Which among the following species has unequal bond lengths?
Question: Which among the following species has unequal bond lengths?$\mathrm{XeF}_{4}$$\mathrm{SiF}_{4}$$B F_{4}^{-}$$\mathrm{SF}_{4}$Correct Option: , 4 Solution: $\mathrm{Sp}^{3} \mathrm{~d}$ Hybridisation Sea-saw shape $\backslash \$ axial bond length is more than equitorial bond length...
Read More →The mean of the marks scored by 50 students was found to be 39.
Question: The mean of the marks scored by 50 students was found to be 39. Latter on it was discovered that a core of 43 was misread as 23. The correct mean is(a) 38.6(b) 39.4(c) 39.8(d) 39.2 Solution: (b) 39.4Mean of the marks scored by 50 students = 39 Sum of the marks scored by 50 students $=(39 \times 50)=1950$ Correct sum $=(1950+43-23)=1970$ $\therefore$ Mean $=\frac{1970}{50}=39.4$...
Read More →A particle of mass $m$ is moving along
Question: A particle of mass $m$ is moving along the $x$-axis with initial velocity $u \hat{i}$. It collides elastically with a particle of mass 10 $\mathrm{m}$ at rest and then moves with half its initial kinetic energy (see figure). If $\sin \theta_{1}=\sqrt{n} \sin \theta_{2}$, then value of $n$ is ______ Solution: From momentum conservation in perpendicular direction of initial motion. $m u_{1} \sin \theta_{1}=10 m v_{1} \sin \theta_{2}$ ...(1) It is given that energy of $m$ reduced by half....
Read More →Let the functions
Question: Let the functions $f: \mathbb{R} \rightarrow \mathbb{R}$ and $\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}$ be defined as : $f(x)=\left\{\begin{array}{ll}x+2, x0 \\ x^{2}, x \geq 0\end{array}\right.$ and $g(x)= \begin{cases}x^{3}, x1 \\ 3 x-2, x \geq 1\end{cases}$ Then, the number of points in $\mathbb{R}$ where $(f \circ g)(x)$ is NOT differentiable is equal to : (1) 3(2) 1(3) 0(4) 2Correct Option: , 2 Solution: $f(g(x))= \begin{cases}g(x)+2, g(x)0 \\ (g(x))^{2}, g(x) \geq 0\end{case...
Read More →The mean weight of six boys in a groups is 48 kg.
Question: The mean weight of six boys in a groups is 48 kg. The individual weights of five of them are 51 kg, 45 kg, 49 kg, 46 kg and 44 kg. The weight of the 6th boy is(a) 52 kg(b) 52.8 kg(c) 53 kg(d) 47 kg Solution: (c) 53 kgMean weight of six boys = 48 kgLet the weight of the 6th boy bexkg. We know : Mean $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$ $=\frac{51+45+49+46+44+x}{6}$ $=\frac{235+x}{6}$ Given : Mean $=48 \mathrm{~kg}$ $\Rightarrow \frac{235+x}...
Read More →According to molecular orbital theory,
Question: According to molecular orbital theory, the species among the following that does not exist is:$\mathrm{He}_{2}^{-}$$\mathrm{He}_{22}^{+}$$\mathrm{O}_{2}^{2-}$$\mathrm{Be}_{2}$Correct Option: , 4 Solution: B. O. of $B e_{2}$ is zero, So it does not exist....
Read More →The correct shape and I-I-I bond angles respectively in $mathrm{I}_{3}^{-}$ion are :
Question: The correct shape and I-I-I bond angles respectively in $\mathrm{I}_{3}^{-}$ion are :Trigonal planar; $120^{\circ}$Distorted trigonal planar; $135^{\circ}$ and $90^{\circ}$Linear; $180^{\circ}$T-shaped; $180^{\circ}$ and $90^{\circ}$Correct Option: , 3 Solution: $\mathrm{I}_{3}^{-} \mathrm{sp}^{3} \mathrm{~d}$ hybridisation (2BP + 3L.P.) Linear geometry...
