List of practice Questions

The first order integrated rate equation is

A light ray going from air is incident (as shown in figure) at one end of a glass fibre (refractive index $ \mu = 1.5$) making an incidence angle of $60^\circ$ on the lateral surface,

so that it undergoes a total internal reflection. How much time would it take to traverse the straight fibre of length 1 km?

A particle of mass $2 \times 10^{-3}$ kg, charge $4 \times 10^{-3}$ C enters in an electric field of 5 V/m, then its kinetic energy after 10 s is

In unilocular ovary with a single ovule the placentation is

Transport of food material in higher plants takes place through

Keel is characteristic of the flowers of

Study the cycle shown below and select the . option which gives correct words for all the four blank A, B, C and D.

Algae have cell wall made up of

Consider the following four statements (i), (ii), (iii) and (iv) and select the right option for two correct statements. Statements : (i) In vexillary aestivation, the large posterior petal is called-standard, two lateral ones are wings and two small anterior petals are termed keel (ii) The floral formula for liliaceae is $\bigoplus ⚥ P_{3 + 3} \, A_{3+3} + \underline{G}_3$ (iii) In pea flower the stamens are monadelphous (iv) The floral formula for solanaceae is $\bigoplus ⚥ K_{(3)} C_{(3)} A_{(4)} + \underline{G}_2$ The correct statements are

Carrot is a

Cleavage polyembryony occurs in

In Pinus, male cone bears a large number of

Podocytes are the cells, present in

Apomictic embryos in Citrus arise from

The correct floral formula of soyabean is

The vector equation of the straight line $ 6x-8=2y-7=3z $ is

The unit normal vector to the plane $ 3x+2y-2z=8\sqrt{17} $ is

if the straight lines $ 2x+5ay-1=0 $ and $ 3x+7y+7=0 $ are mutually perpendicular, then value of $a$ is

If $A$ is a square matrix of order $3$ and if $ \det \,(A)=3, $ then $ \det \,[adj\,\,\{adj\,(adj\,A)\}] $ is equal to

If $A$ and $B$ are square matrices of order $3$ such that $ det\text{ }A=1 $ and $ det\text{ }B=-1 $ then $ det\text{ (-10}\,\text{AB)} $ is equal to

If $ {{\tan }^{-1}}\,(1-x),\,\,{{\tan }^{-1}}\,(x) $ and $ {{\tan }^{-1}}\,(1+x) $ are in $A.P.$, then the value of $ {{x}^{3}}+{{x}^{2}} $ is equal to

$ \int_{0}^{\pi /2}{\frac{{{\sin }^{100}}x}{{{\sin }^{100}}x+{{\cos }^{100}}x}\,\,dx} $ is equal to

Four arithmetic means between $-10$ and $25$ are inserted. Then the $5^{th}$ term in the series is

If $A$ and $B$ are square matrices of order 3 such that $det A = 1$ and $ det B = -1$, then $det (- 10 AB) = ? $

If $\begin{vmatrix} a_1 &b_1 &c_1 \\[0.3em] a_2 &b_2 &c_2 \\[0.3em] a_ 3&b_3 &c_3 \end{vmatrix}=\,\,\,\,3,\, $ then $ \begin{vmatrix} 3a_1 &9b_1 &3c_1 \\[0.3em] a_2 &3b_2 &c_2 \\[0.3em] 3a_ 3&9b_3 &3c_3 \end{vmatrix}=$,