Who was the Viceroy of India, when the Rowlatt Act was passed?
b.
Lord Chelmsford
Correct Answer
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The Rowlatt Act was passed in 1919, when Lord Chelmsford was the Viceroy of India.
Which one of the following is the softest?
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Among the given metals, lithium is the softest; it is a very soft alkali metal and can be cut with a knife.
As a non-member who can participate in the proceedings of either House of Parliament?
c.
Attorney General
Correct Answer
d.
Chief Election Commissioner
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The Attorney General of India has the right to participate in the proceedings of either House of Parliament, though not to vote.
Which is the river on which Indira Sagar Dam is planned to be constructed?
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The Indira Sagar Dam is constructed on the Narmada River.
The first astronomer who gave the idea, 'The earth rotates on its axis', is
b.
Aryabhatta
Correct Answer
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Aryabhatta is credited with proposing that the Earth rotates on its axis.
Which one of the following angles cannot be constructed using an unmarked ruler and compass only?
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Angles such as 90°, 75° and 22.5° are constructible by standard straightedge-and-compass constructions, but 50° is not generally constructible by those tools alone.
For a Frequency Polygon, the points are plotted against
a.
mid-point of the class interval vs frequency
Correct Answer
b.
lower limit of the class interval vs frequency
c.
upper limit of the class interval vs frequency
d.
real limit of the class interval vs frequency
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A frequency polygon is drawn by plotting class mid-points on one axis and frequencies on the other, then joining the points with straight lines.
AICTE was established in
c.
November, 1985
Correct Answer
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The All India Council for Technical Education (AICTE) was established in November 1985.
One of the main publications of John Dewey is
b.
Education Today
Correct Answer
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'Education Today' is listed among John Dewey's main publications; the other options are associated with different authors.
According to David Ausubel, "Verbal Learning" is
a.
learning a new language
c.
understanding verbal information
Correct Answer
d.
passive learning experience
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Ausubel's verbal learning refers to meaningful learning of verbal material, i.e. understanding verbal information rather than mere rote repetition.
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The Southern Regional Office of UGC is in
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National Population Policy was evolved in the year
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According to Abraham Maslow, 'Self-Actualisation' in the hierarchy is
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Who is the author of 'Emile'?
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The university that has no affiliated colleges is
b.
Madurai Kamaraj University
c.
Thanjavur Tamil University
d.
Manonmanium Sundaranar University
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Human Rights Day is
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Which one of the following models is not on curriculum development?
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The chief objective of pre-primary education is to promote ..................... of the child.
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If the teacher finds in learner's activities something new or original, then the child is supposed to be
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Which one of the following is not a learning domain?
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A particle is projected with a velocity of 24 m/sec at an angle of $30^\circ$. The time of flight is
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A stone is dropped into a well and reaches the bottom with a velocity 30 m/sec and the sound of the splash on the water reaches the top of the well in $3\frac{182}{981}$ second from the time the stone starts. The velocity of sound =
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If the greatest height attained by the particle is a quarter of its range on the horizontal plane, the angle of projection is
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The horizontal range of a projectile is maximum when angle of projection is
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If two velocities are equal in magnitude, then magnitude of resultant velocity is
a.
$2V\sin\frac{\alpha}{2}$
b.
$2V\cos\frac{\alpha}{2}$
c.
$2V^2\cos\frac{\alpha}{2}$
d.
$V\cos\frac{\alpha}{2}$
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The acceleration component in the normal direction is
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If $\mu$ is the coefficient of friction as the equilibrium is limiting, then
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Two parallel forces $P$ and $Q$ act at the points $A$ and $B$, then their resultant $R$ passes through a point $C$ which divides $AB$ in the ratio
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If the resultant of two forces $3P$ and $5P$ is $7P$, the angle between the forces is
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G is the centroid of $\triangle ABC$ and $P$ is any point in the plane of the triangle. Then $PA + PB + PC =$
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The singular points for $f(z)=\dfrac{z+1}{z^2(z^2+1)}$ are
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Any two harmonic conjugates of a given harmonic function $u(x,y)$ differ by
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The image of the circle $|z-3i|=3$ under the map $w=\frac{1}{z}$ is a
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The value of $\int_C \frac{e^z}{z^n}\,dz$, where $C$ is the circle $|z|=1$, is
c.
