List of practice Questions

Quality of storing food using simple inorganic material belongs to plants which are
If \[ \left|\frac{z_1-7z_2}{\,7-z_1\overline{z_2}\,}\right|=1 \quad \text{and} \quad |z_2|\neq 1, \text{ then } |z_1|\neq \]
If \(\alpha\) be a root of the equation \(4x^2+2x-1=0\), then the other root is
Let \(a_1,a_2,a_3,\ldots\) be the terms of an A.P. If \[ \frac{a_1+a_2+\cdots+a_p}{a_1+a_2+\cdots+a_q}=\frac{p^2}{q^2}\quad (p\neq q), \] then \(\dfrac{a_6}{a_{21}}=\)
For \(x,y\in \mathbb{R}\), define a relation \(R\) by \(xRy\) if and only if \(x-y+\sqrt{2}\) is an irrational number. Then \(R\) is
If \[ y=\frac{1}{2}\sin^{-1}\!\left(\frac{2xy}{x^2+y^2}\right) \] and \(y<x\), then \[ \lim_{y\to 0} x = \]
If the first term of an A.P. is \(2\) and the sum of first five terms is equal to one fourth of the sum of the next five terms, then the sum of the first \(30\) terms is
A set \(A\) has 3 elements and another set \(B\) has 6 elements. Then
Consider the non-empty set consisting of children in a house. Consider a relation \(R\): \(xRy\) if \(x\) is brother of \(y\). The relation \(R\) is:
\(f:\mathbb{R}\rightarrow\mathbb{R}\) is a function defined by \[ f(x)=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}} \] Then \(f\) is
The vectors \(\overrightarrow{AB}=-3\hat{i}+4\hat{k}\) and \(\overrightarrow{AC}=5\hat{i}-2\hat{j}+4\hat{k}\) are the sides of a triangle \(ABC\). The length of the median through \(A\) is
The contrapositive of the statement “if \(2^2 = 5\), then I got first class” is
If \(A=\{x \mid x^2-5x+6=0\}\), \(B=\{2,4\}\), \(C=\{4,5\}\), then \(A \times (B \cap C)=\)
The graph of the function \(y=f(x)\) is symmetrical about the line \(x=2\), then
If \(z_1, z_2, z_3\) are three distinct complex numbers and \(a,b,c\) are three positive real numbers such that \[ \frac{a}{|z_2-z_3|}=\frac{b}{|z_3-z_1|}=\frac{c}{|z_1-z_2|} \] then \[ \frac{a^2}{z_2-z_3}+\frac{b^2}{z_3-z_1}+\frac{c^2}{z_1-z_2}= \]
For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) A diatomic molecule has a dipole moment of \(1.2\,\text{D}\). If the bond distance is \(1.0\,\text{\AA}\), the fraction of an electronic charge on each atom is _____
For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) The entropy of a sample of a certain substance increases by \(0.836\,\text{J K}^{-1}\) on adding reversibly \(0.3344\,\text{J}\) of heat at constant temperature. The temperature of the sample is _____ K
For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) Human blood gives rise to an osmotic pressure of approximately \(7.65\) atm at body temperature, \(37^\circ\text{C}\). Hence, molarity of an intravenous glucose solution to have the same osmotic pressure as blood is _____ M
For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) 20.4 g of \( \mathrm{H_2O_2} \) solution on decomposition gives 1.68 L of \( \mathrm{O_2} \) at STP. Percentage strength by weight of the solution is _____
For the following question, enter the correct numerical value up to TWO decimal places. If the numerical value has more than two decimal places, round-off the value to TWO decimal places. (For example: Numerical value 5 will be written as 5.00 and 2.346 will be written as 2.35) Elevation in boiling point of an aqueous urea solution is \(0.52^\circ\). (\(K_b = 0.52\,\text{mol}^{-1}\,\text{kg}\)). Hence, mole fraction of urea in this solution is _____
If the relation \(R: A \rightarrow B\) where \(A=\{1,2,3,4\}\), \(B=\{1,3,5\}\) is defined by \(R=\{(x,y): x<y,\; x\in A,\; y\in B\}\), then \(R\circ R^{-1}=\)
If \(2f(x)-3f\!\left(\dfrac{1}{x}\right)=x^2,\; x\neq 0\), then \(f(2)=\)
Probability of finding electron in YZ plane for \(p_x\) orbital is:
In which pair or pairs is the stronger bond found in the first species? I: \(O_2^{2-},\, O_2\)
II: \(N_2,\, N_2^+\)
III: \(NO^+,\, NO\)
Intensive property among the following is: