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The value of the determinant |(1+a^(2)-...

The value of the determinant `|(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^(2),2a),(2b,-2a,1-a^(2)-b^(2))|` is equal to

A

0

B

`(1+a^(2)+b^(2))`

C

`(1+a^(2)+b^(2))^(2)`

D

`(1+a^(2)+b^(2))^(3)`

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|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," "2a),(" "2b," "-2a,1-a^2-b^2):}|=(1+a^2+b^2)^3

If a^(2) + b^(2) + c^(2) + ab + bc + ca le 0 for all, a, b, c in R , then the value of the determinant |((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))| , is equal to

Factorise : 1-a^(2)+2ab-b^(2)

Factorise : a^(2)-ab+b^(2)

By using properties of determinants. Show that: |1+a^2-b^2; 2ab; -2b: 2ab;1-a^2+b^2; 2a: 2b;-2a;1-a^2-b^2|=(1+a^2+b^2)^3

If a,b,c are in H.P , b,c,d are in G.P and c,d,e are in A.P. , then the value of e is (a) (ab^(2))/((2a-b)^(2)) (b) (a^(2)b)/((2a-b)^(2)) (c) (a^(2)b^(2))/((2a-b)^(2)) (d) None of these

prove that , |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|=-(a^3+b^3)^2

((a^(2)b^(-2))/(a^(-2)b^(2)))^(3)xx((ab^(-1))/(a^(-1)b))^(-2)

prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the value of the following determinant : |{:(2ab,a^2,b^2),(a^2,b^2,2ab),(b^2,2ab,a^2):}|

Factorise : (x-1)^(2)a^(2)+2(x^(2)+1)ab+(x+1)^(2)b^(2)

WB JEE PREVIOUS YEAR PAPER-QUESTION PAPER 2013-MULTIPLE CHOICE QUESTIONS
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  2. The value of 1000[(1)/(1xx2)+(1)/(2xx3)+(1)/(3xx4)+……+(1)/(999xx1000)]...

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  3. The value of the determinant |(1+a^(2)-b^(2),2ab,-2b),(2ab,1-a^(2)+b^...

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  5. For the curve x^(2)+4xy+8y^(2)=64 the tangents are parallel to the x-a...

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  6. The value of I=int(0)^((pi)/(4))(tan^(n+1)x)dx+(1)/(2)int(0)^((pi)/(2)...

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  7. Let f(theta)=(1+sin^(2)theta)(2-sin^(2)theta). Then for all values of ...

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  8. Let f(x)={{:(x^(3)-3x+2", "xlt2),(x^(3)-6x^(2)+9x+2", " x ...

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  9. The limit of sum(n=1)^(1000)(-1)^(e )x^(e ) as x to oo

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  10. If f(x)=e^(x)(x-2)^(2) then

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  11. Let f:R to R be such that f is injective and f(x)f(y)=f(x+y) for all x...

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  12. The number of solutions of the equation (1)/(2)log(sqrt(3))((x+1)/(x+5...

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  13. The area of the region bounded by the parabola y=x^(2)-4x+5 and the st...

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  14. The value of the integral int(1)^(2)e^(-x)(log(e )x+(x+1)/(x))dx is

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  15. Let P=1+(1)/(2xx2)+(1)/(3xx2^(2))+ …………. and Q=(1)/(1xx2)+(1)/(3xx4...

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  16. Let f(x)=sin x + 2 cos^(2)x, (pi)/(4)le x le (3pi)/(4). Then f attains...

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  17. Each of a and b can take value 1 or 2 with probability. The probabilit...

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  18. There are two coins, one unbiased with probability (1)/(2) of getting ...

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  19. For the variable t, the locus of the points of intersection of lines 3...

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  20. Cards are drawn one - by - one without replacement from a well shuffle...

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