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Questions and Answers
The length of the perpendicular from the point (-4, 3) to the line $5x + 12y + 9 = 0$ is $13/5$.
The length of the perpendicular from the point (-4, 3) to the line $5x + 12y + 9 = 0$ is $13/5$.
True
The eccentricity of the parabola defined by $x^2 = 4ay$ is $2$.
The eccentricity of the parabola defined by $x^2 = 4ay$ is $2$.
False
The transverse axis of the hyperbola represented by $x^2/a^2 - y^2/b^2 = 1$ is $2b$.
The transverse axis of the hyperbola represented by $x^2/a^2 - y^2/b^2 = 1$ is $2b$.
False
The radius of the circle given by the equation $x^2 + y^2 + 2x + 6y + 7 = 0$ is $ rac{
oot3}{3}$.
The radius of the circle given by the equation $x^2 + y^2 + 2x + 6y + 7 = 0$ is $ rac{ oot3}{3}$.
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For any angle, it holds true that $Sin20° * Sin40° * Sin60° * Sin80° = rac{3}{16}$.
For any angle, it holds true that $Sin20° * Sin40° * Sin60° * Sin80° = rac{3}{16}$.
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If $(a + ib)^3 = x + iy$, then it is true that $ rac{a}{x} + rac{b}{y} = 4(x^2 - y^2)$.
If $(a + ib)^3 = x + iy$, then it is true that $ rac{a}{x} + rac{b}{y} = 4(x^2 - y^2)$.
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The radius and center of the circle given by $x^2 + y^2 + 2x + 6y + 7 = 0$ are at $(1, 3)$.
The radius and center of the circle given by $x^2 + y^2 + 2x + 6y + 7 = 0$ are at $(1, 3)$.
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The perpendicular distance from the point (-4, 3) to the line $5x + 12y + 9 = 0$ results in an independent value per trigonometric standards.
The perpendicular distance from the point (-4, 3) to the line $5x + 12y + 9 = 0$ results in an independent value per trigonometric standards.
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The result of $tan(a) * tan(60° - α) * tan(60° + α) = cos(3α)$ holds true for all values of $α$.
The result of $tan(a) * tan(60° - α) * tan(60° + α) = cos(3α)$ holds true for all values of $α$.
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The equation $(bc-ab)/(c+ab+cb) + (ca-bc)/(a+bc+ac) + (ab-ca)/(b+ca+c) = 0$ for all non-zero variables is universally true.
The equation $(bc-ab)/(c+ab+cb) + (ca-bc)/(a+bc+ac) + (ab-ca)/(b+ca+c) = 0$ for all non-zero variables is universally true.
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If $cos^2x + cos^2y + cos^2z = rac{ ext{π}}{2}$, then $x^2 + y^2 + z^2 + 2xyz = 0$.
If $cos^2x + cos^2y + cos^2z = rac{ ext{π}}{2}$, then $x^2 + y^2 + z^2 + 2xyz = 0$.
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The equation $cos^2x + cos^2y + cos^2z = π$ implies that the individual values of $cos^2x$, $cos^2y$, and $cos^2z$ can be greater than 1.
The equation $cos^2x + cos^2y + cos^2z = π$ implies that the individual values of $cos^2x$, $cos^2y$, and $cos^2z$ can be greater than 1.
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If $A + B = 45°$, then $(1 + tan A)(1 + tan B) = 1$.
If $A + B = 45°$, then $(1 + tan A)(1 + tan B) = 1$.
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If $A + B = 45°$, then $tan(A + B) = 1$.
If $A + B = 45°$, then $tan(A + B) = 1$.
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The partial fraction of $ rac{3x + 1}{(x - 1)(x^2 + 1)}$ can be expressed as $ rac{A}{x - 1} + rac{Bx + C}{x^2 + 1}$.
The partial fraction of $ rac{3x + 1}{(x - 1)(x^2 + 1)}$ can be expressed as $ rac{A}{x - 1} + rac{Bx + C}{x^2 + 1}$.
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The coefficients of terms in the expansion of $(1 + x)^n$ for the 14th, 15th, and 16th terms can only be in arithmetic progression if $n > 16$.
The coefficients of terms in the expansion of $(1 + x)^n$ for the 14th, 15th, and 16th terms can only be in arithmetic progression if $n > 16$.
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The expansion of $(1 + x)^n$ is guaranteed to have the 14th, 15th, and 16th coefficients in an arithmetic progression for any integer $n$ greater than 16.
