eSaral - JEE | NEET | Class 8-10 Exam Prep App

The oxidation states of nitrogen in NO,

Question: The oxidation states of nitrogen in $\mathrm{NO}, \mathrm{NO}_{2}$, $\mathrm{N}_{2} \mathrm{O}$ and $\mathrm{NO}_{3}^{-}$are in the order of:$\mathrm{NO}_{3}^{-}\mathrm{NO}_{2}\mathrm{NO}\mathrm{N}_{2} \mathrm{O}$$\mathrm{NO}_{2}\mathrm{NO}_{3}^{-}\mathrm{NO}\mathrm{N}_{2} \mathrm{O}$$\mathrm{N}_{2} \mathrm{O}\mathrm{NO}_{2}\mathrm{NO}\mathrm{NO}_{3}^{-}$$\mathrm{NO}\mathrm{NO}_{2}\mathrm{N}_{2} \mathrm{O}\mathrm{NO}_{3}^{-}$Correct Option: 1 Solution: The oxidation states of Nitrogen ...

A particle is moving along the x-axis with its coordinate with time ' t ' given by

Question: A particle is moving along the $x$-axis with its coordinate with time ' $t$ ' given by $x(t)=10+8 t-3 t^{2}$. Another particle is moving along the $y$-axis with its coordinate as a function of time given by $y(t)=5-8 t^{3}$. At $t=1 \mathrm{~s}$, the speed of the second particle as measured in the frame of the first particle is given as $\sqrt{v}$. Then $v($ in $\mathrm{m} / \mathrm{s})$ is________ Solution: $(580)$ At $t=1 \mathrm{sec}$ $\vec{V}_{A}=(8-6 t) \hat{i}=2 \hat{i}$ and $\ve...

A point on the straight line,

Question: A point on the straight line, $3 x+5 y=15$ which is equidistant from the coordinate axes will lie only in :(1) $4^{\text {th }}$ quadrant(2) $1^{\text {st }}$ quadrant(3) $1^{\text {st }}$ and $2^{\text {nd }}$ quadrants(4) $1^{\text {st }}, 2^{\text {nd }}$ and $4^{\text {th }}$ quadrantsCorrect Option: , 3 Solution: A point which is equidistant from both the axes lies on either $y=x$ and $y=-x$. Since, point lies on the line $3 x+5 y=15$ Then the required point $3 x+5 y=15$ $\frac{x+...

The number of ionisable hydrogens present in the product obtained

Question: The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is:3021Correct Option: , 3 Solution:...

When a particle of mass m is attached to a vertical spring of spring constant k

Question: When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $y(t)=y_{0} \sin ^{2} \omega \mathrm{t}$, where ' $y$ ' is measured from the lower end of unstretched spring. Then $\omega$ is :(1) $\frac{1}{2} \sqrt{\frac{g}{y_{0}}}$(2) $\sqrt{\frac{g}{y_{0}}}$(3) $\sqrt{\frac{g}{2 y_{0}}}$(4) $\sqrt{\frac{2 g}{y_{0}}}$Correct Option: , 3 Solution: (3) $y=y_{0} \sin ^{2} \omega t$ $\Rightarrow y=\frac{y_{0}}{2}(1-\cos 2 \omega...

Let C be the centroid of the triangle

Question: Let $\mathrm{C}$ be the centroid of the triangle with vertices $(3,-1)$, $(1,3)$ and $(2,4)$. Let $P$ be the point of intersection of the lines $x+3 y-1=0$ and $3 x-y+1=0$. Then the line passing through the points $C$ and $P$ also passes through the point:(1) $(-9,-6)$(2) $(9,7)$(3) $(7,6)$(4) $(-9,-7)$Correct Option: 1 Solution: Coordinates of centroides $C=\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$ $=\left(\frac{3+1+2}{3}, \frac{-1+3+4}{3}\right)=(2,2)$ Th...

Match List-I with List-II

Question: Choose the most appropriate answer from the options given below -$a-i i, b-i v, c-i, d-i i i$$\mathrm{a}-\mathrm{i}, \mathrm{b}-\mathrm{iii}, \mathrm{c}-\mathrm{ii}, \mathrm{d}-\mathrm{iv}$$a-i i i, b-i, c-i v, d-i i$$\mathrm{a}-\mathrm{iv}, \mathrm{b}-\mathrm{ii}, \mathrm{c}-\mathrm{i}, \mathrm{d}-\mathrm{iii}$Correct Option: 1 Solution: In manufacture of $\mathrm{H}_{2} \mathrm{SO}_{4}$ (contact process), $\mathrm{V}_{2} \mathrm{O}_{5}$ is used as a catalyst. $\mathrm{Ni}$ catalysts ...

Let the normal at a point P on the curve

Question: Let the normal at a point $P$ on the curve $y^{2}-3 x^{2}+y+10=0$ intersect the $y$-axis at $\left(0, \frac{3}{2}\right)$. If $m$ is the slope of the tangent at $P$ to the curve, then $|m|$ is equal to__________. Solution: $P \equiv\left(x_{1}, y_{1}\right)$ $2 y y^{\prime}-6 x+y^{\prime}=0$ $\Rightarrow \quad y^{\prime}=\left(\frac{6 x_{1}}{1+2 y_{1}}\right)$ $\left(\frac{\frac{3}{2}-y_{1}}{-x_{1}}\right)=-\left(\frac{1+2 y_{1}}{6 x_{1}}\right)$ [By point slope form, $\left.y-y_{1}=m\...

A clock has a continuously moving second's hand of 0.1 m length.

Question: A clock has a continuously moving second's hand of $0.1$ $\mathrm{m}$ length. The average acceleration of the tip of the hand (in units of $\mathrm{ms}^{-2}$ ) is of the order of:(1) $10^{-3}$(2) $10^{-4}$(3) $10^{-2}$(4) $10^{-1}$Correct Option: 1 Solution: (1) Here, $R=0.1 \mathrm{~m}$ $\omega=\frac{2 \pi}{T}=\frac{2 \pi}{60}=0.105 \mathrm{rad} / \mathrm{s}$ Acceleration of the tip of the clock second's hand, $a=\omega^{2} R=(0.105)^{2}(0.1)=0.0011=1.1 \times 10^{-3} \mathrm{~m} / \m...

Let two points be A(1,-1) and B(0,2).

Question: Let two points be $A(1,-1)$ and $B(0,2)$. If $a$ point $P\left(x^{\prime}, y^{\prime}\right)$ be such that the area of $\triangle P A B=5 \mathrm{sq}$. units and it lies on the line, $3 x+y-4 \lambda=0$, then a value of $\lambda$ is:(1) 4(2) 3(3) 1(4) $-3$Correct Option: , 2 Solution: $D=\frac{1}{2}\left|\begin{array}{rrr}0 2 1 \\ 1 -1 1 \\ x^{\prime} y^{\prime} 1\end{array}\right|=5$ $\Rightarrow-2\left(1-x^{\prime}\right)+\left(y^{\prime}+x^{\prime}\right)=\pm 10$ $\Rightarrow-2+2 x^...

The set that represents the pair of neutral oxides of nitrogen is:

Question: The set that represents the pair of neutral oxides of nitrogen is:$\mathrm{NO}$ and $\mathrm{N}_{2} \mathrm{O}$$\mathrm{N}_{2} \mathrm{O}$ and $\mathrm{N}_{2} \mathrm{O}_{3}$$\mathrm{N}_{2} \mathrm{O}$ and $\mathrm{NO}_{2}$$\mathrm{NO}$ and $\mathrm{NO}_{2}$Correct Option: 1 Solution: $\mathrm{N}_{2} \mathrm{O}$ and $\mathrm{NO}$ are neutral oxides of nitrogen $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{2}$ are acidic oxides....

A beam of plane polarised light of large cross-sectional area

Question: A beam of plane polarised light of large cross-sectional area and uniform intensity of $3.3 \mathrm{Wm}^{-2}$ falls normally on a polariser (cross sectional area $3 \times 10^{-4} \mathrm{~m}^{2}$ ) which rotates about its axis with an angular speed of $31.4 \mathrm{rad} / \mathrm{s}$. The energy of light passing through the polariser per revolution, is close to:(1) $1.0 \times 10^{-5} \mathrm{~J}$(2) $1.0 \times 10^{-4} \mathrm{~J}$(3) $1.5 \times 10^{-4} \mathrm{~J}$(4) $5.0 \times 1...

