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10th Maths Monthly Test -Algebra

St. Britto Hr. Sec. School - Madurai

10th Maths Monthly Test -Algebra-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The square root of \(\frac { 256{ x }^{ 8 }{ y }^{ 4 }{ z }^{ 10 } }{ 25{ x }^{ 6 }{ y }^{ 6 }{ z }^{ 6 } } \) is equal to

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

If A = \(\left( \begin{matrix} 1 & 2 & 3 \\ 3 & 2 & 1 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 0 \\ 2 & -1 \\ 0 & 2 \end{matrix} \right) \) and C = \(\left( \begin{matrix} 0 & 1 \\ -2 & 5 \end{matrix} \right) \), Which of the following statements are correct?
(i) AB +C = \(\left( \begin{matrix} 5 & 5 \\ 5 & 5 \end{matrix} \right) \)
(ii) BC = \(\left( \begin{matrix} 0 & 1 \\ 2 & -3 \\ -4 & 10 \end{matrix} \right) \)
(iii) BA + C = \(\left( \begin{matrix} 2 & 5 \\ 3 & 0 \end{matrix} \right) \)
(iv) (AB)C = \(\left( \begin{matrix} -8 & 20 \\ -8 & 13 \end{matrix} \right) \)

(i) and (ii) only
(ii) and (iii) only
(iii) and (iv) only
all of these

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

2 x 3
3 x 2
3 x 4
4 x 3

A Quadratic polynomial whose one zero is 5 and sum of the zeroes is 0 is given by

x²-25
x²-5
x²-5x
x²-5x+5

Choose the correct answer
(i) Every scalar matrix is an identity matrix
(ii) Every identity matrix is a scalar matrix
(iii) Every diagonal matrix is an identity matrix
(iv) Every null matrix is a scalar matrix

(i) and (iii) only
(iii) only
(iv) only
(ii) and (iv) only

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

3
4
2
5

If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is

3
5
6
8

Which of the following can be calculated from the given matrices A = \(\left( \begin{matrix} 1 & 2 \\ 3 & 4 \\ 5 & 6 \end{matrix} \right) \), B = \(\left( \begin{matrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{matrix} \right) \),
(i) A²
(ii) B²
(iii) AB
(iv) BA

(i) and (ii) only
(ii) and (iii) only
(ii) and (iv) only
all of these

If \(A=\left[ \begin{matrix} y & 0 \\ 3 & 4 \end{matrix} \right] \) and \(I=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \) then A²=16I for:

y=4
y=5
y=-4
y=16

The product of the sum and product of roots of equation
(a²-b²)x2-(a+b)²x+(a³-b³)=0 is

\(\cfrac { { a }^{ 2 }+ab+{ b }^{ 2 } }{ (a-b) } \)
\(\cfrac { a-b }{ a+b } \)
\(\cfrac { a-b }{ a+b } \)
\(\cfrac { a-b }{ { a }^{ 2 }+ab+{ b }^{ 2 } } \)

Part - B

Generic 2 - Answer All Question

If A = \(\left[ \begin{matrix} 2 & 1 \\ 1 & 3 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 3 \end{matrix} \right] \) find AB and BA. Check if AB = BA

Solve 3x + y -3z = 1; -2x - y + 2z = 1; -x - y + z = 2.

Reduce the rational expressions to its lowest form
\(\frac { { x }^{ 2 }-16 }{ { x }^{ 2 }+8x+16 } \)
If α and β are the roots of x² + 7x + 10 = 0 find the values of
\(\frac { \alpha }{ \beta } +\frac { \beta }{ \alpha } \)

Using quadratic formula solve the following equations.
p²x² + (P² -q²) X - q² = 0

In an interschool atheletic meet, with 24 individual events, securing a total of 56 points, a first place secures 5 points, a second place secures 3 points, and a third place secures 1 point. Having as many third place finishers as first and second place finishers, find how many athletes finished in each place.

If α and β are the roots of x² + 7x + 10 = 0 find the values of
α³ - β³

If α, β are the roots of the equation 3x² + 7x - 2 = 0, find the values of
\(\frac { { \alpha }^{ 2 } }{ \beta } +\frac { { \beta }^{ 2 } }{ \alpha } \)

Find the excluded values of the following expressions (if any).
\(\frac { 7p+2 }{ 8{ p }^{ 2 }+13p+5 } \)

If α, β are the roots of the equation 2x² - x - 1 = 0, then form the equation whose roots are
2α + β, 2β + α

Find the value of a, b, c, d from the equation \(\left( \begin{matrix} a-b & 2a+c \\ 2a-b & 3c+d \end{matrix} \right) =\left( \begin{matrix} 1 & 5 \\ 0 & 2 \end{matrix} \right) \)

Part - C

Generic 5 - Answer All Question

Determine the nature of roots for the following quadratic equations
x² - x - 20 = 0

If A = \(\left[ \begin{matrix} 5 & 4 & -2 \\ \frac { 1 }{ 2 } & \frac { 3 }{ 4 } & \sqrt { 2 } \\ 1 & 9 & 4 \end{matrix} \right] \), B = \(\left[ \begin{matrix} -7 & 4 & -3 \\ \frac { 1 }{ 4 } & \frac { 7 }{ 2 } & 3 \\ 5 & -6 & 9 \end{matrix} \right] \), find 4A - 3B.
Find the sum and product of the roots for each of the following quadratic equations:
x² + 8x - 65 = 0

Find the LCM of the following
8x⁴y², 48x²y⁴

Discuss the nature of solutions of the following quadratic equations.
x² + x - 12 = 0

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