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

Identify the correct molecular picture showing

Question: Identify the correct molecular picture showing what happens at the critical micellar concentration (CMC) of an aqueous solution of a surfactant (polar head,non-polar tail,water $)$. (D)(B)(A)(C)Correct Option: Solution: (a) In micelle formation, above "CMC" hydrocarbon chains are pointing towards the centre of sphere with $\mathrm{COO}^{-}$part remaining outward on the surface....

Find the distance of each of the following points from the origin:

Question: Find the distance of each of the following points from the origin:(i)A(5, 12)(ii)B(5, 5)(iii)C(, 6)4 Solution: (i)A(5, 12)Let O(0, 0) be the origin. $O A=\sqrt{(5-0)^{2}+(-12-0)^{2}}$ $=\sqrt{(5)^{2}+(-12)^{2}}$ $=\sqrt{25+144}$ $=\sqrt{169}$ $=13$ units (ii)B(5, 5)Let O(0, 0) be the origin. $O B=\sqrt{(-5-0)^{2}+(5-0)^{2}}$ $=\sqrt{(-5)^{2}+(5)^{2}}$ $=\sqrt{25+25}$ $=\sqrt{50}$ $=\sqrt{25 \times 2}$ $=5 \sqrt{2}$ units (iii)C(4, 6)Let O(0,0) be the origin. $O C=\sqrt{(-4-0)^{2}+(-6-0...

Prove that the lines joining the middle points of the opposite sides of a quadrilateral

Question: Prove that the lines joining the middle points of the opposite sides of a quadrilateral and the join of the middle points of its diagonals meet in a point and bisect one another. Solution: Let us consider a Cartesian plane having a parallelogram OABC in which O is the origin. We have to prove that middle point of the opposite sides of a quadrilateral and the join of the mid-points of its diagonals meet in a point and bisect each other. Let the co-ordinate of $\mathrm{A}$ be $\left(x_{1...

A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye,

Question: A sample of red ink (a colloidal suspension) is prepared by mixing eosin dye, egg white, HCHO and water. The component which ensures stabilitiy of the ink sample is :Egg whiteWaterHCHOEosin dyeCorrect Option: 1 Solution: Egg white is used to stabilise the prepared colloidal solution of red ink....

An ionic micelle is formed on the addition of:

Question: An ionic micelle is formed on the addition of:liquid diethyl ether to aqueous $\mathrm{NaCl}$ solutionexcess water to liquid sodium stearate to pure tolueneCorrect Option: , 3 Solution: Due to presence of hydrophobic chain it forms micelle....

Prove analytically that the line segment joining the middle

Question: Prove analytically that the line segment joining the middle points of two sides of a triangle is equal to half of the third side. Solution: Let $\triangle \mathrm{OAB}$ be any triangle such that $\mathrm{O}$ is the origin and the other co-ordinates are $\mathrm{A}\left(x_{1}, y_{1}\right) ; \mathrm{B}\left(x_{2}, y_{2}\right) . \mathrm{P}$ and $\mathrm{R}$ are the mid-points of the sides $\mathrm{OA}$ and $\mathrm{OB}$ respectively. We have to prove that line joining the mid-point of a...

Find the distance between the points:

Question: Find the distance between the points:(i)A(9, 3) andB(15, 11)(ii)A(7, 4) andB(5, 1)(iii)A(6, 4) andB(9, 12)(iv)A(1, 3) andB(4, 6)(v)P(a+b,ab) andQ(ab, a +b)(vi)P(asin ,acos ) andQ(acos , asin ) Solution: (i)A(9, 3) andB(15, 11)The given points areA(9, 3) andB(15, 11).Then (x1= 9,y1= 3) and (x2= 15,y2= 11) $A B=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$ $=\sqrt{(15-9)^{2}+(11-3)^{2}}$ $=\sqrt{(15-9)^{2}+(11-3)^{2}}$ $=\sqrt{(6)^{2}+(8)^{2}}$ $=\sqrt{36+64}$ $=\sqrt...

