Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)...

Evaluate `|{:(.^(x)C_(1),,.^(x)C_(2),,.^(x)C_(3)),(.^(y)C_(1),,.^(y)C_(2),,.^(y)C_(3)),(.^(z)C_(1),,.^(z)C_(2),,.^(z)C_(3)):}|`

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`(1)/(12)xyz(x-y)(y-z)(z-x)`

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If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + ...+ C_(n)x^(n) , prove that (C_(1))/(2) + (C_(3))/(4) + (C_(5))/(6) + …= (2^(n)-1)/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + C_(3) x^(3) + …+ C_(n) x^(n) prove that (C_(0))/(1) + (C_(2))/(3) + (C_(4))/(5) + ...= (2^(n))/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n) , Show that (2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2))/((n+1)(n+2))

If A(x_(1), y_(1)), B(x_(2), y_(2)) and C (x_(3), y_(3)) are the vertices of a Delta ABC and (x, y) be a point on the internal bisector of angle A, then prove that b|(x,y,1),(x_(1),y_(1),1),(x_(2),y_(2),1)|+c|(x,y,1),(x_(1),y_(1),1),(x_(3),y_(3),1)|=0 where, AC = b and AB = c.

The order of the differential equation of family of curver y=C_(1)sin^(-1)x+C_(2)cos^(-1)x+C^(3)tan^(-1)x+C^(4)cot^(-1)x (where C_(1),C_(2),C_(3) and C_(4) are arbitrary constants) is

If (1 + x)^(n) = sum_(r=0)^(n) C_(r) x^(r),(1 + (C_(1))/(C_(0))) (1 + (C_(2))/(C_(1)))...(1 + (C_(n))/(C_(n-1))) is equal to

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(6) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

ARIHANT MATHS-DETERMINANTS -Exercise (Subjective Type Questions)

Prove that |{:(b+c,a,a),(b,c+a,b),(c,c,a+b):}| = 4 abc
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Prove: |[a-b-c,2a,2a],[2b,b-c-a,2b],[2c,2c,c-a-b]|=(a+b+c)^3
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Find the value of determinant |[sqrt((13))+sqrt(3),2sqrt(5),sqrt(5)],[...
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Find the value of the determinant |(bc,ca, ab),( p, q, r),(1, 1, 1)|,w...
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Without expanding the determinant at any stage prove that |{:(-5,3+5i...
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Prove without expansion that |{:(a h+bg,g,ab+ch), (bf+ba,f,hb+bc), (af...
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In a triangleABC, if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB...
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The value of |{:(betagamma,betagamma'+beta'gamma,beta'gamma'),(gammaal...
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If y=(u)/(v), where u & v are functions of 'x' show that v^(3)(d^(2)y)...
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Show that the determinant Delta(x) given by Delta(x) = |{:(sin(x+al...
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Evaluate |{:(.^(x)C(1),,.^(x)C(2),,.^(x)C(3)),(.^(y)C(1),,.^(y)C(2),,....
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Find maximum value of f(x)=|{:(1+sin^(2)x,cos^(2)x,4sin2x),(sin^(2)...
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If f(x) = |[x^2-4x+6,2x^2+4x+10,3x^2-2x+16],[x-2,2x+2,3x-1],[1,2,3]| t...
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If |A| = 2 and A = | (2x, 6) , (5x, 1)| then find the value of x
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Find the value of t for which the following system of equations has a ...
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Find dy/dx if y=13x-y^2
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If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx ...
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