$\dfrac{2\pi}{(n-1)!}$
d.
$\dfrac{2\pi i}{(n-1)!}$
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The function $f(z)=|z|^2$ is
a.
differentiable at $z=0$
b.
differentiable at $z\ne 0$
c.
nowhere differentiable
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If the function $f(z)=\dfrac{z}{1+z}$, $u(x,y)+iv(x,y) =$
a.
$\dfrac{x}{x^2+y^2}-\dfrac{iy}{x^2+y^2}$
b.
$\dfrac{x^2+x+y^2}{(x+1)^2+y^2}+\dfrac{iy}{(x+1)^2+y^2}$
d.
$\dfrac{x^2+y^2}{(x+1)^2+y^2}+\dfrac{iy}{(x+1)^2+y^2}$
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$\displaystyle\sum \frac{(-1)^{n-1}x^n}{n}$ converges if
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The series $\displaystyle\sum \frac{(-1)^n}{n^p}$ is absolutely convergent if
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The sequence $\big((-1)^n\big)$
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The value of $\displaystyle\lim_{n\to\infty}\frac{1^2+2^2+\cdots+n^2}{n^3}$ is
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The incorrect statement from the following is
a.
$\mathbb{N}$ is countable set
b.
$\mathbb{Q}$ is countable set
c.
$\mathbb{Q}^c$ is countable set
d.
$\mathbb{Z}$ is countable set
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In $\mathbb{R}$ with usual metric, the incorrect statement is
a.
$(0,1)$ is an open set
b.
$\{0\}$ is an open set
c.
$(0,\infty)$ is an open set
d.
$(-\infty,0)$ is an open set
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Which one of the following is a vector space? $\mathbb{R}\times\mathbb{R}$ with usual addition and scalar multiplication defined by
b.
$\alpha(a,b)=(\alpha a,\alpha^2 b)$
c.
$\alpha(a,b)=(\alpha a,\alpha b)$
d.
$\alpha(a,b)=(|\alpha|a,|\alpha|b)$
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If $A$ and $B$ are two subspaces of a vector space $V$ over a field $F$, then
a.
$A\cup B$ is a subspace of $V$
b.
$A\times B$ is a subspace of $V$
c.
$A\cap B$ is a subspace of $V$
d.
$AB$ is a subspace of $V$
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If $A$ and $B$ are subgroups of an Abelian group $G$, then
a.
$A\cup B$ is a subgroup of $G$
b.
$A\times B$ is a subgroup of $G$
c.
$AB$ is a subgroup of $G$
d.
$A*B$ is a subgroup of $G$
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If $H$ is a subgroup of $G$ and $N$ is a normal subgroup of $G$, then
a.
$HN$ is a subgroup of $G$
b.
$H$ is a normal subgroup of $G$
c.
$H\cap N$ is a normal subgroup of $G$
d.
$H\cup N$ is a normal subgroup of $G$
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The angle between the planes $2x-y+z=6$ and $x+y+2z=7$ is
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$G=\left\{\begin{pmatrix}x&x\\x&x\end{pmatrix}\mid x\in \mathbb{R}^*\right\}$ is a group under matrix multiplication. The identity element of $G$ is
a.
$\begin{pmatrix}\frac{x}{4}&\frac{x}{4}\\[2pt]\frac{x}{4}&\frac{x}{4}\end{pmatrix}$
b.
$\begin{pmatrix}\frac12&\frac12\\[2pt]\frac12&\frac12\end{pmatrix}$
c.
$\begin{pmatrix}\frac14&\frac14\\[2pt]\frac14&\frac14\end{pmatrix}$
d.
$\begin{pmatrix}\frac{x}{2}&\frac{x}{2}\\[2pt]\frac{x}{2}&\frac{x}{2}\end{pmatrix}$
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The equation of the sphere which has the line joining the points $(2,7,5)$ and $(8,-5,1)$ as diameter is
b.
