List of practice Questions

Umbel inflorescence is found in

In Pinus, the third tier of embryonal cells from below is known as

The conversion of ammonia into nitrites and nitrates is called :

The capitulum type of inflorescence is found in :

In which of the following process, convection does not take place primarily?

A machine which is $75\%$ efficient, uses $12\, J$ of energy in lifting $1 \,kg$ mass through a certain distance. The mass is then allowed to fall through the same distance. The velocity at the end of its fall is

In an equilateral triangle $ABC$, $ F_{1},F_{2} $ and $ F_{3} $ are three forces acting along the sides $AB, BC$ and $AC$ as shown in the given figure. What should be the magnitude of $F_3$, so that the total torque about $ O $ is zero ?

The torque of force $\vec{ F }=(2 \hat{ i }-3 \hat{ j }+4 \hat{ k }) N$ acting at a point $\vec{ r }=(3 \hat{ i }+2 \hat{ j }+3 \hat{ k }) m$ about origin is

$300\, J$ of work is done in sliding a $2 \,kg$ block up an inclined plane of height $10 \,m$. The work done against friction is ( Take $g=10\, m / s ^{2}$ )

Suppose refractive index $\mu$ is given as $\mu=A+\frac{B}{\lambda^{2}}$, where $A$ and $B$ are constants and $\lambda$ is wavelength then the dimensions of $B$ are same as that of

We wish to see inside an atom. Assuming the atom to have a diameter of $100 \,pm$, this means that one must be able to resolve a width of say $10\, pm$. If an electron microscope is used, the minimum electron energy required is about

if $p=\begin {bmatrix} \sqrt 3 /2 & 1/2 \\ -1/2 & \sqrt 3/2 \end {bmatrix} , A=\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ and $ Q=PAP^T,\ then$ $P^TQ^{2005}P $ is

If $\int_{sin x}^1 \, t^2 f(t) dt =1-sin x, \forall x \in (0,\pi/2), \, then \, f\bigg(\frac{1}{\sqrt 3}\bigg)$ is

A variable plane $ \frac{x}{a}+ \frac{y}{b}+ \frac{z}{c} =1$ at a unit distance from origin cuts the coordinate axes at A. Band C. Centroid (x, y, z) satisfies the equation $ \frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2} =K.$ The value of K is

The number of ordered pairs $(\alpha, \beta), $ where $\alpha, \beta \in(-\pi, \pi)$ satisfying cos $(\alpha-\beta)=1 and cos (\alpha+\beta)=\frac{1}{e}$ is

In a $\triangle$ ABC, among the following which one is true?

If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is

Let $f (x) = ax^2 + bx + c, a \ne 0$ and $\Delta =b^2 -4ac.$ If $a+ \beta,$ $a^2+ \beta^2$ and $a^3+ \beta^3$ are in GP, then

The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by

The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is

The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is

If f (x) is continuous and differentiable function and f (1/n) = 0 $\forall$ n $\ge$ 1and n $\in$ I, then

If a star can convert all the He nuclei completely into oxygen nuclei. The energy released per oxygen nuclei is : (Mass of the helium nucleus is 4.0026 amu and mass of oxygen nucleus is 15.9994 amu)

Genes were first artificially synthesized by :

The leaves in Utricularia plant are modified into: