List of practice Questions

The velocity of an object moving in a straight line path is given as a function of time by $v = 6t - 3t^2$. where $v$ is in $ms^{-1} , t $ is in $s$. The average velocity of the object between $t = 0$ and $t = 2s$ is

The wave functions of $1s$ orbitals of two hydrogen atoms are $\Psi_A$ and $\Psi_B$. $\Psi_A$ and $\Psi_B$ are linearly combined to form two molecular orbitals ($\sigma$ and $\sigma^{\ast}$). Which of the following statements are collect? I. $\sigma^{*}$ is equal to $(\Psi_{A}-\Psi_{B})$. II. In $\sigma$ - orbital, one nodal plane is present in between two nuclei. III. The energy of $\sigma$ - orbital is lower than the energy of $\sigma^{*}$ -orbital.

Two small spheres of each charge $q$, mass $m$ and material density $d$ are suspended from a fixed point with the help of inextensible light thread. When the spheres are in air, the angle between the threads is $90^{\circ}$. When the spheres are suspended in a liquid of density $\frac{2}{2} d$, the angle between the threads is $60^{\circ}$. The $3$ value of dielectric constant of the liquid is

When a hydrogen atom emits a photon during a transition from $n = 4$ to $n = 2$, its recoil speed is about

Acetic acid on heating with $ {NH_3}$ forms $A$. When $A$ reacts with $ {LiAlH_4}$ followed by hydrolysis gives $B$. When $B$ is heated with chloroform in $KOH$ medium gives $C$. What are $B$ and $C$ respectively?

An $\alpha$-particle moves in a circular path of radius $1\, cm$ in a uniform magnetic field of $0.125\, T$. The de Broglie wavelength associated with the $\alpha$-particle is

$KMnO _{4}$ oxidises $S _{2} O _{3}^{2-}$ to $SO _{4}^{2-}$ in medium $x$ and $NO^{-}_2$ to $NO^{-}_3$ in medium $y, x$ and $y$ are respectively

$KO _{2}$, reacts with water to form $A, B$ and $C .$ $B$ forms $C$ when it reacts with iodine in basic medium. What are $B$ and $C$ respectively?

Noble metals like gold and platinum are soluble in which of the following mixtures?

Observe the following molecules. $PCl_5, BrF_5, ClF_5, PF_5, ClF_3, XeF_4, XeF_2, IF_5 $ The number of molecules having square pyramidal geometry from the above is

The walls of a closed cubical box of edge $60\, cm$ are made of material of thickness $1\, mm$ and thermal conductivity $4 \times 10^{-4} \; cal \; s^{-1} \; cm^{-1} {^{\circ}C^{-1}}$. The interior of the box is maintained $1000 \; {^{\circ}C}$ above the outside temperature by a heater placed inside the box and connected across $400\, V\, DC$ supply. The resistance of the heater is

Which of the following are carbonate ores? l) Magnetite II) Kaolinite III) Siderite IV) Calamine

Which of the following is water-gas shift reaction?

Which of the following metals exist in liquid state duiing summer season?

Which of the following reactions can be used to prepare diborane? I) $ {BF_3 + LiAlH_4 ->[ether]}$ II) $ {BF_3 + NaH ->[450 k]}$ III) $ {Na_2B_4O_7 + H_2O -> }$ IV) $ { NaBH_4 + I_2 ->}$

Which one of the following has maximum number of hybrid orbitals ?

Which one of the following is not present in the nitration mixture?

White phosphorus is heated with concentrated $NaOH$ in $CO _{2}$ atmosphere to form a gas $A$ and compound $B$. When $A$ is bubbled into aqueous $CuSO _{4}$ solution copper phosphide and $C$ are formed, $B$ and $C$ are respectively

$\cos ^{2} 5^{\circ}-\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}+\sin ^{2} 35^{\circ}$ $+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ}=$

If $'a'$ is the middle term in the expansion of $(2x - 3y)^8$ and $b, c$ are the middle terms in the expansion of $(3x + 4y)^7$ , then the value of $\frac{b +c}{a}$ ,when $x = 2$ and $y = 3$, is

If $a$ makes an acute angle with $b , r \cdot a =0$ and $r \times b = c \times b$, then $r =$

If a random variable $X$ has the probability distribution given by $P(X = 0) = 3C^3, P(X = 2 ) = 5C - 10C^2 $ and $P(X = 4) = 4C - 1$, then the variance of that distribution is

If $ABCD$ is a cyclic quadrilateral with $AB = 6, BC = 4, CD = 5, DA = 3$ and $\angle ABC$ = $\theta$ then $cos\, \theta$ =

If $\alpha$ and $\beta$ are the roots of $x^{2}+7 x+3=0$ and $\frac{2 \alpha}{3-4 \alpha}, \frac{2 \beta}{3-4 \beta}$ are the roots of $a x^{2}+b x+c=0$ and $GCD$ of $a, b, c$ is $1$ , then $a+b+c=$

If $\alpha , \beta , \gamma$ are the roots of $x^3 - 6x^2 + 11x - 6 = 0 $ , then the equation having the roots $\alpha^2 + \beta^2 + \gamma^2$ and $\gamma^2 + \alpha^2$ is