$x^2+y^2+z^2-10x-2y-6z-14=0$
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The point of intersection of the line $\frac{x-1}{2}=\frac{y-2}{-3}=\frac{z+3}{4}$ with the plane $2x+4y-z+1=0$ is
a.
$\left(\frac{10}{3},-\frac{3}{2},\frac{5}{3}\right)$
b.
$\left(\frac{20}{7},\frac{17}{2},-\frac{2}{3}\right)$
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The unit normal to the surface $x^3-xyz+z^3=1$ at $(1,1,1)$ is
a.
$\frac{2\hat i+2\hat k}{3}$
d.
$\frac{2\hat i-\hat j+2\hat k}{3}$
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$L(x^n)=$
a.
$\frac{\Gamma(n+1)}{s^{n+1}}$
b.
$\frac{\Gamma(n)}{s^n}$
c.
$\frac{\Gamma(n+1)}{s^n}$
d.
$\frac{\Gamma(n-1)}{s^{n-1}}$
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If $L(x^n)=?$
a.
$\dfrac{\Gamma(n+1)}{s^{n+1}}$
b.
$\dfrac{\Gamma(n)}{s^n}$
c.
$\dfrac{\Gamma(n+1)}{s^n}$
d.
$\dfrac{\Gamma(n-1)}{s^{n-1}}$
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If $L(f(x))=F(s)$, then $L(f(ax))=$
a.
$F\left(\frac{s}{a}\right)$
b.
$aF\left(\frac{s}{a}\right)$
d.
$\frac{1}{a}F\left(\frac{s}{a}\right)$
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The particular solution of $(D^2-4)y=e^{2x}+e^{-4x}$ is
a.
$y=\frac{xe^{2x}}{4}+\frac{e^{-4x}}{12}$
b.
$y=\frac{e^x}{4}+\frac{e^{-4x}}{12}$
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The equation $Pdx+Qdy+Rdz=0$ is integrable if
a.
$P\left(\frac{\partial Q}{\partial y}-\frac{\partial R}{\partial x}\right)+Q\left(\frac{\partial R}{\partial y}-\frac{\partial P}{\partial z}\right)+R\left(\frac{\partial P}{\partial x}-\frac{\partial Q}{\partial y}\right)=0$
b.
$P\left(\frac{\partial Q}{\partial z}-\frac{\partial R}{\partial y}\right)+Q\left(\frac{\partial R}{\partial x}-\frac{\partial P}{\partial z}\right)+R\left(\frac{\partial P}{\partial y}-\frac{\partial Q}{\partial x}\right)=0$
c.
$P\left(\frac{\partial Q}{\partial x}-\frac{\partial R}{\partial y}\right)+Q\left(\frac{\partial R}{\partial z}-\frac{\partial P}{\partial x}\right)+R\left(\frac{\partial P}{\partial y}-\frac{\partial Q}{\partial z}\right)=0$
d.
$P\left(\frac{\partial Q}{\partial z}-\frac{\partial P}{\partial y}\right)-Q\left(\frac{\partial R}{\partial x}-\frac{\partial P}{\partial z}\right)-R\left(\frac{\partial P}{\partial y}-\frac{\partial Q}{\partial x}\right)=0$
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Solution of $p^2-9p+18=0$ is
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The general solution of $(D^2-5D+6)y=0$ is
c.
$y=C_1e^{3x}+C_2e^{2x}$
d.
$y=C_1e^x+e^{2x}\cdot C_2$
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The value of $\displaystyle \int_0^{\pi/2}\sin^6 x\,dx =$
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The radius of curvature for $y=e^x$ at the point where it crosses the $y$-axis is
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The $n^{\text{th}}$ differential coefficient of $xe^x$ is
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The Rolle's constant for the function $f(x)=x^2$ in $[-1,1]$ is
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The maximum value of the function $f(x)=x^3-9x^2+15x$ is
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The values of $(-1)^{1/10}=$
a.
