Match the metals (column I) with the coordination compound
Question: Match the metals (column I) with the coordination compound(s)/enzyme(s) (column II) : (A)-(iii); (B)-(iv); (C)-(i); (D)-(ii)(A)-(i); (B)-(ii); (C)-(iii); (D)-(iv)(A)-(ii); (B)-(i); (C)-(iv); (D)-(iii)(A)-(iv);(B)-(iii); (C)-(i); (D)-(ii)Correct Option: 1 Solution: Wilkinson catalyst : $\left[\mathrm{Rh}(\mathrm{PPh})_{3} \mathrm{Cl}\right]$ Chlorophyll : $\mathrm{C}_{55} \mathrm{H}_{72} \mathrm{O}_{5} \mathrm{~N}_{4} \mathrm{Mg}$ Vitamin $\mathrm{B}_{12}$ contains Co. Carbonic anhydras...
Read More →Negation of the statement:
Question: Negation of the statement: $\sqrt{5}$ is an integer of 5 is irrational is:(1) $\sqrt{5}$ is not an integer or 5 is not irrational(2) $\sqrt{5}$ is not an integer and 5 is not irrational(3) $\sqrt{5}$ is irrational or 5 is an integer.(4) $\sqrt{5}$ is an integer and 5 is irrationalCorrect Option: , 2 Solution: Let $\mathrm{p}$ and $\mathrm{q}$ the statements such that $p=\sqrt{5}$ is an integer $q=5$ is an irrational number. Then, negation of the given statement $\sqrt{5}$ is not an int...
Read More →The radius in kilometer to which the present radius
Question: The radius in kilometer to which the present radius of earth $(\mathrm{R}=6400 \mathrm{~km})$ to be compressed so that the escape velocity is increased 10 time is Solution: (64) $V_{e}=\sqrt{\frac{2 G m}{R}} \quad \cdots$ $10 \mathrm{~V}_{\mathrm{e}}=\sqrt{\frac{2 \mathrm{Gm}}{\mathrm{R}^{\prime}}} \quad \cdots$ $\therefore 10=\sqrt{\frac{\mathrm{R}}{\mathrm{R}^{\prime}}}$ $\Rightarrow \mathrm{R}^{\prime}=\frac{\mathrm{R}}{100}=\frac{6400}{100}=64 \mathrm{~km}$...
Read More →If one wants to remove all the mass of the earth to infinity in order to break
Question: If one wants to remove all the mass of the earth to infinity in order to break it up completely. The amount of energy that needs to be supplied will be $\frac{x}{5} \frac{\mathrm{GM}^{2}}{\mathrm{R}}$ where $\mathrm{x}$ is___ (Round off to the Nearest Integer) ( $M$ is the mass of earth, $R$ is the radius of earth, $G$ is the gravitational constant) Solution: (3) Energy given $=\mathrm{U}_{\mathrm{f}}-\mathrm{U}_{\mathrm{i}}$ $=0-\left(-\frac{3 \mathrm{GM}^{2}}{5} \frac{\mathrm{R}}{\ma...
Read More →Which of the following statements is a tautology?
Question: Which of the following statements is a tautology?(1) $p \vee(\sim q) \rightarrow p \wedge q$(2) $\sim(p \wedge \sim \mathrm{q}) \rightarrow p \vee q$(3) $\sim(p \vee \sim q) \rightarrow P \wedge q$(4) $\sim(P \vee \sim q) \rightarrow p \vee q$Correct Option: , 4 Solution: $(\sim p \wedge q) \rightarrow(p \vee q)$ $\Rightarrow \sim\{(\sim p \wedge q) \wedge(\sim p \wedge \sim q)\}$ $\Rightarrow \sim\{p \wedge f\}$...
Read More →Find the values of k for which the given quadratic equation has real and distinct roots:
Question: Find the values ofkfor which the given quadratic equation has real and distinct roots: (i) $k x^{2}+6 x+1=0$ (ii) $x^{2}-k x+9=0$ (iii) $9 x^{2}+3 k x+4=0$ (iv) $5 x^{2}-k x+1=0$ Solution: (i) The given equation is $k x^{2}+6 x+1=0$. $\therefore D=6^{2}-4 \times k \times 1=36-4 k$ The given equation has real and distinct roots ifD 0. $\therefore 36-4 k0$ $\Rightarrow 4 k36$ $\Rightarrow k9$ (ii) The given equation is $x^{2}-k x+9=0$. $\therefore D=(-k)^{2}-4 \times 1 \times 9=k^{2}-36$...
Read More →The element that usually does NOT show
Question: The element that usually does NOT show variable oxidation states is:CuTiScVCorrect Option: , 3 Solution: Sc shows oxidation state of $+3$ only....
Read More →Which one of the following is a tautology?
Question: Which one of the following is a tautology?(1) $(p \wedge(p \rightarrow q)) \rightarrow q$(2) $q \rightarrow(p \wedge(p \rightarrow q))$(3) $p \wedge(p \vee q)$(4) $p \vee(p \wedge q)$Correct Option: 1 Solution:...