The expansion of $(1 + x)^n$ is guaranteed to have the 14th, 15th, and 16th coefficients in an arithmetic progression for any integer $n$ greater than 16.
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If the eccentricity of an ellipse is $ rac{1}{2}$, then the distance between the foci must be 1.
If the eccentricity of an ellipse is $ rac{1}{2}$, then the distance between the foci must be 1.
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The three angles $x$, $y$, and $z$ must have cosines that fulfill the equation $cos^2x + cos^2y + cos^2z = ext{π}$ to validate the relationship $x^2 + y^2 + z^2 + 2xyz = 1$.
The three angles $x$, $y$, and $z$ must have cosines that fulfill the equation $cos^2x + cos^2y + cos^2z = ext{π}$ to validate the relationship $x^2 + y^2 + z^2 + 2xyz = 1$.
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If a circle touches the line $2x - y - 4 = 0$, it has a fixed radius related to the coordinates of its center at (1, -3).
If a circle touches the line $2x - y - 4 = 0$, it has a fixed radius related to the coordinates of its center at (1, -3).
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The value of $cos(36°)$ is equal to $( rac{√5 + 1}{4})$.
The value of $cos(36°)$ is equal to $( rac{√5 + 1}{4})$.
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The value of $sin(54°)$ is $( rac{√5 - 1}{4})$.
The value of $sin(54°)$ is $( rac{√5 - 1}{4})$.
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If $sin(A) = rac{4}{5}$, then $cos(2A)$ equals $ rac{7}{25}$.
If $sin(A) = rac{4}{5}$, then $cos(2A)$ equals $ rac{7}{25}$.
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The slope of the line $2x + 5y + 6 = 0$ is $ rac{2}{5}$.
The slope of the line $2x + 5y + 6 = 0$ is $ rac{2}{5}$.
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The argument of $Z = -1 - i$ is $3π/4$.
The argument of $Z = -1 - i$ is $3π/4$.
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The value of $sin(15°)$ is $( rac{√3 - 1}{√2})$.
The value of $sin(15°)$ is $( rac{√3 - 1}{√2})$.
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$tan^{-1}(-√3)$ yields a principal value of $-π/3$.
$tan^{-1}(-√3)$ yields a principal value of $-π/3$.
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The value $sin(90° - A)$ equals $cos(A)$ for any angle A.
The value $sin(90° - A)$ equals $cos(A)$ for any angle A.
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$cos(54°)$ is equal to $( rac{√5 + 2}{4})$.
$cos(54°)$ is equal to $( rac{√5 + 2}{4})$.
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If $sin(A) = rac{4}{5}$, then $sin^2(A) + cos^2(A)$ equals 1.
If $sin(A) = rac{4}{5}$, then $sin^2(A) + cos^2(A)$ equals 1.
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The value of $sin(90° - A)$ equals $sin(A)$.
The value of $sin(90° - A)$ equals $sin(A)$.
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The principal value of $tan^{-1}(√3)$ is $π/3$.
The principal value of $tan^{-1}(√3)$ is $π/3$.
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For $A = 30°$, $sin(30°)$ is equal to $ rac{1}{2}$.
For $A = 30°$, $sin(30°)$ is equal to $ rac{1}{2}$.
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The formula $cos(2A) = 1 - 2sin^2(A)$ is incorrect.
The formula $cos(2A) = 1 - 2sin^2(A)$ is incorrect.
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Study Notes
Examination Paper Details
- Subject: Mathematics -I
- Semester: I/II
- Exam Date: 2021 (Odd)
- Time: 3 Hours
- Full Marks: 70
- Passing Marks: 28
Instructions
- Answer all 20 questions from Group A, each carrying 1 mark.
- Answer all 5 questions from Group B, each carrying 4 marks.
- Answer all 5 questions from Group C, each carrying 6 marks.
- All parts of a question must be answered together in a sequence. Otherwise, they may not be evaluated.
- Figures in the right margin indicate marks.
Question Types and Marks Distribution
- Group A: 20 questions (1 mark each)
- Group B: 5 questions (4 marks each)
- Group C: 5 questions (6 marks each)
Important Instructions (General)
- Answer all parts of a question together and in sequence in one location.
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Description
Prepare for your Mathematics -I examination with this comprehensive quiz based on the syllabus for Semester I/II. It covers various question types across Groups A, B, and C, ensuring thorough revision. Evaluate your understanding and readiness for the exam with marks distribution details provided.
