हिंदी

Select the correct option from the given alternatives: If |6i-3i143i-1203i| = x + iy then - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Select the correct option from the given alternatives:

If `|(6"i", -3"i", 1),(4, 3"i", -1),(20, 3, "i")|` = x + iy then

विकल्प

  • x = 3 , y = 1

  • x = 1 , y = 3

  • x = 0 , y = 3

  • x = 0 , y = 0

MCQ

उत्तर

x = 0 , y = 0

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Determinants and Matrices - Miscellaneous Exercise 4(A) [पृष्ठ ७६]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] 11 Standard Maharashtra State Board
अध्याय 4 Determinants and Matrices
Miscellaneous Exercise 4(A) | Q I. (8) | पृष्ठ ७६

संबंधित प्रश्न

Using properties of determinants, prove that `|[2y,y-z-x,2y],[2z,2z,z-x-y],[x-y-z,2x,2x]|=(x+y+z)^3`


 

If ` f(x)=|[a,-1,0],[ax,a,-1],[ax^2,ax,a]| ` , using properties of determinants find the value of f(2x) − f(x).

 

 

Using properties of determinants, prove that 

`|[b+c,c+a,a+b],[q+r,r+p,p+q],[y+z,z+x,x+y]|=2|[a,b,c],[p,q,r],[x,y,z]|`

 

Using the property of determinants and without expanding, prove that:

`|(2,7,65),(3,8,75),(5,9,86)| = 0`


Using the property of determinants and without expanding, prove that:

`|(1, bc, a(b+c)),(1, ca, b(c+a)),(1, ab, c(a+b))| = 0`


By using properties of determinants, show that:

`|(-a^2, ab, ac),(ba, -b^2, bc),(ca,cb, -c^2)| = 4a^2b^2c^2`


By using properties of determinants, show that:

`|(1,1,1),(a,b,c),(a^3, b^3,c^3)|` = (a-b)(b-c)(c-a)(a+b+c)


By using properties of determinants, show that:

`|(x+y+2z, x, y),(z, y+z+2z,y),(z,x,z+x+2y)| = 2(x+y+z)^3`


Evaluate `|(1,x,y),(1,x+y,y),(1,x,x+y)|`


Using properties of determinants, prove that

`|(sin alpha, cos alpha, cos(alpha+ delta)),(sin beta, cos beta, cos (beta + delta)),(sin gamma, cos gamma, cos (gamma+ delta))| = 0`


Using properties of determinants, prove that `|(1,1,1+3x),(1+3y, 1,1),(1,1+3z,1)| = 9(3xyz + xy +  yz+ zx)`


Using properties of determinants, prove 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`


Using properties of determinants, prove the following :

\[\begin{vmatrix}1 & a & a^2 \\ a^2 & 1 & a \\ a & a^2 & 1\end{vmatrix} = \left( 1 - a^3 \right)^2\].

Using properties of determinants, prove that:

`|(a,b,b+c),(c,a,c+a),(b,c,a+b)|` = (a+b+c)(a-c)2 


Using properties of determinants, prove the following:

`|(a, b,c),(a-b, b-c, c-a),(b+c, c+a, a+b)| = a^3 + b^3 + c^3 - 3abc`.


Without expanding determinants, find the value of `|(2014, 2017, 1),(2020, 2023, 1),(2023, 2026, 1)|`


Without expanding evaluate the following determinant:

`|(2, 7, 65),(3, 8, 75),(5, 9, 86)|`


If `|("x"^"k", "x"^("k" + 2), "x"^("k" + 3)),("y"^"k", "y"^("k" + 2), "y"^("k" + 3)),("z"^"k", "z"^("k" + 2), "z"^("k" + 3))|` = (x - y) (y - z) (z - x)`(1/"x"+ 1/"y" + 1/"z") ` then


Answer the following question:

By using properties of determinant prove that `|(x + y, y + z, z + x),(z, x, y),(1, 1, 1)|` = 0


Evaluate: `|("a" - "b" - "c", 2"a", 2"a"),(2"b", "b" - "c" - "a", 2"b"),(2"c", 2"c", "c" - "a" - "b")|`


Prove that: `|(y + z, z, y),(z, z + x, x),(y, x, x + y)|` = 4xyz


If A + B + C = 0, then prove that `|(1, cos"c", cos"B"),(cos"C", 1, cos"A"),(cos"B", cos"A", 1)|` = 0


The number of distinct real roots of `|(sinx, cosx, cosx),(cosx, sinx, cosx),(cosx, cosx, sinx)|` = 0 in the interval `pi/4  x ≤ pi/4` is ______.


If cos2θ = 0, then `|(0, costheta, sin theta),(cos theta, sin theta,0),(sin theta, 0, cos theta)|^2` = ______.


If the value of a third order determinant is 12, then the value of the determinant formed by replacing each element by its co-factor will be 144.


The determinant `abs (("a","bc","a"("b + c")),("b","ac","b"("c + a")),("c","ab","c"("a + b"))) =` ____________


If the ratio of the H.M. and GM. between two numbers a and bis 4 : 5, then a: b is


A system of linear equations represented in matrix form Ax = 0, A is n × n matrix, has a non-zero solution if the determinant of A (i.e., det(A)) is


In a third order matrix B, bij denotes the element in the ith row and jth column. If

bij = 0 for i = j

= 1 for > j

= – 1 for i < j

Then the matrix is


The A.M., H.M. and G.M. between two numbers are `144/15`, 15 and 12, but not necessarily in this order then, H.M., G.M. and A.M. respectively are


The value of the determinant `|(6, 0, -1),(2, 1, 4),(1, 1, 3)|` is ______.


Without expanding evaluate the following determinant.

`|(1, a, a + c),(1, b, c + a),(1, c, a + b)|`


Without expanding determinants, find the value of  `|(10, 57, 107), (12, 64, 124), (15, 78, 153)|`


By using properties of determinant prove that

`|(x+y,y+z,z+x),(z,x,y),(1,1,1)|=0`


By using properties of determinants, prove that 

`|(x+y, y+z, z+x),(z, x, y),(1, 1, 1)|` = 0 


if `|(a, b, c),(m, n, p),(x, y, z)| = k`, then what is the value of `|(6a, 2b, 2c),(3m, n, p),(3x, y, z)|`?


Without expanding determinant find the value of `|(10, 57, 107),(12, 64, 124),(15, 78, 153)|`


By using properties of determinant prove that `|(x+y,y+z,z+x),(z,x,y),(1,1,1)|` = 0.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×