$\cos\dfrac{2k\pi}{10}+i\sin\dfrac{2k\pi}{10},\ k=1,\ldots,9$
b.
$\cos\dfrac{k\pi}{10}+i\sin\dfrac{k\pi}{10},\ k=1,\ldots,9$
c.
$\cos\dfrac{(k+1)\pi}{10}+i\sin\dfrac{(k+1)\pi}{10},\ k=1,\ldots,9$
d.
$\cos\dfrac{(2k+1)\pi}{10}+i\sin\dfrac{(2k+1)\pi}{10},\ k=1,\ldots,9$
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$\tan 4\theta =$
a.
$\dfrac{4\tan\theta+4\tan^2\theta}{1-6\tan^2\theta+\tan^4\theta}$
b.
$\dfrac{4\tan\theta-4\tan^2\theta}{1-6\tan^2\theta+\tan^4\theta}$
c.
$\dfrac{4\tan^2\theta}{1-\tan^4\theta}$
d.
$\dfrac{4\tan^2\theta}{1+\tan^4\theta}$
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With usual notations, if a pair of conjugate diameters meet the hyperbola and its conjugate in $P$ and $D$, then $CP^2-CD^2=$
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The perpendicular line to $p=r\cos(\theta-\alpha)$ is $p'=$
a.
$r\cos(\alpha-\theta)$
b.
$r\cos\left(\dfrac{\pi}{4}+\alpha-\theta\right)$
c.
$r\sin\left(\dfrac{\pi}{2}+\theta-\alpha\right)$
d.
$r\cos\left(\dfrac{\pi}{2}+\theta-\alpha\right)$
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The locus of the poles of chords of a parabola subtending a right angle at the vertex is
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The lines $y=mx$ and $y=m_1x$ are conjugate diameters of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ if $mm_1 =$
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The characteristic roots of the matrix $\begin{pmatrix}\cos\theta & -\sin\theta\\ -\sin\theta & -\cos\theta\end{pmatrix}$ are
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A unitary matrix is
a.
$\begin{pmatrix}0 & i\\ 0 & 0\end{pmatrix}$
b.
$\begin{pmatrix}0 & -i\\ 0 & 0\end{pmatrix}$
c.
$\begin{pmatrix}1 & 1\\ 1 & 1\end{pmatrix}$
d.
$\begin{pmatrix}0 & -i\\ i & 0\end{pmatrix}$
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Sum of the series $\log_3 e - \log_9 e + \log_{27} e - \log_{81} e + \cdots$ is
c.
$\frac{\log_e 2}{\log_e 3}$
d.
$\frac{\log_e 3}{\log_e 2}$
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If $X$ is large, nearly $\sqrt{X^2+16}-\sqrt{X^2+9} =$
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The coefficient of $x^n$ in the series $1 + \frac{b+ax}{1!} + \frac{(b+ax)^2}{2!} + \cdots$ is
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If $p$ is a prime and $p\mid a^2+b^2$ and $p\mid b^2+c^2$, then
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A person is hurt on kicking a stone due to
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Which of the following harbours is not a natural harbour?
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Recently one Indian cricket player has become the sixth batsman to score 10,000 runs in Test Cricket. The name of the player is
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The battle of Wandiwash was fought between
a.
Marathas and Portuguese
b.
the English and the French
c.
the English and Portuguese
d.
Marathas and the English
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Linear programming is designed by
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Which of the following first identified the Secondary Education as a weak link and suggested improvement?
a.
The Tarachand Committee (1948)
b.
The Secondary Education Commission (1954)
c.
The University Education Commission (1949)
d.
The Education Commission (1966)
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Intelligence test scores are reasonably stable after the age of
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Which one is not an S-R theory with reinforcement?
a.
E. L. Thorndike's theory
c.
B. F. Skinner's theory
d.
Tolman's theory of learning
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The emphasis of National Board for Adult Education on Curriculum is that it must be
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World First Aid Day is
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For the following scores 10, 11, 13, 10, 15, 17, 18, 15, 10, the value of mode is
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Educational Technology means
a.
Technology in Education
b.
Technology of Education
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Which one of the following is not a cause for forgetting?
a.
When something learned and not used repeatedly
b.
Interference with present learning
c.
Lack of reorganisation of the learning material
d.
Learning on the basis of short-term remembrance
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When the reason for acting is in the action, motivation is said to be
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National Integration Day is
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The importance of Teacher Education was first emphasized by
c.
Calcutta University Commission
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Taxonomy of educational objectives was first developed by
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SSA is established for achievement of
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Whose philosophy is characterised as "Naturalistic in its setting, Idealistic in its aim and Pragmatic in its method and Programme of work"?
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Multi-factor theory of Intelligence was developed by
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The time of flight on the inclined plane of angle $\alpha$ inclined at an angle $\beta$ is
b.
\frac{2u\sin(\alpha-\beta)}{g}
c.
\frac{u\sin(\alpha-\beta)}{g}
d.
\frac{2u\sin(\alpha-\beta)}{g\cos\beta}
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Time taken by the projectile to reach the greatest height is
b.
\frac{u^2\sin 2\alpha}{g}
c.
\frac{u\sin\alpha}{g^2}
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The time of flight of a projectile is
b.
\frac{2u\sin\alpha}{g}
c.
\frac{u^2\sin 2\alpha}{g}
d.
\frac{u^2\sin^2\alpha}{2g}
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If forces $P$ and $Q$ are at right angles to each other, then the magnitude of their resultant is $R$
b.
$R=\sqrt{P^2+Q^2+2PQ}$
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A uniform ladder rests with one of its ends on a rough ground ($\mu$ = coefficient of friction) and the other end on a smooth wall. The angle which it makes with the horizontal is
c.
\tan^{-1}\left(\frac{\mu}{2}\right)
d.
\tan^{-1}\left(\frac{1}{2\mu}\right)
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$ABC$ is a triangle and $O$ is the incentre of the triangle. Forces $P$, $Q$, $R$ acting along the lines $OA$, $OB$, $OC$ are in equilibrium. $P:Q:R =$
a.
$\cos\frac{A}{2}:\cos\frac{B}{2}:\cos\frac{C}{2}$
c.
$\sin A:\sin B:\sin C$
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When one body in contact with another is in equilibrium, the friction exerted is just sufficient to maintain equilibrium and is called
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The resultant of two equal forces $P, P$ at an angle $\alpha$ is
a.
$2P\cos\dfrac{\alpha}{2}$
b.
$2\cos\dfrac{\alpha}{2}$
d.
$2P\sin\dfrac{\alpha}{2}$
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The resultant of two forces $P$ and $Q$ is $R$. If $Q$ is doubled, $R$ is doubled. $R$ is also doubled when $Q$ is reversed. Then $P:Q:R =$
a.
$\sqrt{3}:\sqrt{2}:\sqrt{2}$
b.
$\sqrt{2}:\sqrt{3}:\sqrt{2}$
c.
$\sqrt{2}:\sqrt{2}:\sqrt{3}$
d.
$\sqrt{3}:\sqrt{2}:\sqrt{3}$
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The Taylor's series for $\dfrac{1}{z}$ about $z=1$ is
a.
$1+z+\dfrac{z^2}{2!}+\cdots$
b.
$1-(z-1)+(z-1)^2-(z-1)^3+\cdots$
c.
$1+(z-1)+(z-1)^2+\cdots$
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The residue of $\dfrac{z+1}{z^2-2z}$ at $z=2$ is
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The value of $\lim_{z\to 2}\dfrac{z^2-4}{z-2}$ is
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The angle of rotation at $z=1+i$ under the map $w=z^2$ is
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The series $\sum \dfrac{n^2+1}{5^n}$
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If $f(z)=a(x^2-y^2)+ibxy+c$ is differential at every point, the constants
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If $a_n=1+\dfrac{1}{1!}+\dfrac{1}{2!}+\cdots+\dfrac{1}{n!}$, then $(a_n)$ is
a.
strictly monotonic decreasing sequence
b.
monotonic decreasing sequence
c.
monotonic increasing sequence
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The series $\sum (-1)^n\left[\sqrt{n^2+1}-n\right]$ is
b.
conditionally convergent
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If $d$ is a metric on $M$, the incorrect statement is
a.