Two vertices of a triangle are (1, 2), (3, 5) and its

Question: Two vertices of a triangle are (1, 2), (3, 5) and its centroid is at the origin. Find the coordinates of the third vertex. Solution: We have to find the co-ordinates of the third vertex of the given triangle. Let the co-ordinates of the third vertex be. The co-ordinates of other two vertices are (1, 2) and (3, 5) The co-ordinate of the centroid is (0, 0) We know that the co-ordinates of the centroid of a triangle whose vertices are $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\...

Tyndall effect is observed when :

Question: Tyndall effect is observed when :The diameter of dispersed particles is much larger than the wavelength of light used.The diameter of dispersed particles is much smaller than the wavelength of light used.The refractive index of dispersed phase is greater than that of the dispersion medium.The diameter of dispersed particles is similar to the wavelength of light used.Correct Option: , 4 Solution: Tyndall effect is observed only when the following two conditions are satisfied. (i) The di...

Find the centroid of the triangle whose vertices are:

Question: Find the centroid of the triangle whose vertices are: (i) $(1,4)(-1,-1),(3,-2)$ (ii) $(-2,3)(2,-1)(4,0)$ Solution: We know that the co-ordinates of the centroid of a triangle whose vertices are $\left(x_{1}, y_{1}\right),\left(x_{2}, y_{2}\right),\left(x_{3}, y_{3}\right)$ is- $\left(\frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right)$ (i) The co-ordinates of the centroid of a triangle whose vertices are (1, 4); (1,1); (3,2) are- $=\left(\frac{1-1+3}{3}, \frac{4-1-2}{3}\rig...

Amongst the following statements regarding adsorption,

Question: Amongst the following statements regarding adsorption, those that are valid are : (a) $\Delta \mathrm{H}$ becomes less negative as adsorption proceeds. (b) On a given adsorbent, ammonia is adsorbed more than nitrogen gas. (c) On adsorption, the residual force acting along the surface of the adsorbent increases. (d) With increase in temperature, the equilibrium concentration of adsorbate increases.(d) and (a)(b) and (c)(a) and (b)(c) and (d)Correct Option: , 3 Solution: (i) When gas is ...

If G be the centroid of a triangle ABC, prove that:

Question: IfGbe the centroid of a triangle ABC, prove that: $\mathrm{AB}^{2}+\mathrm{BC}^{2}+\mathrm{CA}^{2}=3\left(\mathrm{GA}^{2}+\mathrm{GB}^{2}+\mathrm{GC}^{2}\right)$ Solution: Let $\mathrm{A}\left(x_{1}, y_{1}\right) ; \mathrm{B}\left(x_{2}, y_{2}\right) ; \mathrm{C}\left(x_{3}, y_{3}\right)$ be the coordinates of the vertices of $\triangle \mathrm{ABC}$. Let us assume that centroid of the $\triangle \mathrm{ABC}$ is at the origin $\mathrm{G}$. So, the coordinates of $\mathrm{G}$ are $\mat...

The mass of gas adsorbed, x, per unit mass of adsorbate, m, was measured at various pressures, p.

Question: The mass of gas adsorbed, $x$, per unit mass of adsorbate, $m$, was measured at various pressures, $p$. A graph between $\log \frac{x}{m}$ and $\log p$ gives a straight line with slope equal to 2 and the intercept equal to $0.4771$. The value of $\frac{x}{m}$ at a pressure of $4 \mathrm{~atm}$ is : (Given $\log 3=0.4771$ ) Solution: (6) $\left(\frac{x}{m}\right)=k(p)^{\frac{1}{n}}$ $\log \left(\frac{x}{m}\right)=\log k+\frac{1}{n} \log p$ Slope $=\frac{1}{n}=2$, so $n=\frac{1}{2}$. Int...

Which of the following is used for the preparation of colloids?

Question: Which of the following is used for the preparation of colloids?Ostwald ProcessVan Arkel MethodBredig's Arc MethodMond ProcessCorrect Option: , 3 Solution: Bredig's Arc method is used for preparation of colloidal sol's of less reactive metal like $\mathrm{Au}, \mathrm{Ag}, \mathrm{Pt}$....