If the foot of the perpendicular drawn

Question: If the foot of the perpendicular drawn from the point $(1,0,3)$ on $a$ line passing through $(\alpha, 7,1)$ is $\left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$, then $\alpha$ is equal to__________. Solution: Since, $P Q$ is perpendicular to $\mathrm{L}$ $Q\left(\frac{5}{3}, \frac{7}{3}, \frac{17}{3}\right)$ $\therefore \quad\left(1-\frac{5}{3}\right)\left(\alpha-\frac{5}{3}\right)+\left(\frac{-7}{3}\right)\left(7-\frac{7}{3}\right)$ $+\left(3-\frac{17}{3}\right)\left(1-\frac{17}{3...

The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of product 'A'.

Question: The reaction of white phosphorus on boiling with alkali in inert atmosphere resulted in the formation of product 'A'. The reaction $1 \mathrm{~mol}$ of 'A' with excess of $\mathrm{AgNO}_{3}$ in aqueous medium gives_______________ $\operatorname{mol}(\mathrm{s})$ of $\mathrm{Ag}$. (Round off to the Nearest Integer). Solution: (4)...

A bead of mass $m$ stays at point P(a, b)

Question: A bead of mass $m$ stays at point $P(a, b)$ on a wire bent in the shape of a parabola $y=4 C x^{2}$ and rotating with angular speed $\omega$ (see figure). The value of $\omega$ is (neglect friction) : (1) $2 \sqrt{2 g C}$(2) $2 \sqrt{g C}$(3) $\sqrt{\frac{2 g C}{a b}}$(4) $\sqrt{\frac{2 g}{C}}$Correct Option: 1 Solution: (1) $y=4 C x^{2} \Rightarrow \frac{d y}{d x}=\tan \theta=8 C x$ At $P, \tan \theta=8 \mathrm{Ca}$ For steady circular motion $m \omega^{2} a \cos \theta=m g \sin \thet...

The INCORRECT statement regarding the structure of

Question: The INCORRECT statement regarding the structure of $\mathrm{C}_{60}$ is:The six-membered rings are fused to both six and five-membered rings.Each carbon atom forms three sigma bonds.The five-membered rings are fused only to six-membered rings.It contains 12 six-membered rings and 24 five-membered rings.Correct Option: Solution:...

The locus of the mid-points of the

Question: The locus of the mid-points of the perpendiculars drawn from points on the line, $x=2 y$ to the line $x=y$ is:(1) $2 x-3 y=0$(2) $5 x-7 y=0$(3) $3 x-2 y=0$(4) $7 x-5 y=0$Correct Option: , 2 Solution: Since, slope of $P Q=\frac{k-\alpha}{h-2 \alpha}=-1$ $\Rightarrow \quad k-\alpha=-h+2 \alpha$ $\Rightarrow \alpha=\frac{h+k}{3}$ Also, $2 h=2 \alpha+\beta$ and $2 k=\alpha+\beta$ $\Rightarrow \quad 2 h=\alpha+2 k$ $\Rightarrow \quad \alpha=2 h-2 k$ From (i) and (ii), we have $\frac{h+k}{3}...

The trajectory a projectile in a vertical plane

Question: The trajectory a projectile in a vertical plane is $y=\alpha x-\beta x^{2}$, where $\alpha$ and $\beta$ are constants and $x \backslash y$ are respectively the horizontal and vertical distance of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained $\mathrm{H}$ are respectively given by:(1) $\tan ^{-1} \alpha, \frac{\alpha^{2}}{4 \beta}$(2) $\tan ^{-1} \beta, \frac{\alpha^{2}}{2 \beta}$(3) $\tan ^{-1}\left(\frac{\beta}{\alpha}\ri...

Solve the following

Question: $\mathrm{Fex}_{2}$ and $\mathrm{Fey}_{3}$ are known when $\mathrm{x}$ and $\mathrm{y}$ are:$\mathrm{x}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$ and $\mathrm{y}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}$$x=F, C l, B r$ and $y=F, C l, B r, I$$\mathrm{x}=\mathrm{Cl}, \mathrm{Br}, \mathrm{I}$ and $\mathrm{y}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$$\mathrm{x}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$ and $\mathrm{y}=\mathrm{F}, \mathrm{Cl}, \mathrm{Br}, \mathrm{I}$Corr...

