List of practice Questions

$A$ and $B$ are two independent events such that $P\left(A\cup B'\right)=0.8$, and $P\left(A\right)=0.3$ Then, $P(B)$ is

If $\alpha, \beta $ be the roots of $x^{2}-a(x-1)+b=0$, then the value of $\frac{1}{\alpha^{2}-a\alpha}+\frac{1}{\beta^{2}-a\beta}+\frac{2}{a+b}$ is

The equation of the tangent to the conic $x^{2}-y^{2}-8x+2y+11=0$ at $(2,1)$ is

Which one of the following formulae does not represent an organic compound?

What is the particle $X$ in the following nuclear reaction : $^{9}_{4}Be +^{4}_{2}He \to \,^{12}_{6} C +X$

DNA multiplication is called

$Al _{2} O _{3}$ is reduced by electrolysis at low potentials and high currents. If $4.0 \times 10^{4}$ amperes of current is passed through molten $Al _{2} O _{3}$ for 6 hours, what mass of aluminium is produced ? (Assume $100 \%$ current efficiency, at. mass of $Al =27\, g\, mol ^{-1}$ ) -

The slope at any point of a curve $y = f(x )$ is given by $\frac{d y}{d x}=3x^{2}$ and it passes through $(-1 ,1 )$ The equation of the curve is

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x + y = 2$ are

A convex lens made of glass has focal length $0.15\, m$ in air. If the refractive index of glass is $3/2$, and that of water is $4/3$ the focal length of lens when immersed in water is

A wire of resistance $12$ ohms per meter is bent to form a complete circle of radius $10 \,cm$. The resistance between its two diametrically opposite points, $A$ and $B$ as shown in the figure is

The number of electron in $2$ coulomb of charge is

A dorsal horn is present on the___________of mulberry silk worm (caterpillar).

A RBC and a plant cell (with thick cell wall) are placed in distilled water. The solute concentration is the same in both the cells . What changes would be observed in them

A beam of light of wavelength 600 nm from a distant source falls on a single slit I mm wide and the resulting diffraction-pattern is observed on a screen 2m away. The distance between the first dark fringes on either side of the central bright fringe is

For the constructive interference the path difference between the two interfering waves must be equal to

An organic compound on heating with $CuO$ produces $CO_2$, but no water. The organic compound may be

A door of $1.6\, m$ wide requires a force of $1 \,N$ to be applied at the free end to open or close it. The force that is required at a point $0.4\, m$ distant from the hinges for opening or closing the door is

Which of the following does not show optical isomerism? (en = ethylenediamine)

A cow is tied to a post by a rope. The cow moves along the circular path always keeping the rope tight. If it describes $44\, metres$, when it has traced out $72^\circ$ at the centre, the length of the rope is

The complex number $\frac {1+2i}{1-i}$ lies in

For the parabola $y^2 = 4x$, the point $P$ whose focal distance is $17$, is

The area bounded between the parabola $y^2= 4x$ and the line $y = 2x - 4$ is equal to

Nosema bombycis which causes pebrine in silk worms is a

The number of subgroups of the group $(Z_5, +_5)$is