List of practice Questions

If a variable point P on an ellipse of eccentricity e is joined to the foci $S_1$ and $S_2$ then the incentre of the triangle $PS_1S_2$ lies on

If a vector $\vec{A}$ makes an angles $\alpha$, $\beta$ and $\gamma$ respectively with the $x$, $y$ and $z$ axes respectively. Then $sin^{2}\alpha+sin^{2}\beta+sin^{2}\gamma$ is equal to

If a variable frequency ac source is connected to a capacitor then with decrease in frequency the displacement current will

"If a system A is in thermal equilibrium with B and B is in thermal equilibrium with C, then A and C are in thermal equilibrium with each other. " This is a statement of

If $A^T, B^T$ are transpose matrices of the square matrices A, B respectively, then$(AB)^T$ is equal to

If a thermometer reads freezing point of water as $ 20{}^\circ C $ and boiling point as $ 150{}^\circ C $ , how much thermometer read, when the actual temperature is $ 60{}^\circ C $ ?

If a tissue has at a given time $1024$ cells, how many cycles of mitosis had the original parental single cell undergone?

If a particle moves in a circle describing equal angles in equal intervals of times, the velocity vector

If a relation $R$ on the set $\{1$, $2$, $3\}$ be defined by $R = \{(1$, $2)\}$, then $R$ is

If a solid has a sharp melting point, then it means that the solid is :

If a man goes $10 \,m$ toward north and $20\, m$ toward east, then his displacement is

If a line makes angles 60?, 45?, 45? and $\theta$ with the four diagonals of a cube then $sin^2 \, \theta = $

If a letter is chosen at random from the letter of English alphabet, then the probability that it is a letter of the word ??ELHI?

If a line makes an angle a with the positive direction of x-axis, then the slope of the line is given by :

If $A$ is the void set $\phi$, then $P\left(A\right)$ has just one element $\phi$ i.e. $P[\phi] = \left\{\phi\right\}$. So number of elements of $P\left[P\left(P\left(\phi\right)\right)\right]$ is

If a leaf cell of Agave has $x$ chromosomes then what will be the number of chromosomes in a cell of its bulbil?

If A is symmetric as well as skew-symmetric matrix, then A is

If A is a square matrix, then $AA^T$ is a

If A is a square matrix, then A + A' is

If A is a square matrix, then $A - A^t$ is a

If A is a square matrix such that $A^2 = I$, then $A^{-1}$ is equal to

If A is a square matrix such that $A^2 = I$, then $(A - I)^3 + (A + I)^3 - 7A$ is equal to

If A is a skew symmetric matrix, then trace of A is

If A is a square matrix such that $A^2=A$, then $(1-A)^3+A$ is equal to

If a is a positive integer, then the number of values of a satisfying $\displaystyle\int_0^{\pi/2}\begin{Bmatrix}a^2\left(\frac{\cos 3x}{4}+\frac{3}{4}\cos\,x\right)+a\,\sin\,x-20\,\cos\,x\end{Bmatrix}dx\leq-\frac{a^2}{3}$ is