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Each question has four choices a, b, c and d, out of which only one is correct. Each question contains STATEMENT 1 and STATEMENT 2.
Both the statements are TRUE and STATEMENT 2 is the correct explanation of STATEMENT1.
Both the statements are TRUE but STATEMENT 2 is NOT the correct explanation of STATEMENT 1.
STATEMENT 1 is TRUE and STATEMENT 2 is FALSE.
STATEMENT 1 is FALSE and STATEMENT 2 is TRUE.
Statement 1: if `A ,B ,C` are the angles of a triangles and `|[1, 1, 1], [ 1+sin A ,1+sinB, 1+sin C], [ sin A+sin^2A, sin B+sin^2B,sin C+sin^2C]|=0` , then triangle may not be equilateral
Statement 2: if any two rows of a determinant are the same, then the value of that determinant is zero.

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CENGAGE ENGLISH-DETERMINANTS-All Questions
  1. Consider the system of the equation k x+y+z=1,x+k y+z=k ,a n dx+y+k z=...

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  2. If x+y+z=0 prove that |[a x, b y, c z],[ c y, a z ,b x],[ b z ,c x ,a ...

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  3. Each question has four choices a, b, c and d, out of which only one is...

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  4. If a ,b ,c in R , then find the number of real roots of the equat...

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  5. Delta = |(a, a^2, 0),(1, 2a+b,(a+b)),(0, 1, 2a+3b)| is divisible by a....

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  6. Without expanding at any stage, prove that the value of each of the...

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  7. If a,b,c are positive and are the pth, qth rth terms respectively of a...

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  8. If the entries in a 3xx3 determinant are either 0 or 1, then the grea...

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  9. The value of the determinant of n^(t h) order, being given by |[x, 1, ...

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  10. Prove that a!=0,|[x+a, x,x],[x,x+a,x],[x,x,x+a^2]|=0 represents a stra...

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  11. If =|[a b c, b^2c,c^2b],[ a b c,c^2a, c a^2],[a b c, a^2b,b^2a]|=0,(a ...

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  12. The value of |[yz, z x,x y],[ p,2p,3r],[1, 1, 1]|,w h e r ex ,y ,z ar...

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  13. Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a ...

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  14. If x!=0,y!=0,z!=0 and |[1+x,1,1],[1+y,1+2y,1],[1+z,1+z,1+3z]|=0, then ...

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  15. If x!=y!=za n d|[x,x^2, 1+x^3],[y ,y^2 ,1+y^3],[z, z^2, 1+z^3]|=0, th...

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  16. Prove that |2alpha+beta+gamma+deltaalphabeta+gammadelta alpha+beta+g...

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  17. Solve for x , |[x,-6,-1], [ 2,-3x,x-3], [-3, 2x, x+2]|=0.

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  18. The value of the determinant |{:(1,,1,,1),(.^(m)C(1),,.^(m+1)C(1),...

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  19. Solve the equation |[a-x, c, b], [ c, b-x, a], [b, a, c-x]|=0 where a...

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  20. If a^2+b^2+c^2=-2a n df(x)= |1+a^2x(1+b^2)x(1+c^2)x(1+a^2)x1+b^2x(1+c...

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