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## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.19

Multiple choice questions.

Question 1.

A system of three linear equations in three variables is inconsistent if their planes

(1) intersect only at a point

(2) intersect in a line

(3) coincides with each other

(4) do not intersect.

Solution:

(4) do not intersect

Question 2.

The solution of the system x + y – 3z = – 6, -7y + 7z = 7, 3z = 9 is …………

(1) x = 1, y = 2, z = 3

(2) x = -1, y = 2, z = 3

(3) x = -1, y = -2, z = 3

(4) x = 1, y = 2, z = 3

Answer:

(1) x = 1, y = 2, z = 3

Hint.

x + y – 3x = – 6 ….(1)

– 7y + 7z = 7 ….(2)

3z = 9 ….(3)

From (3) we get

z = \(\frac { 9 }{ 3 } \) = 3

Substitute the value of z in (2)

-7y + 7(3) = 7

-7y = -14

Substitute the value of y = 2 and z = 3 in (1)

x + 2 – 3(3) = -6

x + 2 – 9 = -6

x = -6 + 7

x = 1

The value of x = 1, y = 2 and z = 3

Question 3.

If (x – 6) is the HCF of x^{2} – 2x – 24 and x^{2} – kx – 6 then the value of k is

(1) 3

(2) 5

(3) 6

(4) 8

Solution:

(2) 5

Question 4.

Solution:

(1) \(\frac{9 y}{7}\)

Question 5.

\(\mathbf{y}^{2}+\frac{\mathbf{1}}{y^{2}}\) is not equal to

Solution:

(2) \(\left(y+\frac{1}{y}\right)^{2}\)

Hint:

\(y^{2}+\frac{1}{y^{2}} \neq\left[y+\frac{1}{y}\right]^{2}\)

Question 6.

Solution:

(3) \(\frac{x^{2}-7 x+40}{(x+5)(x-5)(x+1)}\)

Hint:

Question 7.

Solution:

(4) \(\frac{16}{5}\left|\frac{x z^{2}}{y}\right|\)

Hint:

Question 8.

Which of the following should be added to make x^{4} + 64 a perfect square ……….

(1) 4x^{2}

(2) 16x^{2}

(3) 8x^{2}

(4) -8x^{2}

Answer:

(2) 16x^{2}

Hint.

x^{2} + 64 = (x^{2})^{2} + 8^{2} – 2 × x^{2} × 8

= (x^{2} – 8)^{2}

2 × x^{2} × 8 must be added

i.e, 16x^{2} must be added

Question 9.

The solution of (2x – 1)^{2} = 9 is equal to

(1) -1

(2) 2

(3) -1, 2

(4) None of these

Solution:

(3) -1, 2

Hint:

(2x – 1)^{2} = (±3)^{2}

⇒ 2x – 1 = +3

2x – 1 = 3, 2x – 1 = – 3

2x = 4, 2x = – 2

x = 2,-1

Question 10.

The values of a and b if 4x^{4} – 24x^{3} + 76x^{2} + ax + b is a perfect square are

(1) 100, 120

(2) 10, 12

(3) -120, 100

(4) 12, 10

Solution:

(3) -120, 100

Hint:

Question 11.

If the roots of the equation q^{2}x^{2} + p^{2}x + r^{2} = 0 are the squares of the roots of the equation qx^{2} +px + r = 0, then q,p, r are in ______.

(1) A.P

(2) G.P

(3) Both A.P and G.P

(4) none of these

Solution:

(2) G.P

Hint: q^{2}x^{2} + p^{2}x + r^{2} = 0

(2) G.P.

Question 12.

Graph of a linear polynomial is a …………..

(1) straight line

(2) circle

(3) parabola

(4) hyperbola

Answer:

(1) straight line

Question 13.

The number of points of intersection of the T quadratic polynomial x^{2} + 4x + 4 with the X axis.

(1) 0

(2) 1

(3) 0 or 1

(4) 2

Solution:

(2) 1

(x + 2)^{2} = (x + 2)(x + 2)

= x = -2, -2 = 1

Question 14.

For the given matrix A = \(\left[\begin{array}{cccc}{1} & {3} & {5} & {7} \\ {2} & {4} & {6} & {8} \\ {9} & {11} & {13} & {15}\end{array}\right]\) the order of the matrix A^{T} is

(1) 2 × 3

(2) 3 × 2

(3) 3 × 4

(4) 4 × 3

Solution:

(3) 3 × 4

Hint:

Question 15.

If A is a 2 × 3 matrix and B is a 3 × 4 matrix, how many columns does AB have

(1) 3

(2) 4

(3) 2

(4) 5

Solution:

(2) 4

Hint:

Question 16.

If a number of columns and rows are not equal in a matrix then it is said to be a …………..

(1) diagonal matrix

(2) rectangular matrix

(3) square matrix

(4) identity matrix

Answer:

(2) rectangular matrix

Question 17.

Transpose of a column matrix is

(1) unit matrix

(2) diagonal matrix

(3) column matrix

(4) row matrix

Solution:

(4) row matrix

Question 18.

Solution:

(2) \(\left(\begin{array}{cc}{2} & {2} \\ {2} & {-1}\end{array}\right)\)

Hint:

Question 19.

Which of the following can be calculated from the given matrices

A = \(\left[\begin{array}{ll}{1} & {2} \\ {3} & {4} \\ {5} & {6}\end{array}\right]\), B = \(\left[\begin{array}{lll}{1} & {2} & {3} \\ {4} & {5} & {6} \\ {7} & {8} & {9}\end{array}\right]\)

(i) A^{2}

(ii) B^{2}

(iii) AB

(iv) BA

(1) (i) and (ii) only

(2) (ii) and (iiii) only

(3) (ii) and (iv) only

(4) all of these

Solution:

(3) (ii) and (iv) only

Hint:

Question 20.

(1) (i) and (ii) only

(2) (ii) and (iii) only

(3) (ii) and (iv) only

(4) all of these

Solution:

(1) (i) and (ii) only

Hint: