List of practice Questions

If A, B, C are the angles of $\Delta ABC$ then $\cot \, A. \cot \, B + \cot \, B. \cot \, C + \cot \, C. \cot \, A =$
If $f(x) = \begin{cases} x^2 + \alpha & \text{for } x \ge 0 \\[2ex] 2\sqrt{x^2 + 1} + \beta & \text{for} x < 0 \end{cases}$ is continuous at x = 0 and $f \left(\frac{1}{2} \right) = 2 $ then $\alpha^2+ \beta^2$ is
If $\log_{10} \left(\frac{x^{3} - y^{3} }{x^{3} + y^3} \right) = 2$ then $ \frac{dy}{dx} = $
If $y = \left(\tan^{-1} x\right)^{2}$ then $ \left(x^{2} + 1\right)^{2} \frac{d^{2}y}{dx^{2} } + 2x \left(x^{2} + 1 \right) \frac{dy}{dx} = $
A coin is tossed three times. If X denotes the absolute difference between the number of heads and the number of tails then P(X = 1) =
Letters in the word HULULULU are rearranged. The probability of all three L being together is
If $f : R - \{2\} \to R$ is a function defined by $f(x) = \frac{x^2 - 4}{x - 2}$ , then its range is
The sum of the first 10 terms of the series 9 + 99 + 999 + ?., is
The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
Which of the following pituitary hormone works indirectly?
Which of the following molecules represents the order of hybridisation sp2 , sp2 , sp, sp from left to right atoms ?
A man in a car at location $Q$ on a straight highway is moving with speed $v$. He decides to reach a point $P$ in a field at a distance d from the highway (point $M$) as shown in the figure. Speed of the car in the field is half to that on the highway. What should be the distance $RM$, so that the time taken to reach $P$ is minimum ?
If molar conductivity of \(Ca^{2+}\) and \(Cl^-\) ions are 119 and 71 Scm2 mol-1 respectivily, then the molar conductivity of \(CaCl_2\) at infinite dilution is
If 10 L of an ideal gas at a pressure of 5 atm expands isothermally and reversibly to a final volume of 100 L. the work done and heat absorbed in this process (in Lit-atm), respectively are
Hydrogen peroxide reacts with lead sulphide to produce lead sulphate. Identify the other product formed
Nylon 6 is prepared from
\Mien borax is heated dining borax bead test along with CoO (Cobalt Oxide) on a loop of platinum (Pt) wire, it swells up and produces a blue colored bead. Which of the following compounds is responsible for the blue color?
The volume of $O_2$ (in L) that can be produced at STP by heating 112 g of $ {KClO_3}$ is approximately (Molar mass of $ {KCIO_3 = 122.6 \, g \, mol^{-1}}$)
Producer gas is a mixture of
The number of resonance structures possible for anisole is
A gill throws a stone horizontally from the roof of a house 12 in above the ground with a speed of If 15 m/s. Neglecting air resistance, the time it takes tor the stone to reach the ground is
A rocket is about to launch upwards from its platform. The engine ejects gas at a rate of 2100 kg/s and the molecules are expelled at 50 m/s. If the above condition is just sufficient to make it rise upwards, the mass of the rocket is (Assume $g = 10\, ms^2$)
Consider a 50 in high water falls, with water flowing at a rate of $1.2 \times 10^6 \, kg/s$. Using the power generated due to this process, assuming 100% efficiency, the number of 60W bulbs that can be light up is
In analysing the problems of inelastic collisions, the law of conservation of momentum and the law of conservation of mechanical energy are to be employed Since the laws of conservation of momentum and mechanical energy are fundamental laws, they should hold good in any situation. Which of the following is true?
Elastic strain energy of 10 J is stored in a loaded copper rod of cross-sectional area $2 times 10^{-4} m^2$ and length 0,2 in, Hie Young?? modulus for copper is 125 GPa. The load on the copper rod in kN is