Read More →The maximum and minimum distances of a comet from the Sun are
Question: The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \mathrm{~m}$ and $8.0 \times 10^{10} \mathrm{~m}$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4} \mathrm{~ms}^{-1}$, the speed at the farthest point is :(1) $1.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$(2) $6.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$(3) $3.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$(4) $4.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$Correct Option: 3 Solution: (...
Read More →Find the values k for which of roots of
Question: Find the values $k$ for which of roots of $9 x^{2}+8 k x+16=0$ are real and equal Solution: Given: $9 x^{2}+8 k x+16=0$ Here, $a=9, b=8 k$ and $c=16$ It is given that the roots of the equation are real and equal; therefore, we have: $D=0$ $\Rightarrow\left(b^{2}-4 a c\right)=0$ $\Rightarrow(8 k)^{2}-4 \times 9 \times 16=0$ $\Rightarrow 64 k^{2}-576=0$ $\Rightarrow 64 k^{2}=576$ $\Rightarrow k^{2}=9$ $\Rightarrow k=\pm 3$ $\therefore k=3$ or $\mathrm{k}=-3$...
Read More →of gold and silver, respectively, are:
Question: The electrolytes usually used in the electroplating of gold and silver, respectively, are:$\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-}$and $\left[\mathrm{Ag}(\mathrm{CN})_{2}\right]^{-}$$\left[\mathrm{Au}(\mathrm{CN})_{2}\right]^{-}$and $\left[\mathrm{Ag} \mathrm{Cl}_{2}\right]^{-}$$\left[\mathrm{Au}(\mathrm{OH})_{4}\right]^{-}$and $\left[\mathrm{Ag}(\mathrm{OH})_{2}\right]^{-}$$\left[\mathrm{Au}\left(\mathrm{NH}_{3}\right)_{2}\right]^{+}$and $\left[\mathrm{Ag}(\mathrm{CN})_{2}\right...
Read More →Let A, B, C and D be four non-empty sets.
Question: Let $A, B, C$ and $D$ be four non-empty sets. The contrapositive statement of "If $A \subseteq B$ and $B \subseteq D$, then $A \subseteq C$ " is:(1) If $A \not \subset C$, then $A \subseteq B$ and $B \subseteq D$(2) If $A \subseteq C$, then $B \subset A$ or $D \subset B$(3) If $A \not \subset$, then $A \not B$ and $B \subseteq D$(4) If $A \not \subset$, then $A \not \subset B$ or $B \nsubseteq D$Correct Option: , 4 Solution: Let $P=A \subseteq B, Q=B \subseteq D, R=A \subseteq C$ Contr...
Read More →The effect of lanthanoid contraction in the lanthanoid series of
Question: The effect of lanthanoid contraction in the lanthanoid series of elements by and large means:increase in both atomic and ionic radiidecrease in atomic radii and increase in ionic radiidecrease in both atomic and ionic radiiincrease in atomic radii and decrease in ionic radiiCorrect Option: , 2 Solution: Due to lanthanoid contraction, size of atom as well as ion of lanthanoid decreases....
Read More →The logical statement
Question: The logical statement $(p \Rightarrow q)^{\wedge}(q \Rightarrow \sim p)$ is equivalent to:(1) $p$(2) $q$(3) $\sim P$(4) $\sim q$Correct Option: , 3 Solution: Clearly $(p \Rightarrow q) \wedge(q \Rightarrow \sim p)$ is equivalent to $\sim p$...
Read More →Find the value of α for which the equation
Question: Find the value of a for which the equation $(\alpha-12) x^{2}+2(\alpha-12) x+2=0$ has equal roots. Solution: Given: $(\alpha-12) x^{2}+2(\alpha-12) x+2=0$ Here, $a=(\alpha-12), b=2(\alpha-12)$ and $c=2$ It is given that the roots of the equation are equal; therefore, we have: $D=0$ $\Rightarrow\left(b^{2}-4 a c\right)=0$ $\Rightarrow\{2(\alpha-12)\}^{2}-4 \times(\alpha-12) \times 2=0$ $\Rightarrow 4\left(\alpha^{2}-24 \alpha+144\right)-8(\alpha-12)=0$ $\Rightarrow 4 \alpha^{2}-96 \alph...
Read More →Consider the statement: "For an integer n,
Question: Consider the statement: "For an integer $n$, if $n^{3}-1$ is even, then $\mathrm{n}$ is odd." The contrapositive statement of this statement is:(1) For an integer $\mathrm{n}$, if $\mathrm{n}$ is even, then $\mathrm{n}^{3}-1$ is odd.(2) For an intetger $\mathrm{n}$, if $\mathrm{n}^{3}-1$ is not even, then $\mathrm{n}$ is not odd.(3) For an integer $\mathrm{n}$, if $\mathrm{n}$ is even, then $\mathrm{n}^{3}-1$ is even.(4) For an integer $\mathrm{n}$, if $\mathrm{n}$ is odd, then $\mathr...
Read More →The transition element thăt has lowest enthalpy of atomisation is:
Question: The transition element thăt has lowest enthalpy of atomisation is:FeCuVZnCorrect Option: , 4 Solution: As zinc has no unpaired of electrons to take part in the bond, it has least enthalpy of atomisation amongst the given transition elements....