Read More →If each observation of the data is increased by 8, then their mean
Question: If each observation of the data is increased by 8, then their mean(a) remains the same(b) is decreased by 8(c) is increased by 5(d) becomes 8 times the original mean Solution: (b) is decreased by 8 Let the numbers be $x_{1}, x_{2} \ldots x_{n} .$ Hence, mean $=\frac{x_{1}+x_{2}+\ldots+x_{n}}{n}$ Now the new numbers after decreasing every number by $8:\left(x_{1}-8\right),\left(x_{2}-8\right) \ldots,\left(x_{n}-8\right)$ New Mean $=\frac{\left(x_{1}-8\right)+\left(x_{2}-8\right)+\ldots+...
Read More →A square shaped hole of side
Question: A square shaped hole of side $l=\frac{a}{2}$ is carved out at a distance $d=\frac{a}{2}$ from the centre ' $O$ ' of a uniform circular disk of radius $a$. If the distance of the centre of mass of the remaining portion from $O$ is $-\frac{a}{X}$, value of $X$ (to the nearest integer) is_____ Solution: Let $\sigma$ be the mass density of circular disc. Original mass of the disc, $m_{0}=\pi a^{2} \sigma$ Removed mass, $m=\frac{a^{2}}{4} \sigma$ Remaining, mass, $m^{\prime}=\left(\pi a^{2}...
Read More →If x is the mean of x1, x2, x3, ..., xn, then
Question: If $\bar{x}$ is the mean of $x_{1}, x_{2}, x_{3}, \ldots, x_{n}$, then $\sum_{i=1}^{n}\left(x_{i}-\bar{x}\right)=?$ (a) $-1$ (b) 0(c) 1 (d)n 1 Solution: (b) 0 If $\bar{x}$ is the mean of $x_{1}, x_{2}, x_{3}, x_{4, \ldots} x_{n}$, then we have: $\sum_{i=1}^{n} x_{i}=\bar{x}$ $\mathrm{O} r$ $\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}-\overline{\mathrm{x}}=0$...
Read More →Which of the following are isostructural pairs?
Question: Which of the following are isostructural pairs? (A) $\mathrm{SO}_{4}^{2-}$ and $\mathrm{CrO}_{4}^{2-}$ (B) $\mathrm{SiCl}_{4}$ and $\mathrm{TiCl}_{4}$ (c) $\mathrm{NH}_{3}$ and $\mathrm{NO}_{3}^{-}$ (D) $\mathrm{BCl}_{3}$ and $\mathrm{BrCl}_{3}$A and $C$ only$A$ and $B$ only$B$ and $C$ onlyC and D onlyCorrect Option: , 2 Solution: (a) $\mathrm{SO}_{4}^{-2}$ and $\mathrm{CrO}_{4}{ }^{2-}$ both have tetrahedral structure. (b) $\mathrm{SiCl}_{4}$ and $\mathrm{TiCl}_{4}$ both have Tetrahed...
Read More →The number of species below that have two lone pairs of electrons in their central atom is
Question: The number of species below that have two lone pairs of electrons in their central atom is ________________(Round off to the Nearest integer) Solution: (2) Two l.p. on central atom is $=\mathrm{ClF}_{3}, \mathrm{XeF}_{4}$...
Read More →A particle of mass m with an initial velocity
Question: A particle of mass $m$ with an initial velocity $u \hat{i}$ collides perfectly elastically with a mass $3 \mathrm{~m}$ at rest. It moves with a velocity $v \hat{j}$ after collision, then, $v$ is given by:(1) $v=\sqrt{\frac{2}{3}} u$(2) $v=\frac{u}{\sqrt{3}}$(3) $v=\frac{u}{\sqrt{2}}$(4) $v=\frac{1}{\sqrt{6}} u$Correct Option: Solution: (3) From conservation of inear momentum $m u \hat{i}+0=m v \hat{j}+3 m \overrightarrow{v^{\prime}}$ $\overrightarrow{v^{\prime}}=\frac{u}{3} \hat{i}-\fr...
