The coefficient of
Question: The coefficient of $x^{7}$ in the expression $(1+x)^{10}+x(1+x)^{9}+x^{2}(1+x)^{8}+\ldots+x^{10}$ is :120330210420Correct Option: , 2 Solution:...
Read More →The value of
Question: The value of $\alpha$ for which $4 \alpha \int_{-1}^{2} \mathrm{e}^{-\alpha||_{\mid}} \mathrm{dx}=5$, is :$\log _{e}\left(\frac{3}{2}\right)$$\log _{e}\left(\frac{4}{3}\right)$$\log _{\mathrm{e}} 2$$\log _{\mathrm{e}} \sqrt{2}$Correct Option: , 3 Solution:...
Read More →Prove the following
Question: If $3 x+4 y=12 \sqrt{2}$ is a tangent to the ellipse $\frac{\mathrm{x}^{2}}{\mathrm{a}^{2}}+\frac{\mathrm{y}^{2}}{9}=1$ for some $\mathrm{a} \in \mathrm{R}$, then the distance between the foci of the ellipse is :4$2 \sqrt{7}$$2 \sqrt{5}$$2 \sqrt{2}$Correct Option: , 2 Solution:...
Read More →Let A , B , C and D be four non - empaty sets,
Question: Let $\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$ be four non-empty sets. The contrapositive statement of "If $\mathrm{A} \subseteq \mathrm{B}$ and $\mathrm{B} \subseteq \mathrm{D}$, then $\mathrm{A} \subseteq \mathrm{C}^{\prime \prime}$ is :If $\mathrm{A} \subseteq \mathrm{C}$, then $\mathrm{B} \subset \mathrm{A}$ or $\mathrm{D} \subset \mathrm{B}$If $\mathrm{A} \nsubseteq \subseteq \mathrm{C}$, then $\mathrm{A} \nsubseteq \subseteq \mathrm{B}$ or $\mathrm{B} \not \subseteq \m...
Read More →Let a1, a2, a3,..........be an G.P. such a1 < 0,
Question: Let $a_{1}, a_{2}, a_{3}, \ldots$ be a G.P. such that $a_{1}0$, $a_{1}+a_{2}=4$ and $a_{3}+a_{4}=16 .$ If $\sum_{i=1}^{9} a_{1}=4 \lambda$, then $\lambda$ is equal to :$-171$171$\frac{511}{3}$$-513$Correct Option: 1 Solution:...
Read More →How much amount of
Question: How much amount of $\mathrm{NaCl}$ should be added to $600 \mathrm{~g}$ of water $(\rho=1.00 \mathrm{~g} / \mathrm{mL})$ to decrease the freezing point of water to $-0.2{ }^{\circ} \mathrm{C}$ ? (The freezing point depression constant for water $=2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ ) Solution:...
Read More →Prove the following
Question: Let $A=\left[a_{i j}\right]$ and $B=\left[b_{i j}\right]$ be two $3 \times 3$ real matrices such that $b_{i j}=(3)^{(i+j-2)} a_{j i}$, where $\mathrm{i}, \mathrm{j}=1,2,3$. If the determinant of $\mathrm{B}$ is 81 , then the determinant of $\mathrm{A}$ is :3$1 / 3$$1 / 81$$1 / 9$Correct Option: , 4 Solution:...
Read More →The number of ordered pairs
Question: The number of ordered pairs $(\mathrm{r}, \mathrm{k})$ for which $6 \cdot{ }^{35} \mathrm{C}_{\mathrm{r}}=\left(\mathrm{k}^{2}-3\right) \cdot{ }^{36} \mathrm{C}_{\mathrm{r}+1}$, where $\mathrm{k}$ is an integer, is :3246Correct Option: , 3 Solution:...
Read More →The mass percentage of nitrogen in histamine is
Question: The mass percentage of nitrogen in histamine is Solution:...
Read More →Solve this following
Question: $108 \mathrm{~g}$ of silver (molar mass $108 \mathrm{~g} \mathrm{~mol}^{-1}$ ) is deposited at cathode from $\mathrm{AgNO}_{3}(\mathrm{aq})$ solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at $273 \mathrm{~K}$ and 1 bar pressure from water by the same quantity of electricity is Solution:...
Read More →If theta_1 and theta_2 be respectively the smallest
Question: If $\theta_{1}$ and $\theta_{2}$ be respectively the smallest and the largest values of $\theta$ in $(0,2 \pi)-\{\pi\}$ which satisfy the equation, $2 \cot ^{2} \theta-\frac{5}{\sin \theta}+4=0$, then $\int_{\theta_{1}}^{\theta_{2}} \cos ^{2} 3 \theta d \theta$ is equal to : $\frac{2 \pi}{3}$$\frac{\pi}{3}+\frac{1}{6}$$\frac{\pi}{9}$$\frac{\pi}{3}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: The molarity of $\mathrm{HNO}_{3}$ in a sample which has density $1.4 \mathrm{~g} / \mathrm{mL}$ and mass percentage of $63 \%$ is (Molecular Weight of $\mathrm{HNO}_{3}=63$ ) Solution:...
Read More →The hardness of a water sample containing
Question: The hardness of a water sample containing $10^{-3} \mathrm{M} \mathrm{MgSO}_{4}$ expressed as $\mathrm{CaCO}_{3}$ equivalents (in ppm) is (molar mass of $\mathrm{MgSO}_{4}$ is $120.37 \mathrm{~g} / \mathrm{mol}$ ) Solution:...
