List of practice Questions

If $\begin{bmatrix}1&x&1\end{bmatrix} \begin{bmatrix}1&3&2\\ 2&5&1\\ 15&3&2\end{bmatrix}\begin{bmatrix}1\\ 2\\ x\end{bmatrix} = 0 $, then x can be

If $ {{c}_{1}},{{c}_{2}},{{c}_{3}},{{c}_{4}},{{c}_{5}} $ and $ {{c}_{6}} $ are constants, then the order of the differential equation whose general solution is given by $ y={{c}_{1}}cos $ $ (x+{{c}_{2}})+{{c}_{3}}\sin (x+{{c}_{4}})+{{c}_{5}}{{e}^{x}}+{{c}_{6}} $

The area of the plane region bounded by the curve $ x={{y}^{2}}-2 $ and the line $ y=-x $ is (in square units)

The chord joining the points $(5, 5)$ and $(11, 227)$ on the curve $y =3x^{2}-11x-15$ is parallel to tangent at a point on the curve. Then the abscissa of the point is

Two distinct numbers $x$ and $y$ are chosen from $1,2,3,4,5$. The probability that the arithmetic mean of $x$ and $y$ is an integer is

A man of $2\,m$ height walks at a uniform speed of $6 \,km/h$ away from a lamp post of $6 \,m$ height. The rate at which the length of his shadow increases is

If $a = e^{i \theta}$ , then $\frac{1 + a}{1-a}$ is equal to

A complete cycle of a traffic light takes $60\, seconds$. During each cycle the light is green for $25\, seconds$, yellow for $5 \,seconds$ and red for $30\, seconds$. At a randomly chosen time, the probability that the light will not be green, is

If $A = \begin{pmatrix}1&0\\ 1&1\end{pmatrix}$ , then $A^n + nI$ is equal to

If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is

If $ y={{\sin }^{-1}}\sqrt{1-x}, $ then $ \frac{dy}{dx} $ is equal to

An insoluble dye is reduced to a soluble colourless leuco form by an alkaline reducing agent. The fibre is soaked in the dye solution and then exposed to air to develop the colour. The dye is

The reaction of $H_2$ is given below $H_2 + CO + R - CH = CH_2 \to R - CH_2 - CH_2 - CHO$ is specifically called as

A compound ?A?with molecular formula CHO gives a positive 2, 4 DNP test but a negative Tollen?s test. On treatment with sodium hypochlorite, it gives CHCl and compound ?B?. Compound ?B? is

Air at sea level is dense. This is a practical implimentation of:

Allyl cyanide molecule contains

An element 'X' belongs to fourth period and fifteenth group of the Periodic Table. Which one of the following is true ?

Aniline is separated from aniline-water mixture by

At $ 500 \,K $ , the half-life period of a gaseous reaction at an initial pressure of $ 80\, kPa $ is $ 350 \,s $ . When the pressure is $ 40 \,kPa $ , the half-life period is $ 175 \,s $ . The order of the reaction is

Chlorination of benzene in the presence of halogen carrier is an example of

Chlorobenzene on treatment with sodium in dry ether gives diphenyl. The name of the reaction is

Choose the amide which on reduction with $ LiAl{{H}_{4}} $ yields a secondary amine

Identify the product/s in the following reaction. $ 3C{{H}_{3}}CH=C{{H}_{2}}\xrightarrow[{}]{B{{H}_{3}}}X\xrightarrow[{}]{{{H}_{2}}{{O}_{2}}/O{{H}^{-}}} $ $ product/s+{{H}_{3}}B{{O}_{3}} $

If the kinetic energy of the particle is increased to $16$ times its previous value, the percentage change in the de Broglie wavelength of the particle is

In the Hofmann rearrangement of primary amides having optically active group with S-configuration, the product amine has