Read More →Determine the values of p for which the quadratic equation
Question: Determine the values of $p$ for which the quadratic equation $2 x^{2}+p x+8=0$ has real roots. Solution: Given: $2 x^{2}+p x+8=0$ Here, $a=2, b=p$ and $c=8$ Discriminant $D$ is given by : $D=\left(b^{2}-4 a c\right)$ $=p^{2}-4 \times 2 \times 8$ $=\left(p^{2}-64\right)$ If $D \geq 0$, the roots of the equation will be real. $\Rightarrow\left(p^{2}-64\right) \geq 0$ $\Rightarrow(p+8)(p-8) \geq 0$ $\Rightarrow p \geq 8$ and $p \leq-8$ Thus, the roots of the equation are real for $p \geq ...
Read More →The negation of the Boolean expression
Question: The negation of the Boolean expression $p \vee(\sim p \wedge q)$ is equivalent to:(1) $p \wedge \sim q$(2) $\sim p \wedge \sim q$(3) $\sim p \vee \sim q$(4) $\sim p \vee q$Correct Option: , 2 Solution: Negation of given statement $=\sim(p \vee(\sim p \wedge q))$ $=\sim p \wedge \sim(\sim p \wedge q)=\sim p \wedge(p \vee \sim q)$ $=(\sim p \wedge q) \vee(\sim p \wedge \sim q)$ $=F \vee(\sim p \wedge \sim q)=\sim p \wedge \sim q$...
Read More →Thermal decomposition of a Mn compound (X) at
Question: Thermal decomposition of a Mn compound (X) at $513 \mathrm{~K}$ results in compound $\mathrm{Y}, \mathrm{MnO}_{2}$ and a gaseous product. $\mathrm{MnO}_{2}$ reacts with $\mathrm{NaCl}$ and concentrated $\mathrm{H}_{2} \mathrm{SO}_{4}$ to give a pungent gas Z. X, Y, and Z, respectively, are :$\mathrm{K}_{3} \mathrm{MnO}_{4}, \mathrm{~K}_{2} \mathrm{MnO}_{4}$ and $\mathrm{Cl}_{2}$$\mathrm{K}_{2} \mathrm{MnO}_{4}, \mathrm{KMnO}_{4}$ and $\mathrm{SO}_{2}$$\mathrm{KMnO}_{4}, \mathrm{~K}_{2}...
Read More →A metal plate of area
Question: A metal plate of area $1 \times 10^{-4} \mathrm{~m}^{2}$ is illuminated by a radiation of intensity $16 \mathrm{~mW} / \mathrm{m}^{2}$. The work function of the metal is $5 \mathrm{eV}$. The energy of the incident photons is $10 \mathrm{eV}$ and only $10 \%$ of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be: $\left[1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right]$(1) $10^{14}$ and $10 \mathrm{eV}$(2) $10...
Read More →If the roots of the equation
Question: If the roots of the equation $\left(c^{2}-a b\right) x^{2}-2\left(a^{2}-b c\right) x+\left(b^{2}-a c\right)=0$ are real and equal, show that either $a=0$ or $\left(a^{3}+b^{3}+c^{3}\right)=3 a b c$. Solution: Given: $\left(c^{2}-a b\right) x^{2}-2\left(a^{2}-b c\right) x+\left(b^{2}-a c\right)=0$ Here, $a=\left(c^{2}-a b\right), b=-2\left(a^{2}-b c\right), c=\left(b^{2}-a c\right)$ It is given that the roots of the equation are real and equal; therefore, we have: $D=0$ $\Rightarrow\lef...
Read More →The statement
Question: The statement $(p \rightarrow(q \rightarrow p)) \rightarrow(p \rightarrow(p \vee q))$ is :(1) equivalent to $(p \wedge q) \vee(\sim q)$(2) a contradiction(3) equivalent to $(p \vee q) \wedge(\sim p)$(4) a tautologyCorrect Option: , 4 Solution: The truth table of $(p \rightarrow(q \rightarrow p)) \rightarrow(p \rightarrow(p \vee q))$ is Hence, the statement is tautology....
Read More →The metal that gives hydrogen gas upon treatment with both acid as well as base is :
Question: The metal that gives hydrogen gas upon treatment with both acid as well as base is :magnesiummercuryzincironCorrect Option: , 3 Solution:...
Read More →If the equation
Question: If the equation $\left(1+m^{2}\right) x^{2}+2 m c x+\left(c^{2}-a^{2}\right)=0$ has equal roots, prove that $c^{2}=a^{2}\left(1+m^{2}\right)$. Solution: Given: $\left(1+m^{2}\right) x^{2}+2 m c x+\left(c^{2}-a^{2}\right)=0$ Here, $a=\left(1+m^{2}\right), b=2 m c$ and $c=\left(c^{2}-a^{2}\right)$ It is given that the roots of the equation are equal; therefore, we have: $D=0$ $\Rightarrow\left(b^{2}-4 a c\right)=0$ $\Rightarrow(2 m c)^{2}-4 \times\left(1+m^{2}\right) \times\left(c^{2}-a^...
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