A ray of light coming from the point

Question: A ray of light coming from the point $(2,2 \sqrt{3})$ is incident at an angle $30^{\circ}$ on the line $x=1$ at the point $\mathrm{A}$. The ray gets reflected on the line $x=1$ and meets $x$-axis at the point $\mathrm{B}$. Then, the line $\mathrm{AB}$ passes through the point:(1) $\left(3,-\frac{1}{\sqrt{3}}\right)$(2) $\left(4,-\frac{\sqrt{3}}{2}\right)$(3) $(3,-\sqrt{3})$(4) $(4,-\sqrt{3})$Correct Option: , 3 Solution: Slope of $A B=\tan 120^{\circ}=-\sqrt{3}$ $\therefore$ Equation o...

A boy pushes a box of mass 2 kg

Question: A boy pushes a box of mass $2 \mathrm{~kg}$ with a force $\overrightarrow{\mathrm{F}}=(20 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}) \mathrm{N}$ on a frictionless surface. If the box Was initially at rest, then_______ $\mathrm{m}$ is displacement along the $x$-axis after $10 \mathrm{~s}$. Solution: (500) $\mathrm{F}=20 \hat{\mathrm{i}}+10 \hat{\mathrm{j}}$ $\mathrm{F}_{\mathrm{x}}=20 \mathrm{~N}$ $F_{y}=10 N$ $a_{x}=\frac{F_{x}}{M}=\frac{20}{2}=10 \mathrm{~m} / \mathrm{s}^{2}$ $a_{y}=\frac{...

A group 15 element, which is a metal and forms a hydride with strongest reducing power among group 15 hydrides.

Question: A group 15 element, which is a metal and forms a hydride with strongest reducing power among group 15 hydrides. The element is :Sb PAsBiCorrect Option: , 4 Solution: In $\mathrm{NH}_{3}$, hydrogen atom gets partial positive charge due to less electronegativity. But in $\mathrm{BiH}_{3}$, hydrogen atom gets partial negative charge because hydrogen is more electronegative than bismuth. i.e. $\mathrm{BiH}_{3}$ is a strong reducing agent than others because we know that $\mathrm{H}^{-}$ is...

A particle is moving with uniform speed along the circumference of a circle of radius R under

Question: A particle is moving with uniform speed along the circumference of a circle of radius $\mathrm{R}$ under the action of a central fictitious force $\mathrm{F}$ which is inversely proportional to $\mathrm{R}^{3}$. Its time period of revolution will be given by:(1) $\mathrm{T} \propto \mathrm{R}^{\frac{5}{2}}$(2) $\mathrm{T} \propto \mathrm{R}^{2}$(3) $\mathrm{T} \propto \mathrm{R}^{\frac{4}{3}}$(4) $\mathrm{T} \propto \mathrm{R}^{\frac{3}{2}}$Correct Option: , 2 Solution: (2) $F \propto ...

Match List-I with List-II :

Question: Match List-I with List-II : Choose the correct answer from the options given below: $(\mathrm{a})-(\mathrm{v}),(\mathrm{b})-(\mathrm{i}),(\mathrm{c})-(\mathrm{ii}),(\mathrm{d})-(\mathrm{iii})$(a) - (iv), (b) - (i), (c) - (ii), (d) - (iii)(a)-(iv), (b)-(v), (c)-(ii), (d)-(iii)(a) - (v), (b) - (iv), (c) - (ii), (d) - (iii)Correct Option: 1 Solution: (a) Hypophosphorus acid : $\mathrm{H}_{3} \mathrm{PO}_{2}(+1) 3+x+(-2) 2=0$ $x=+1$ (b) Orthophosphoric acid: $\mathrm{H}_{3} \underline{\mat...

The point A moves with a uniform speed along the circumference

Question: The point A moves with a uniform speed along the circumference of a circle of radius $0.36 \mathrm{~m}$ and cover $30^{\circ}$ in $0.1 s$. The perpendicular projection 'P' form ' $A^{\prime}$ on the diameter MN represents the simple harmonic motion of 'P'. The restoration force per unit mass when P touches M will be: (1) $100 \mathrm{~N}$(2) $50 \mathrm{~N}$(3) $9.87 \mathrm{~N}$(4) $0.49 \mathrm{~N}$Correct Option: , 3 Solution: The point a covers $30^{\circ}$ in $0.1$ sec. Means $\fr...

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