List of practice Questions

The compound(s) that is(are) removed as slag during the extraction of copper is : 
  1. \(CaO\) 
  2.  \(FeO\) 
  3.  \(Al _2 O _3\) 
  4.  \(ZnO\)
  5.  \(NiO\) 
    Choose the correct answer from the options given below :
In two different experiments, an object of mass $5\, kg$ moving with a speed of $25 \,ms ^{-1}$ hits two different walls and comes to rest within
(i) 3 second, 
(ii) 5 seconds, respectively.
Choose the correct option out of the following :
Given below are two statements :
Statement I: In polluted water values of both dissolved oxygen and BOD are very low.
Statement II: Eutrophication results in decrease in the amount of dissolved oxygen.
In the light of the above statements, choose the most appropriate answer from the options given below :
 NCC parade is going at a uniform speed of $9\, km / h$ under a mango tree on which a monkey is sitting at a height of $196\, m$ At any particular instant, the monkey drops a mango A cadet will receive the mango whose distance from the tree at time of drop is : (Given g= 9.8 m/s2)
The dimensions of $\left(\frac{ B ^2}{\mu_0}\right)$ will be :(if $\mu_0$ : permeability of free space andB : magnetic field)
Which one is an amphoteric oxide:
A baby cools from 50°C to 40°C in 5 min. The surrounding temperature is 20°C. In what further time (in minutes) will it cool to 30°C?
A,B and C are voltmeters of resistance R, \(\frac{3}{2}R\) and 3R respectively. When some potential difference is applied between X and Y, the voltmeters readings are VA, VB and VC respectively. Then:
Write down the structure of picric acid
are radish and carrot the root modification?

Volatility of following solutions : H2O , H2Se, H2Te, H2PO

What is Acrolein?

The radius of hydrogen atom in the ground state is 0.53 Å .After collision with an electron it is found to have a radius of 2.1 Å, the principal quantum number 'n' of the state of the atom is 

The IS–LM model for a closed economy is given below, where $Y$ is output, $C$ is consumption, $I$ is investment, $T$ is income tax, $\dfrac{M^d}{P}$ is money demand, $P$ is price level, $r$ is real interest rate, $\pi^e$ is expected inflation rate and $G$ is government expenditure: \[ C = 200 + 0.8(Y - T) - 500r, \] \[ I = 200 - 500r, \] \[ T = 20 + 0.25Y, \] \[ \frac{M^d}{P} = 0.5Y - 250(r + \pi^e). \] If $G = 196$, $\pi^e = 0.1$, the nominal money supply equals 9890 and the full employment output equals 1000, the full employment equilibrium price level in the economy is ___________. (in integer) 
 

Individuals in a country start earning and consuming at the age of 18 years, retire at the age of 60 years and die at the age of 90 years, without leaving any debt and bequests. The income of an individual at age $t$ (in years) is given by the expression $100t - t^2$. The price level is constant and the interest rate is zero. According to the life cycle theory of consumption, the average annual consumption of an individual is _____________. (in integer) 
 

The aggregate production function for a country is $Y = 10N - 0.005N^2$, where $N$ is the quantity of labor input. The aggregate labor supply function is $N = 55 + 5w$, where $w$ is the real wage rate. Assuming perfectly competitive labor and product markets, the equilibrium real wage is ___________. (in integer) 
 

Let $X_1, X_2, X_3, X_4$ be independent random variables following the standard normal distribution. Let $Y$ be defined as \[ Y = (X_1 + X_2)^2 + (X_3 + X_4)^2. \] Then the variance of $Y$ equals __________. (in integer) 
 

For $\beta>0$, let the variables $x_1$ and $x_3$ be the optimal basic feasible solution of the linear programming problem \[ \text{maximize } \; z = x_1 + 2x_2 + 3x_3 \] 


If the optimal value is 7, then $\beta$ equals ____________. (in integer) 
 

The optimal value of the constrained optimization problem \[ \text{minimize } 2xy \quad \text{subject to } 9x^2 + 4y^2 \leq 36 \] is _____________. (in integer) 
 

Let $y(x) > 0$ be a solution of the differential equation \[ \frac{dy}{dx} + y = y^2. \] If $y(\ln 2) = \dfrac{1}{3}$, where $\ln$ denotes the natural logarithmic function, then $y(\ln 3)$ equals ___________. (round off to 2 decimal places)
A firm has two manufacturing plants, 1 and 2 to produce the same product. The total costs of production are given by \[ TC_1 = 500 + 30Q_1 \quad \text{and} \quad TC_2 = 1500 + 20Q_2 \] in plants 1 and 2, respectively, where $Q_1$ and $Q_2$ are the respective quantities. The demand for the product is given by $Q^d = 150 - \dfrac{P}{3}$, where $P$ is the price per unit. The value of $Q_1$ that maximizes the profit of the firm is ___________. (in integer)

The supply and demand curves of a vaccine are \[ q = 14 + 5p \quad \text{and} \quad q = 329 - 5p, \] respectively, where $p$ is the price per unit of vaccine and $q$ is quantity of vaccine. The government decides that the maximum price of the vaccine would be Rs. 25 per unit. To avoid any shortage in supply at the ceiling price, the government also decides to subsidize the sellers so that the market clears. Subsidy is given on per unit basis. The total expenditure of the government in providing the subsidy is Rs. _________. (in integer) 
 

Amar has an endowment of food $F_A = 2$ and water $W_A = 5$. Barun has an endowment of food $F_B = 8$ and water $W_B = 5$. Amar’s utility function is given by \[ U_A(f_A, w_A) = f_A^2 w_A; \] where $f_A$ and $w_A$ are his consumption of food and water, respectively. Barun’s utility function is given by \[ U_B(f_B, w_B) = \min\{f_B, w_B\}; \] where $f_B$ and $w_B$ are his consumption of food and water, respectively. They exchange food and water at prices $p_f$ and $p_w$, respectively, to maximize their utilities. In the competitive equilibrium, $\dfrac{p_f}{p_w}$ equals __________. (in integer)

The following data relate to a country’s GDP in 2012–13 (in local currency). 

The value of this country’s imports (in local currency) in 2012–13 is __________. (in integer) 
 

The utility function of a consumer from consumption of $x_1$ and $x_2$ is given by \[ u(x_1, x_2) = x_1 + 2\sqrt{x_2}. \] At the current prices and income, the consumer’s optimal consumption bundle is given by $(x_1 = 10, x_2 = 10)$. The consumer’s optimal choice of $x_2$, if his income increases by 50% but prices remain unchanged, is __________. (in integer)