Read More →If
Question: If $\frac{z-\alpha}{z+\alpha}(\alpha \in \mathrm{R})$ is a purely imaginary number and $|\mathrm{z}|=2$, then a value of $\alpha$ is : (1) 2(2) 1(3) $\frac{1}{2}$(4) $\sqrt{2}$Correct Option: 1 Solution: Let $t=\frac{z-\alpha}{z+\alpha}$ $\because t$ is purely imaginary number. $\therefore \quad t+\bar{t}=0$ $\Rightarrow \quad \frac{z-\alpha}{z+\alpha}+\frac{\bar{z}-\alpha}{\bar{z}+\alpha}=0$ $\Rightarrow \quad(z-\alpha)(\bar{z}+\alpha)+(\bar{z}-\alpha)(z+\alpha)=0$ $\Rightarrow \quad ...
Read More →The total number is irrational terms in the binomial expansion of
Question: The total number is irrational terms in the binomial expansion of $\left(7^{1 / 5}-3^{1 / 10}\right)^{60}$ is:(1) 55(2) 49(3) 48(4) 54Correct Option: , 4 Solution: Let the general term of the expansion $T_{r+1}={ }^{60} C_{r}\left(7^{\frac{1}{5}}\right)^{60-r}\left(-3^{\frac{1}{10}}\right)^{r}$ $={ }^{60} C_{r} \cdot(7)^{12-\frac{r}{5}}(-1)^{r} \cdot(3)^{\frac{r}{10}}$ Then, for getting rational terms, $r$ should be multiple of L.C.M. of $(5,10)$ Then, $r$ can be $0,10,20,30,40,50,60$....
Read More →In the following molecules,
Question: In the following molecules, Hybridisation of carbon $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ respectively are :$\mathrm{sp}^{3}, \mathrm{sp}, \mathrm{sp}$$\mathrm{sp}^{3}, \mathrm{sp}^{2}, \mathrm{sp}$$\mathrm{sp}^{3}, \mathrm{sp}^{2}, \mathrm{sp}^{2}$$\mathrm{sp}^{3}, \mathrm{sp}, \mathrm{sp}^{2}$Correct Option: , 3 Solution:...
Read More →If the mean of x, x + 3, x + 5, x + 7, x + 10 is 9, the mean of the last three observations is
Question: If the mean ofx,x+ 3,x+ 5,x+ 7,x+ 10 is 9, the mean of the last three observations is (a) $10 \frac{1}{3}$ (b) $10 \frac{2}{3}$ (c) $11 \frac{1}{3}$ (d) $11 \frac{2}{3}$ Solution: (c) $11 \frac{1}{3}$ Mean of 5 observations = 9We know: Mean $=\frac{\text { Sum of observations }}{\text { Total number of observations }}$ $\Rightarrow 9=\frac{x+x+3+x+5+x+7+x+10}{5}$ $\Rightarrow 9=\frac{5 x+25}{5}$ $\Rightarrow 5 x+25=45$ $\Rightarrow 5 x=20$ $\Rightarrow x=4$ Therefore, the last three ob...
Read More →Let z be a complex number such that
Question: Let $\mathrm{z}$ be a complex number such that $|\mathrm{z}|+\mathrm{z}=3+\mathrm{i}$ $($ where $\mathrm{i}=\sqrt{-1})$. Then $|z|$ is equal to:(1) $\frac{\sqrt{34}}{3}$(2) $\frac{5}{3}$(3) $\frac{\sqrt{41}}{4}$(4) $\frac{5}{4}$Correct Option: , 2 Solution: Since, $|z|+z=3+i$ Let $z=a+i b$, then $|z|+z=3+i \Rightarrow \sqrt{a^{2}+b^{2}}+a+i b=3+i$ Compare real and imaginary coefficients on both sides $b=1, \sqrt{a^{2}+b^{2}}+a=3$ $\sqrt{a^{2}+1}=3-a$ $a^{2}+1=a^{2}+9-6 a$ $6 a=8$ $a=\f...
