))/(x^2)` is equal to (a) 0 (b) -1 (c) 2 (d) 3

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`f(x)=[[cos x, x , 1], [2 sin x, x, 2 x], [sin x, x , x]]`
`R_{2} -> R_{2}-2 R_{3} `
`f(x)=[[cos x, x, 1],[ sin x , 0 , x] , ...
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RD SHARMA-DETERMINANTS-Solved Examples And Exercises
  1. If the determinant |[a ,b,2a alpha+3b],[b ,c, 2b alpha+3c],[2a alpha+3...

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  2. If 1.omega, omega^2 are the roots of unity, then Delta=|(1,omega^n,ome...

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  3. If a >0 and discriminant of a x^2+2b x+c is negative, then |[a,b,ax+...

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  4. The value of /\=|[5^2, 5^3, 5^4],[ 5^3, 5^4, 5^5],[ 5^4, 5^5, 5^6]| is...

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  5. |(log)3 512(log)4 3(log)3 8(log)4 9|xx|(log)2 3(log)8 3(log)3 4(log)3 ...

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  6. If a, b, c, are in A.P, then the determinant|x+2x+3x+2a x+3x+4x+2b x+4...

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  7. If A+B+C=pi, then the value of [[sin(A+B+C) , sin(A+C) , cosC],[-sinB...

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  8. The number of distinct real roots of |{:(cosec x, secx, secx), (secx...

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  9. Let A=[[1,sintheta,1],[sintheta,1,sintheta],[-1,-sintheta,1]] where 0l...

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  10. If |(2,x,5, 8,x)|=|(6,-2, 7, 3)| , then x= (a) 3 (b) +-3 (c) +-6 (d) ...

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  11. If f(x)=|0x-a x-b x+a0x-c x+b x+c0|,t h e n f(x)=0 (b) f(b)=0 (c) f...

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  12. If x , y , z are different from zero and [[1+x,1, 1],[ 1 ,1+y,1 ],[1 ,...

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  13. The determinant |{:(b^2-ab, b-c, bc-ac), (a b-a^2, a-b, b^2-ab) ,(b c-...

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  14. If x , y in R , then the determinant =|cosx-sinx1sinxcosx1cos(x+y)-si...

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  15. The maximum value of =[[1, 1, 1],[ 1, 1+sintheta,1],[ 1,1,1+costheta]...

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  16. The value of the determinant [[x,x+y, x+2y],[ x+2y, x,x+y],[ x+y, x+2y...

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  17. Let f(x)=|cosx x 1 2sinx x2xsinx x x| , then (lim)(x->0)(f(x))/(x^2) i...

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  18. If there are two values of a which makes determinant, Delta=|(1,-2,5...

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  19. If Delta=|(a,p,x),(b,q,y),(c,r,z)|=16 then Delta(1)=|(p+x,a+x,a+p),(q+...

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  20. The value of |1 1 1\ ^n C1\ ^(n+2)C1\ ^(n+4)C1\ ^n C2\ ^(n+2)C2\ ^(n+4...

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