11th Maths Monthly Test-3 (Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-3 (Basic Algebra )-Aug 2020

Time : 2.00 Hours

Part - A

Generic 2 - Answer All Question

Represent the following inequalities in the interval notation:
\(-2x>0\) or \(3x-4<11\)

Simplify \({ \left( { x }^{ \frac { 1 }{ 2 } }{ y }^{ -3 } \right) }^{ \frac { 1 }{ 2 } }\) , where x,y ≥ 0.

Compute log₃5 log₂₅27

Prove \({ log }_{ a^{ 2 } }a\times { log }_{ b^{ 2 } }b\times { log }_{ c^{ 2 } }c=\frac { 1 }{ 8 } \)

Find the complete set of values of a for which the quadratic x² - ax + a + 2 = 0 has equal roots.

Discuss the nature of roots of -x² + 3x + 1 = 0

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

A solution is to be kept between 68^oF and 77^oF. What is the range in temperature in degree Celsius (c) or Fahrenheit (F),conversion formula is given by \(F=\frac { 9 }{ 5 } \)C + 32?

Solve the following system of linear inequalities 3x-9≥0, 4x-10≤6;

Solve the equation \(\frac { x+2 }{ x+3 } =\frac { x+4 }{ 2x+3 } \)

Given log₂¹⁶ =4.Find log₁₆²

Solve the linear inequalities 2x - 4≥0; 3x + 9 ≤ 3.

Determine the region in the Plane determined by the inequalities. \(x\le 3y,x\ge y\)

Let b>0 and b≠1. Express y = b^x in logarithmic form.Also state the domain and range of the logarithmic function.

Part - B

Generic 3 - Answer All Question

If one root of the equation 3x²+kx-81=0 is the square of the other then find k

Find the roots of the polynomial equation (x - 1)³ (x + 1)² (x + 5) = 0 and state their multiplicity.

If \(\frac { log \ x }{ y-z } =\frac { log \ y }{ z-x } =\frac { log \ z }{ x-y } \) , then prove that xyz= 1

Prove that \(log2+16log\frac { 16 }{ 15 } +12log\frac { 25 }{ 24 } +7log\frac { 81 }{ 80 } =1\)

Solve log₈x+log₄x+log₂x=11

Find the real roots of x⁴=16

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

Prove that ap + q = 0 if f(x) = x³ - 3px + 2q is divisible by g(x) = x² + 2ax + a².

Simplify: \({{3\sqrt{2}}\over{\sqrt{6}-\sqrt{3}}}={{4\sqrt{3}}\over{\sqrt{6}-\sqrt{2}}}+{{2\sqrt{3}}\over{\sqrt{6}+\sqrt{2}}}\)

If a²+b²=c², show that a⁶+b⁶+3a²b²c²=c⁶.

Ravi obtained 70 and 75 marks in first two unit tests.Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Shade reaion given by the linear inequality x + 2y > 3.

If x=\(\sqrt { 2 } +\sqrt { 3 } \) find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-1 } \)

Find x if \({{1}\over{2}}\) log₁₀ \((11+4\sqrt{7})\) = log₁₀ (2+x).

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11th Maths Monthly Test-3 (Basic Algebra )

St. Britto Hr. Sec. School - Madurai

11th Maths Monthly Test-3 (Basic Algebra )-Aug 2020

Part - A

Generic 2 - Answer All Question

Represent the following inequalities in the interval notation: \(-2x>0\) or \(3x-4<11\)

Simplify \({ \left( { x }^{ \frac { 1 }{ 2 } }{ y }^{ -3 } \right) }^{ \frac { 1 }{ 2 } }\) , where x,y ≥ 0.

Compute log35 log2527

Prove \({ log }_{ a^{ 2 } }a\times { log }_{ b^{ 2 } }b\times { log }_{ c^{ 2 } }c=\frac { 1 }{ 8 } \)

Find the complete set of values of a for which the quadratic x2 - ax + a + 2 = 0 has equal roots.

Discuss the nature of roots of -x2 + 3x + 1 = 0

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

A solution is to be kept between 68oF and 77oF. What is the range in temperature in degree Celsius (c) or Fahrenheit (F),conversion formula is given by \(F=\frac { 9 }{ 5 } \)C + 32?

Solve the following system of linear inequalities 3x-9≥0, 4x-10≤6;

Solve the equation \(\frac { x+2 }{ x+3 } =\frac { x+4 }{ 2x+3 } \)

Given log216 =4.Find log162

Solve the linear inequalities 2x - 4≥0; 3x + 9 ≤ 3.

Determine the region in the Plane determined by the inequalities. \(x\le 3y,x\ge y\)

Let b>0 and b≠1. Express y = bx in logarithmic form.Also state the domain and range of the logarithmic function.

Part - B

Generic 3 - Answer All Question

If one root of the equation 3x2+kx-81=0 is the square of the other then find k

Find the roots of the polynomial equation (x - 1)3 (x + 1)2 (x + 5) = 0 and state their multiplicity.

If \(\frac { log \ x }{ y-z } =\frac { log \ y }{ z-x } =\frac { log \ z }{ x-y } \) , then prove that xyz= 1

Prove that \(log2+16log\frac { 16 }{ 15 } +12log\frac { 25 }{ 24 } +7log\frac { 81 }{ 80 } =1\)

Solve log8x+log4x+log2x=11

Find the real roots of x4=16

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

Prove that ap + q = 0 if f(x) = x3 - 3px + 2q is divisible by g(x) = x2 + 2ax + a2.

Simplify: \({{3\sqrt{2}}\over{\sqrt{6}-\sqrt{3}}}={{4\sqrt{3}}\over{\sqrt{6}-\sqrt{2}}}+{{2\sqrt{3}}\over{\sqrt{6}+\sqrt{2}}}\)

If a2+b2=c2, show that a6+b6+3a2b2c2=c6.

Ravi obtained 70 and 75 marks in first two unit tests.Find the minimum marks he should get in the third test to have an average of at least 60 marks.

Shade reaion given by the linear inequality x + 2y > 3.

If x=\(\sqrt { 2 } +\sqrt { 3 } \) find \(\frac { { x }^{ 2 }+1 }{ { x }^{ 2 }-1 } \)

Find x if \({{1}\over{2}}\) log10 \((11+4\sqrt{7})\) = log10 (2+x).

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Tamilnadu Stateboardszs - Class

Represent the following inequalities in the interval notation:
\(-2x>0\) or \(3x-4<11\)

Compute log₃5 log₂₅27

Find the complete set of values of a for which the quadratic x² - ax + a + 2 = 0 has equal roots.

Discuss the nature of roots of -x² + 3x + 1 = 0

A solution is to be kept between 68^oF and 77^oF. What is the range in temperature in degree Celsius (c) or Fahrenheit (F),conversion formula is given by \(F=\frac { 9 }{ 5 } \)C + 32?

Given log₂¹⁶ =4.Find log₁₆²

Let b>0 and b≠1. Express y = b^x in logarithmic form.Also state the domain and range of the logarithmic function.

If one root of the equation 3x²+kx-81=0 is the square of the other then find k

Find the roots of the polynomial equation (x - 1)³ (x + 1)² (x + 5) = 0 and state their multiplicity.

Solve log₈x+log₄x+log₂x=11

Find the real roots of x⁴=16

Prove that ap + q = 0 if f(x) = x³ - 3px + 2q is divisible by g(x) = x² + 2ax + a².

If a²+b²=c², show that a⁶+b⁶+3a²b²c²=c⁶.

Find x if \({{1}\over{2}}\) log₁₀ \((11+4\sqrt{7})\) = log₁₀ (2+x).