Mathematics -I Semester Exam 2021

The length of the perpendicular from the point (-4, 3) to the line $5x + 12y + 9 = 0$ is $13/5$.

The eccentricity of the parabola defined by $x^2 = 4ay$ is $2$.

The transverse axis of the hyperbola represented by $x^2/a^2 - y^2/b^2 = 1$ is $2b$.

The radius of the circle given by the equation $x^2 + y^2 + 2x + 6y + 7 = 0$ is $rac{ oot3}{3}$.

For any angle, it holds true that $Sin20° * Sin40° * Sin60° * Sin80° = rac{3}{16}$.

If $(a + ib)^3 = x + iy$, then it is true that $rac{a}{x} + rac{b}{y} = 4(x^2 - y^2)$.

The radius and center of the circle given by $x^2 + y^2 + 2x + 6y + 7 = 0$ are at $(1, 3)$.

The perpendicular distance from the point (-4, 3) to the line $5x + 12y + 9 = 0$ results in an independent value per trigonometric standards.

The result of $tan(a) * tan(60° - α) * tan(60° + α) = cos(3α)$ holds true for all values of $α$.

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.

If $cos^2x + cos^2y + cos^2z = rac{ ext{π}}{2}$, then $x^2 + y^2 + z^2 + 2xyz = 0$.

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.

If $A + B = 45°$, then $(1 + tan A)(1 + tan B) = 1$.

If $A + B = 45°$, then $tan(A + B) = 1$.

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}$.

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 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.

If the eccentricity of an ellipse is $rac{1}{2}$, then the distance between the foci must be 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 $x^2 + y^2 + z^2 + 2xyz = 1$.

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).

The value of $cos(36°)$ is equal to $(rac{√5 + 1}{4})$.

The value of $sin(54°)$ is $(rac{√5 - 1}{4})$.

If $sin(A) = rac{4}{5}$, then $cos(2A)$ equals $rac{7}{25}$.

The slope of the line $2x + 5y + 6 = 0$ is $rac{2}{5}$.

The argument of $Z = -1 - i$ is $3π/4$.

The value of $sin(15°)$ is $(rac{√3 - 1}{√2})$.

$tan^{-1}(-√3)$ yields a principal value of $-π/3$.

The value $sin(90° - A)$ equals $cos(A)$ for any angle A.

$cos(54°)$ is equal to $(rac{√5 + 2}{4})$.

If $sin(A) = rac{4}{5}$, then $sin^2(A) + cos^2(A)$ equals 1.

The value of $sin(90° - A)$ equals $sin(A)$.

The principal value of $tan^{-1}(√3)$ is $π/3$.

For $A = 30°$, $sin(30°)$ is equal to $rac{1}{2}$.

The formula $cos(2A) = 1 - 2sin^2(A)$ is incorrect.