$\sqrt{d}$ is a metric on $M$
b.
$\frac{d}{1+d}$ is a metric on $M$
c.
$d^2$ is a metric on $M$
d.
$nd$ is a metric on $M$, $n\in\mathbb{N}$
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Which one of the following sets of vectors is linearly dependent?
a.
$\{(1,4,-2),(-2,1,3),(-4,11,5)\}$
b.
$\{(1,2,1),(2,1,0),(1,-1,2)\}$
c.
$\{(1,0,0),(0,1,0),(1,1,0)\}$
d.
$\{(0,0,0),(2,5,3),(-1,0,6)\}$
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Which one of the following sets of vectors is not a basis for $V_3(\mathbb{R})$?
b.
$\{(1,0,0),(0,1,0),(0,0,1)\}$
c.
$\{(1,0,0),(0,1,0),(1,1,1)\}$
d.
$\{(1,1,0),(0,1,1),(1,0,1)\}$
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The set $R=\left\{\begin{pmatrix}a&b\\-b&a\end{pmatrix}\mid a,b\in\mathbb{R}\right\}$ is a ring under matrix addition and multiplication. The inverse of $\begin{pmatrix}a&b\\-b&a\end{pmatrix}$ is
a.
$\begin{pmatrix}-a&b\\-b&a\end{pmatrix}$
b.
$\begin{pmatrix}a&-b\\-b&a\end{pmatrix}$
c.
$\begin{pmatrix}a+b&0\\-b&-a\end{pmatrix}$
d.
$\begin{pmatrix}-a-b&0\\b&-a\end{pmatrix}$
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If a non-empty subset $W$ of a vector space $V$ over a field $F$ is a subspace of $V$, then $\alpha, \beta \in F$ and $u, v \in W \Rightarrow$
a.
$\alpha u+\beta v\notin W$
b.
$\alpha u+\beta v\in W$
c.
$\alpha u+\beta v\in V$
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If $A$ and $B$ are two finite subgroups of group $G$, then
a.
$[G\!:\!A]=[G\!:\!B][B\!:\!A]$
b.
$[G\!:\!B]=[G\!:\!A][A\!:\!B]$
c.
$|AB|=\dfrac{|A||B|}{|A\cap B|}$
d.
$|AB|=\dfrac{|A||B|}{|A\cup B|}$
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Which of the following tables can represent a group?
a.
* | 1 0; 1 | 1 0; 0 | 0 0
b.
* | 1 -1; 1 | 1 -1; -1 | -1 1
c.
* | 0 2; 0 | 0 0; 2 | 0 4
d.
* | 3 4; 3 | 9 12; 4 | 12 16
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The radius of the sphere $2x^2+2y^2+2z^2-2x+2y-4z-5=0$ is
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If $S=0$ and $S_1=0$ represent two spheres, then $S-S_1=0$ is
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The line $\dfrac{x-x_1}{l}=\dfrac{y-y_1}{m}=\dfrac{z-z_1}{n}$ is parallel to the plane $ax+by+cz+d=0$ if
c.
$\dfrac{a}{l}=\dfrac{b}{m}=\dfrac{c}{n}$
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For any constant vector $\mathbf{a}$, $\nabla(\mathbf{a}\cdot\mathbf{r})=$
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If $\mathbf{f}=(ax+3y+4z)\hat i+(x-3y+3z)\hat j+(3x+2y-z)\hat k$ is solenoidal, the value of $a$ is
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$L\{x^2e^{-ax}\}=$
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The particular integral of $(D^2-2D+2)y=e^x\sin x$ is
a.
$\dfrac{e^x\cos x}{2}$
b.
$-\dfrac{xe^x\cos x}{2}$
c.