Read More →The value of c in the Lagrange's mean value theorem
Question: The value of $\mathrm{c}$ in the Lagrange's mean value theorem for the function $f(x)=x^{3}-4 x^{2}+8 x+11$, when $x \in[0,1]$ is :$\frac{2}{3}$$\frac{\sqrt{7}-2}{3}$$\frac{4-\sqrt{5}}{3}$$\frac{4-\sqrt{7}}{3}$Correct Option: , 4 Solution:...
Read More →The electronic configurations of bivalent europium and trivalent cerium are
Question: The electronic configurations of bivalent europium and trivalent cerium are (atomic number: $\mathrm{Xe}=54, \mathrm{Ce}=58, \mathrm{Eu}=63$ )$[\mathrm{Xe}] 4 \mathrm{f}^{4}$ and $[\mathrm{Xe}] 4 \mathrm{f}^{9}$[Xe] $4 \mathrm{f}^{7}$ and [Xe] $4 \mathrm{f}^{1}$$[\mathrm{Xe}] 4 \mathrm{f}^{7} 6 \mathrm{~s}^{2}$ and $[\mathrm{Xe}] 4 \mathrm{f}^{2} 6 \mathrm{~s}^{2}$$[\mathrm{Xe}] 4 \mathrm{f}^{2}$ and [Xe] $4 \mathrm{f}^{7}$Correct Option: , 2 Solution:...
Read More →If the sum of the first 40 terms of the series,
Question: If the sum of the first 40 terms of the series, $3+4+8+9+13+14+18+19+\ldots$ is (102)m, then $\mathrm{m}$ is equal to :2051025Correct Option: 1 Solution:...
Read More →The de Broglie wavelength of an electron in the
Question: The de Broglie wavelength of an electron in the $4^{\text {th }}$ Bohr orbit is : $8 \pi \mathrm{a}_{0}$$2 \pi \mathrm{a}_{0}$$4 \pi \mathrm{a}_{0}$$6 \pi a_{0}$Correct Option: 1 Solution:...
Read More →The compound that cannot act both as oxidising and reducing agent is :
Question: The compound that cannot act both as oxidising and reducing agent is : $\mathrm{H}_{2} \mathrm{O}_{2}$$\mathrm{H}_{2} \mathrm{SO}_{3}$$\mathrm{HNO}_{2}$$\mathrm{H}_{3} \mathrm{PO}_{4}$Correct Option: , 4 Solution:...
Read More →Solve this following
Question: Complex $\mathrm{X}$ of composition $\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6} \mathrm{Cl}_{n}$ has a spin only magnetic moment of $3.83$ BM. It reacts with $\mathrm{AgNO}_{3}$ and shows geometrical isomerism. The IUPAC nomenclature of $X$ is :Tetraaquadichlorido chromium $(\mathrm{II})$ chloride dihydrateHexaaqua chromium (III) chlorideDichloridotetraaqua chromium (IV) chloride dihydrateTetraaquadichlorido chromium(IV) chloride dihydrateCorrect Option: 1 Solution:...
Read More →The major product (Y) in the following reactions is:
Question: The major product (Y) in the following reactions is: Correct Option: , 3 Solution:...
Read More →Which of these will produce the highest yield in Friedel Crafts reaction?
Question: Which of these will produce the highest yield in Friedel Crafts reaction?Correct Option: , 3 Solution:...
Read More →The major product $mathrm{Z}$ obtained in the following reaction scheme is :
Question: The major product $\mathrm{Z}$ obtained in the following reaction scheme is : Correct Option: , 2 Solution:...
Read More →Complexes (ML5) of metals Ni and Fe have ideal
Question: Complexes $\left(\mathrm{ML}_{5}\right)$ of metals $\mathrm{Ni}$ and $\mathrm{Fe}$ have ideal square pyramidal and trigonal bipyramidal grometries, respectively. The sum of the $90^{\circ}, 120^{\circ}$ and $180^{\circ} \mathrm{L}-\mathrm{M} \mathrm{L}$ angles in the two complexes is__________ Solution: NTA Ans. $(20$ to 20$)$...
Read More →The acidic, basic and amphoteric oxides, respectively, are :
Question: The acidic, basic and amphoteric oxides, respectively, are : $\mathrm{MgO}, \mathrm{Cl}_{2} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3}$$\mathrm{Cl}_{2} \mathrm{O}, \mathrm{CaO}, \mathrm{P}_{4} \mathrm{O}_{10}$$\mathrm{Na}_{2} \mathrm{O}, \mathrm{SO}_{3}, \mathrm{Al}_{2} \mathrm{O}_{3}$$\mathrm{N}_{2} \mathrm{O}_{3}, \mathrm{Li}_{2} \mathrm{O}, \mathrm{Al}_{2} \mathrm{O}_{3}$Correct Option: , 4 Solution:...
Read More →B has a smaller first ionization enthalpy than Be. Consider the following statements :
Question: B has a smaller first ionization enthalpy than Be. Consider the following statements : (I) It is easier to remove $2 \mathrm{p}$ electron than $2 \mathrm{~s}$ electron (II) $2 \mathrm{p}$ electron of $\mathrm{B}$ is more shielded from the nucleus by the inner core of electrons than the $2 \mathrm{~s}$ electrons of $\mathrm{Be}$. (III) 2 s electron has more penetration power than 2 p electron. (IV) atomic radius of $\mathrm{B}$ is more than $\mathrm{Be}$ (Atomic number $\mathrm{B}=5, \m...
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