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|{:(101,103,105),(104,105,106),(107,108,...

`|{:(101,103,105),(104,105,106),(107,108,109):}|=0`

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Without expanding the determinants, prove that |(103, 115, 114), (111, 108, 106), (104, 113, 116)|+|(113, 116, 104), (108, 106, 111), (115, 114, 103)|=0

If the standard deviation of 1,2,3,4,5,6 and 7 is 2, then that of 101, 102, 103, 104, 105, 106 and 107 is _____.

If log_(10)2=0.30103, log_(10)3=0.47712 and log_(10)7=0.84510 find the values of log_(10)105

Solution set of ((x-1)^(101)(x-2)^(102)(x-3)^(103))/((x-1)^(201)(x+2)^(202)(x+3)^(203))>0 is

Angle made with the x-axis by a straight line drawn through (1, 2) so that it intersects x+y=4 at a distance (sqrt(6))/3 from (1, 2) is (a) 105^0 (b) 75^0 (c) 60^0 (d) 15^0

If z=(1)/(2)(sqrt(3)-i) , then the least possible integral value of m such that (z^(101)+i^(109))^(106)=z^(m+1) is

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is a. x-4y+6z=106 b. x-8y+13 z=103 c. x-4y+6z=110 d. x-8y+13 z=105

The plane 4x+7y+4z+81=0 is rotated through a right angle about its line of intersection with the plane 5x+3y+10 z=25. The equation of the plane in its new position is a. x-4y+6z=106 b. x-8y+13 z=103 c. x-4y+6z=110 d. x-8y+13 z=105

Find the sign of the values of tan113^0-cos107^0=a and tan107^0-cos105^0=b

Prove that 1 + (cos105^(@) + cos 165^(@))/(sin 105^(@) + sin 375^(@))= 0

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B
  1. |{:(441,442,443),(445,446,447),(449,450,451):}|=0

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  2. Prove |{:(cos(x-a),cos(x+a),cosx),(sin(x+a),sin(x-a),sinx),(cosa tan x...

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  3. |{:(101,103,105),(104,105,106),(107,108,109):}|=0

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  4. |{:(5^2,5^3,5^4),(5^3,5^4,5^5),(5^4,5^6,5^7):}|=0

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  5. |{:(1,alpha,alpha^2),(1,beta,beta^2),(1,gamma,gamma^2):}|=(alpha-beta)...

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  6. |{:(1,1,1),(a,b,c),(bc,ca,ab):}|=(a-b)(b-c)(c-a)

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  7. |{:(1,alpha,alpha^3),(1,beta,beta^3),(1,gamma,gamma^3):}|=(alpha-beta)...

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  8. |{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c,...

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  9. |{:(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=(b-c)(c-a)(a-b)(bc+ca+ab)

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  10. |{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)

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  11. |{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)

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  12. |{:(1+x,1,1),(1,1+y,1),(1,1,1+z):}|=xy+yz+zx+xyz

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  13. |{:(x+4,2x,2x),(2x,x+4,2x),(2x,2x,x+4):}|=(5x+4)(x-4)^2

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  14. |{:(1+a,1,1),(1,1+a,1),(1,1,1+a):}|=a^3+3a^2

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  15. |{:(1,b+c,b^2+c^2),(1,c+a,c^2+a^2),(1,a+b,a^2+b^2):}|=(b-c)(c-a)(a-b)

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  16. |{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|=?

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  17. |{:(-1,b,c),(a,-1,c),(a,b,-1):}|=(a+1)(b+1)(c+1)((a)/(a+1)+(b)/(b+1)+(...

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  18. |{:(x^2+y^2+1,x^2+2y^2+3,x^2+3y^2+4),(y^2+2,2y^2+6,3y^2+8),(y^2+1,2y^2...

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  19. |{:(" "3a," "-a+b,-a+c),(a-b," "3b," "c-b),(a-c," "b-c," "3c):}|...

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  20. |{:(x,a,b),(a,x,b),(a,b,x):}|=(x-a)(x-b)(x+a+b)

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