Read More →Given below are two statements :
Question: Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body 'P' having mass M moving with speed 'u' has head-on collision elastically with another body ' $Q$ ' having mass ' $m$ ' initially at rest. If $\$ m$ Reason $R$ : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:(1) $\mathrm{A}$ is correc...
Read More →The oxide that shows magnetic property is :
Question: The oxide that shows magnetic property is :$\mathrm{SiO}_{2}$$\mathrm{Mn}_{3} \mathrm{O}_{4}$$\mathrm{Na}_{2} \mathrm{O}$$\mathrm{MgO}$Correct Option: , 2 Solution: $\mathrm{Mn}_{3} \mathrm{O}_{4}$ shows magnetic properties...
Read More →If the mean of five observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is
Question: If the mean of five observationsx,x+ 2,x+ 4,x+ 6 andx+ 8 is 11, then the value ofxis(a) 5(b) 6(c) 7(d) 8 Solution: (c) 7Mean of 5 observations = 11We know: Mean $=\frac{\text { Sum of all observations }}{\text { Total number of observations }}$ $\Rightarrow 11=\frac{x+x+2+x+4+x+6+x+8}{5}$ $\Rightarrow 11=\frac{5 x+20}{5}$ $\Rightarrow 5 x+20=55$ $\Rightarrow 5 x=35$ $\Rightarrow x=7$...
Read More →where x and y are real numbers then y-x equals :
Question: Let $\left(-2-\frac{1}{3} i\right)^{3}=\frac{x+i y}{27}(i=\sqrt{-1})$, where $\mathrm{x}$ and $\mathrm{y}$ are real numbers then $y-x$ equals :(1) 91(2) $-85$(3) 85(4) $-91$Correct Option: 1 Solution: $-(6+i)^{3}=x+i y$ $\Rightarrow \quad-\left[216+i^{3}+18 i(6+i)\right]=x+i y$ $\Rightarrow \quad-[216-i+108 i-18]=x+i y$ $\Rightarrow \quad-216+i-108 i+18=x+i y$ $\Rightarrow \quad-198-107 i=x+i y$ $\Rightarrow \quad x=-198, y=-107$ $\Rightarrow \quad y-x=-107+198=91$...
Read More →Solve the following
Question: $A \mathrm{X}$ is a covalent diatomic molecule where $\mathrm{A}$ and $X$ are second row elements of periodic table. Based on Molecular orbital theory, the bond order of $\mathrm{AX}$ is 25 . The total number of electrons in $\mathrm{AX}$ is ___________ (Round off to the Nearest Integer). Solution: (15) AX is a covalent diatomic molecule. The molecule is NO. Total no. of electrons is 15 ....
Read More →Solve the following
Question: $A \mathrm{X}$ is a covalent diatomic molecule where $\mathrm{A}$ and $X$ are second row elements of periodic table. Based on Molecular orbital theory, the bond order of $\mathrm{AX}$ is 25 . The total number of electrons in $\mathrm{AX}$ is (Round off to the Nearest Integer). Solution: (15) AX is a covalent diatomic molecule. The molecule is NO. Total no. of electrons is 15 ....
Read More →respectively denote the real and imaginary parts of z, then:
Question: Let $z=\left(\frac{\sqrt{3}}{2}+\frac{\mathrm{i}}{2}\right)^{5}+\left(\frac{\sqrt{3}}{2}-\frac{\mathrm{i}}{2}\right)^{5}$. If $\mathrm{R}(z)$ and $\mathrm{I}(z)$ respectively denote the real and imaginary parts of $z$, then:(1) $\mathrm{I}(z)=0$(2) $\mathrm{R}(z)0$ and $\mathrm{I}(z)0$(3) $\mathrm{R}(z)0$ and $\mathrm{I}(z)0$(4) $\mathrm{R}(z)=-(3)$Correct Option: 1 Solution: $z=\left(\frac{\sqrt{3}}{2}+\frac{i}{2}\right)^{5}+\left(\frac{\sqrt{3}}{2}-\frac{i}{2}\right)^{5}$ $=\left(\co...
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