$\dfrac{xe^x\cos x}{2}$
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Clairaut's form of differential equation is
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The particular solution of $(D^2+9)y=\cos 3x$ is
b.
$y=\dfrac{\sin 3x}{6}$
c.
$y=\dfrac{x\sin 3x}{6}$
d.
$y=\dfrac{x^2\sin 3x}{6}$
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If $I=\int \sec^3 x\,dx$, then $2I=$
d.
$\sec x\tan x+\log(\sec x+\tan x)$
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If $Mdx+Ndy=0$ is of the form $y f(xy)dx + x g(xy)dy = 0$, $f(xy)\ne g(xy)$, then integrating factor is
d.
$\dfrac{1}{f(xy)+g(xy)}$
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The centre of curvature at $\left(\dfrac12,\dfrac14\right)$ on $y=x^2$ is
d.
$\left(-\dfrac12,\dfrac54\right)$
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The value of $\int_0^{\pi/2} \cos^5 x\,dx =$
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The value of $c$ of Lagrange's mean value theorem for $f(x)=(x^2-4)^{1/2}$ in $[2,3]$ is
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$\dfrac{d^n}{dx^n}\log(ax+b) =$
a.
$(-1)^{n-1}a^n(n-1)!(ax+b)^{-n}$
b.
$(-1)^{n-1}(n-1)!(ax+b)^{-n}$
c.
$(-1)^{n-1}a^n(ax+b)^{-n}$
d.
$(-1)^{n-1}a^n(n-1)!(ax+b)^n$
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$\cos(\sin x) =$
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If $\dfrac{\sin\theta}{\theta}=\dfrac{863}{864}$, nearly $\theta=$
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If $z=\cos\theta+i\sin\theta$, then $\dfrac{z^2-1}{z^2+1}=$
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$\sin^2\theta\cos^3\theta =$
a.
$-\dfrac{1}{16}[\cos 5\theta+\cos 3\theta-2\cos\theta]$
b.
$\dfrac{1}{8}[\cos 5\theta+\cos 3\theta-2\cos\theta]$
c.
$\dfrac{1}{16}[\sin 5\theta+\sin 3\theta-2\sin\theta]$
d.
$\dfrac{1}{4}[\sin 5\theta+\sin 3\theta-2\sin\theta]$
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The eccentric angles of the ends of a pair of conjugate diameters of an ellipse differ by
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With usual notations the points of intersection of the conjugate diameter and the conjugate hyperbola are
a.
$(\pm ai\tan\theta,\ \pm bi\sec\theta)$
b.
$(\pm i\tan\theta,\ \pm i\sec\theta)$
c.
$(\pm a\tan\theta,\ \pm b\sec\theta)$
d.
$(\pm i\cos\theta,\ \pm i\sin\theta)$
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A skew Hermitian matrix is
a.
$\begin{pmatrix} ib & c+իդ \ -c+id & ib \end{pmatrix}$
b.
$\begin{pmatrix} 0 & -a+ib \ a+ib & ib \end{pmatrix}$
c.
$\begin{pmatrix} ia & -c+id \ c+id & 0 \end{pmatrix}$
d.
$\begin{pmatrix} 0 & a+ib \ ia & 0 \end{pmatrix}$
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The rank of $\begin{pmatrix}1&1&1\\1&2&3\\1&4&7\end{pmatrix}$ is
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The rank of
$$\begin{pmatrix} 1 & 1 & 1 \\ 1 & 2 & 3 \\ 1 & 4 & 7 \end{pmatrix}$$
is
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The smallest degree of an equation with rational coefficients, one of whose roots is $\sqrt{2}+\sqrt{3}$, is
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The Highest Common Factor (H.C.F.) of $2x^3+5x^2+x-2$ and $2x^2-3x+1$ is
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The smallest divisor, greater than 1 of any integer greater than 1 is
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If $x>0$, $$\frac{x-1}{x+1}+\frac{1}{2}\frac{x^2-1}{(x+1)^2}+\frac{1}{3}\frac{x^3-1}{(x+1)^3}+\cdots =$$
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