HSC Science (General) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove that `|(x + y, y + z, z + x),(z + x, x + y, y + z),(y + z, z + x, x + y)| = 2|(x, y, z),(z, x, y),(y, z, x)|`

Using properties of determinant show that

`|("a" + "b", "a", "b"),("a", "a" + "c", "c"),("b", "c", "b" + "c")|` = 4abc

Using properties of determinant show that

`|(1, log_x y, log_x z),(log_y x, 1, log_y z),(log_z x, log_z y, 1)|` = 0

Solve the following equation: 

`|(x + 2, x + 6, x - 1),(x + 6, x - 1, x + 2),(x - 1, x + 2, x + 6)|` = 0

If  `|(4 + x, 4 - x, 4 - x),(4 - x,4 + x,4 - x),(4 - x,4 - x, 4 + x)|` = 0, then find the values of x.

Without expanding determinants show that

`|(1, 3, 6),(6, 1, 4),(3, 7, 12)| + 4|(2, 3, 3),(2, 1, 2),(1, 7, 6)| = 10|(1, 2, 1),(3, 1, 7),(3, 2, 6)|`

Select the correct option from the given alternatives:

The determinant D = `|("a", "b", "a" + "b"),("b", "c", "b" + "c"),("a" + "b", "b" + "c", 0)|` = 0 if

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

Select the correct option from the given alternatives:

Let D = `|(sintheta*cosphi, sintheta*sinphi, costheta),(costheta*cosphi, costheta*sinphi, -sintheta),(-sintheta*sinphi, sintheta*cosphi, 0)|` then

Select the correct option from the given alternatives:

The value of a for which system of equation a³x + (a + 1)³ y + (a + 2)³z = 0 ax + (a +1)y + (a + 2)z = 0 and x + y + z = 0 has non zero Soln. is

Select the correct option from the given alternatives:

`|("b" + "c", "c" + "a", "a" + "b"),("q" + "r", "r" + "p", "p" + "q"),(y + z, z + x, x + y)|` = 

Select the correct option from the given alternatives:

The system 3x – y + 4z = 3, x + 2y – 3z = –2 and 6x + 5y + λz = –3 has at least one Solution when

Select the correct option from the given alternatives:

If x = –9 is a root of `|(x, 3, 7),(2, x, 2),(7, 6, x)|` = 0 has other two roots are

Select the correct option from the given alternatives:

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

Select the correct option from the given alternatives:

Which of the following is correct

Answer the following question:

Evaluate `|(2, 3, 5),(400, 600, 1000),(48, 47, 18)|` by using properties

Answer the following question:

Evaluate `|(101, 102, 103),(106, 107, 108),(1, 2, 3)|` by using properties

Answer the following question:

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

Answer the following question:

Without expanding determinant show that

`|("b" + "c", "bc", "b"^2"c"^2),("c" + "a", "ca", "c"^2"a"^2),("a" + "b", "ab", "a"^2"b"^2)|` = 0

Answer the following question:

Without expanding determinant show that

`|(x"a", y"b", z"c"),("a"^2, "b"^2, "c"^2),(1, 1, 1)| = |(x, y, z),("a", "b", "c"),("bc", "ca", "ab")|`