11th Maths Weekly Test-1( Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-1( Basic Algebra )-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

The solution 5x-1<24 and 5x+1 > -24 is

(4,5)
(-5,-4)
(-5,5)
(-5,4)

If x is real and k = \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

\(k\epsilon \left[ \frac { 1 }{ 3 } ,3 \right] \)
k ≥ 3
\(k\le \frac { 1 }{ 3 } \)
none of these

If a and b are roots of x² + x + 1 = 0 then the value of a² + b² =

1
-1
cannot be determined
0

The number of solution of x²+|x-1|=1 is

The value of log₃ 11.log₁₁ 13.log₁₃ 15log₁₅ 27.log₂₇ 81 is

The factors of the polynomial \(6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 } \) are

\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)
\((2x-5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)
\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x+1)\)
\((2x+5\sqrt { 3 } )(3\sqrt { 3 } x-1)\)

Let \(\alpha\) and \(\beta\) are the roots of a quadratic equation px² + qx + r = 0 then

\(\alpha +\beta=-{p\over r}\)
\(\alpha\beta={p\over r}\)
\(\alpha +\beta={-q\over p}\)
\(\alpha \beta =r\)

If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other then

a = b
a = c
ac = 1
b = c

The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

-2
-8
-4
-9

If \(\frac{1}{\sqrt{3}\times\sqrt{2}}=\sqrt{3}+a\) then a is

\(\sqrt{2}\)
-\(\sqrt{2}\)
\(\sqrt{\frac{3}{2}}\)
\(\sqrt{\frac{2}{3}}\)

Part - B

Generic 2 - Answer All Question

If log₂x+log₄x+log₈x=\(\frac{11}{6}\), find x

Are there two distinct irrational numbers such that their difference is a rational number? Justify.

Find the value of \(\frac { 2-\sqrt { 3 } }{ \sqrt { 3 } } \) when \(\sqrt { 3 } \) =1.732

Draw the graph for |x| < 3.

Part - C

Generic 3 - Answer All Question

Find the value of p for which the difference between the roots of the equation x²+px+8=0 is 2.

Simplify : \(\frac { 1 }{ 2+\sqrt { 3 } } +\frac { 3 }{ 4-\sqrt { 5 } } +\frac { 6 }{ 7-\sqrt { 8 } } \)

Determine the region in the plane determined by the inequalities.
\(2x+3y\le 6,\quad x+4y\le 4,\quad x\ge 0,\quad y\ge 0.\)

Solve |x-1| ≤5,|x|≥2

Part - D

Generic 5 - Answer All Question

Resolve into partial fractions \(\frac { { x }^{ 3 }-1 }{ { x }^{ 2 }+x+1 } \)

Show that \({{1}\over{3-\sqrt{8}}}-{{1}\over{\sqrt{8}-\sqrt{7}}}+{{1}\over{\sqrt{7}-\sqrt{6}}}-{{1}\over{\sqrt{6}-\sqrt{5}}}+{{1}\over{\sqrt{5}-2}}=5\)

Evaluate \(\sqrt [ 3 ]{ {{{(45.4)}^{2}}\over{{(3.2)}^{2}}\times{(6.5)}^{2}} } \)

Find the square root of 7-4\(\sqrt{3}\)

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11th Maths Weekly Test-1( Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test-1( Basic Algebra )-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

The solution 5x-1<24 and 5x+1 > -24 is

If x is real and k = \(\frac { { x }^{ 2 }-x+1 }{ { x }^{ 2 }+x+1 } \) then

If a and b are roots of x2 + x + 1 = 0 then the value of a2 + b2 =

The number of solution of x2+|x-1|=1 is

The value of log3 11.log11 13.log13 15log15 27.log27 81 is

The factors of the polynomial \(6\sqrt { { 3x }^{ 2 } } -47x+5\sqrt { 3 } \) are

Let \(\alpha\) and \(\beta\) are the roots of a quadratic equation px2 + qx + r = 0 then

If one root of the quadratic equation ax2 + bx + c = 0 is the reciprocal of the other then

The value of \({ log }_{ 3 }\frac { 1 }{ 81 } \) is

If \(\frac{1}{\sqrt{3}\times\sqrt{2}}=\sqrt{3}+a\) then a is

Part - B

Generic 2 - Answer All Question

If log2x+log4x+log8x=\(\frac{11}{6}\), find x

Are there two distinct irrational numbers such that their difference is a rational number? Justify.

Find the value of \(\frac { 2-\sqrt { 3 } }{ \sqrt { 3 } } \) when \(\sqrt { 3 } \) =1.732

Draw the graph for |x| < 3.

Part - C

Generic 3 - Answer All Question

Find the value of p for which the difference between the roots of the equation x2+px+8=0 is 2.

Simplify : \(\frac { 1 }{ 2+\sqrt { 3 } } +\frac { 3 }{ 4-\sqrt { 5 } } +\frac { 6 }{ 7-\sqrt { 8 } } \)

Determine the region in the plane determined by the inequalities. \(2x+3y\le 6,\quad x+4y\le 4,\quad x\ge 0,\quad y\ge 0.\)

Solve |x-1| ≤5,|x|≥2

Part - D

Generic 5 - Answer All Question

Resolve into partial fractions \(\frac { { x }^{ 3 }-1 }{ { x }^{ 2 }+x+1 } \)

Show that \({{1}\over{3-\sqrt{8}}}-{{1}\over{\sqrt{8}-\sqrt{7}}}+{{1}\over{\sqrt{7}-\sqrt{6}}}-{{1}\over{\sqrt{6}-\sqrt{5}}}+{{1}\over{\sqrt{5}-2}}=5\)

Evaluate \(\sqrt [ 3 ]{ {{{(45.4)}^{2}}\over{{(3.2)}^{2}}\times{(6.5)}^{2}} } \)

Find the square root of 7-4\(\sqrt{3}\)

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If a and b are roots of x² + x + 1 = 0 then the value of a² + b² =

The number of solution of x²+|x-1|=1 is

The value of log₃ 11.log₁₁ 13.log₁₃ 15log₁₅ 27.log₂₇ 81 is

Let \(\alpha\) and \(\beta\) are the roots of a quadratic equation px² + qx + r = 0 then

If one root of the quadratic equation ax² + bx + c = 0 is the reciprocal of the other then

If log₂x+log₄x+log₈x=\(\frac{11}{6}\), find x

Find the value of p for which the difference between the roots of the equation x²+px+8=0 is 2.

Determine the region in the plane determined by the inequalities.
\(2x+3y\le 6,\quad x+4y\le 4,\quad x\ge 0,\quad y\ge 0.\)