List of practice Questions

Geetanjali Express, which is 250 m longer when moving from Howrah to Tatanagar, crosses Subarnarekha bridge in 30 seconds. What is the speed of Geetanjali Express?
 Statement I: Bombay Mail, which runs at 60 km/h, crosses the Subarnarekha bridge in 30 seconds.
Statement II: Bombay Mail, when running at 90 km/h, crosses a lamp post in 10 seconds.
 

Which of the following expressions correctly represents the equivalent conductance at infinite dilution of ${Al2(SO4)3}$ ? Given that ${\wedge^{\circ}_{Al^{3+}}}$ and ${- \wedge^{\circ}_{SO^{2-}_4}}$ are the equivalent conductances at infinite dilution of the respective ions
The roots of the quadratic equation $x^{2}-2\sqrt{3}x-22 = 0 $ are :
An electron tube was sealed-off during manufacture at a pressure of $ 1.2\times 10^{-7}mm $ of mercury at $ 27^{\circ}C $ . Its volume is $ 100\,cm^{3} $ . The number of molecules that remain in the tube is
Prem invested a certain sum of money in a simple interest bond whose value grew to Rs 300 at the end of 3 years and to Rs 400 at the end of another 5 years. What was the rate of interest in which he invested his sum ?
If 5 students utilize 18 pencils in 9 days, how long at the same rate will 66 pencils last for 15 students?
A charged particle moving with veiocity $4 \times 10^6ms^{-1} $ enters perpendicuiar to a magnetic field $B=2 \, Wbm^{-2}.$ It moves in a circular path of radius 2 cm, then charge per unit mass is
For the magnetic field to be maximum due to a small element of current carrying conductor at a point, the angle between the element and the line joining the element to the given point must be
Two small magnets each of magnetic moment 10 $Am^2$ are placed in end on position 0.1 m apart from their centres. The force acting between them is
According to Boyle's law, the product of pressure and volume is a constant. Hence,
Compare the statements A and B. Statement A : When the urine moves through the descending limb, it becomes hypertonic and as it passes through the ascending limb of Henle's loop, it becomes hypotonic. Statement B : The descending limb is permeable to sodium ions, while the ascending limb is impermeable to sodium ions.
Gastrula has a pore which is known as _________
The diagram of large intestine of man is given below. Identify the parts labelled A, B, C, D, E and F.
The total radiant energy per unit area, normal to the direction of incidence, received at a distance $R$ from the center of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T K$ is given by (where $\sigma$ is Stefan's constant)
If $a > b > 0, Sec^{-1} \left(\frac{a+b}{a-b} \right)= 2 \; Sin^{-1}x $ then $x = $ _____
The number of solutions of the equation $\sin \; (e^{x}) = 5^x + 5^{-x}$, is
If $a^x = b^{y} = c^{z} = d^{u}$ and $a, b,\, c,\, d$ are in $GP$, then $x,\, y,\, z,\, u$ are in
The principal value of $\sin^{-1} \left\{\sin \frac{5\pi}{6}\right\} $ is
The value of $\frac{\cos\theta}{1+ \sin\theta}$ is equal to
If $f(x) = \sqrt{\log_{10} x^2} $ . The set of all values of $x$ for which $f(x)$ is real , is
$\displaystyle\lim_{n\to\infty} \left[\frac{1}{1.2} + \frac{1}{2.3} + \frac{1}{3.4} + .... + \frac{1}{n\left(n+1\right)}\right] $ is equal to
Range of the function $y =\sin^{-1} \left(\frac{x^{2}}{1+x^{2}}\right) $ is
The following two reactions are known ${Fe2O3(s) + 3CO(g) -> 2Fe(s) + 3CO2(g); \Delta H = - 26.8 \, kJ }$ ${FeO(s) + CO (g) -> Fe(s) + CO2(g); \Delta H - 16.5 \, kJ}$ The value of $\Delta H$ for the following reaction ${Fe2O3(s) + CO(g) -> 2FeO(s) + CO2(g) }$ is
The respective number of significant figures for the numbers $23.023$, $0.0003$ and $2.1 \times 10^{-3}$ are
Coolant used in car radiator is aqueous solution of ethylene glycol. In order to prevent the solution from freezing at $-0.3^{\circ} C$. How much ethylene glycol must be added to $5\, kg$ of water ? $\left( K_f =1 \cdot 86\, Kg\, mol ^{-1}\right)$