Find the coordinates of a point A,

Question: Find the coordinates of a pointA, whereABis a diameter of the circle whose centre is (2, 3) andBis (1, 4). Solution: Let the co-ordinates of point A be $(x, y)$. Centre lies on the mid-point of the diameter. So applying the mid-point formula we get, $\frac{x+1}{2}=2$ $x=3$ Similarly, $\frac{y+4}{2}=-3$ $y=-10$ So the co-ordinates of A are (3,10)...

The nature of charge on resulting colloidal particles

Question: The nature of charge on resulting colloidal particles when $\mathrm{FeCl}_{3}$ is added to excess of hot water is:positiveneutralsometimes positive and sometimes negativenegativeCorrect Option: 1 Solution: If $\mathrm{FeCl}_{3}$ is added to excess of hot water, a positively charged sol of hydrated ferric oxide is formed due to adsorption of $\mathrm{Fe}^{3+}$ ions....

In what ratio does the point (−4, 6) divide the line segment

Question: In what ratio does the point (4, 6) divide the line segment joining the points A(6, 10) and B(3,8)? Solution: The co-ordinates of a point which divided two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ internally in the ratio $m: n$ is given by the formula, $(x, y)=\left(\left(\frac{m x_{2}+n x_{1}}{m+n}\right),\left(\frac{m y_{2}+n y_{1}}{m+n}\right)\right)$ Here it is said that the point (4,6)divides the pointsA(6,10) andB(3,8). Substituting these values in the a...

Which one of the following statements is FALSE for hydrophilic sols ?

Question: Which one of the following statements is FALSE for hydrophilic sols ?These sols are reversible in natureThe sols cannot be easily coagulatedThey do not require electrolytes for stability.Their viscosity is of the order of that of $\mathrm{H}_{2} \mathrm{O}$Correct Option: , 4 Solution: Fact base...

The 7th term of an AP is 4 and its common difference is −4.

Question: The 7th term of an AP is 4 and its common difference is 4. What is its first term?(a) 16(b) 20(c) 24(d) 28 Solution: (d) 28T7=a+ 6d⇒a+ 6⨯ (-4) = 4⇒a= 4 + 24 = 28Hence, the first term is 28....

The 8th term of an AP is 17 and its 14th term is 29.

Question: The 8th term of an AP is 17 and its 14th term is 29. The common difference of the AP is(a) 3(b) 2(c) 5(d) 2 Solution: (b) 2T8=a+7d= 17 ...(i)T14=a+13d= 29 ...(ii)On subtracting (i) from (ii), we get:⇒ 6d=12⇒d= 2Hence, the common difference is 2....

If the points A (6, 1), B (8, 2), C (9, 4) and D (k, p)

Question: If the pointsA(6, 1),B(8, 2),C(9, 4) andD(k,p) are the vertices of a parallelogram taken in order, then find the values ofkandp. Solution: Let ABCD be a parallelogram in which the co-ordinates of the vertices are A (6, 1); B (8, 2); C (9, 4) and D (k, p). Since ABCD is a parallelogram, the diagonals bisect each other. Therefore the mid-point of the diagonals of the parallelogram will coincide. In general to find the mid-point $\mathrm{P}(x, y)$ of two points $\mathrm{A}\left(x_{1}, y_{...

In Freundlich adsorption isotherm at moderate pressure,

Question: In Freundlich adsorption isotherm at moderate pressure, the extent of adsorption $\left(\frac{x}{m}\right)$ is directly proportional to $\mathrm{P}^{\mathrm{x}}$. The value of $\mathrm{X}$ is:$\infty$1Zero$\frac{1}{n}$Correct Option: , 4 Solution: $\frac{x}{m}=p^{x}$ the formula is $\frac{x}{m}=p^{1 / n}$ Hence $x=\frac{1}{n}$ The value of 'n' is any natural number....

The 17th term of an AP exceeds its 10th term by 21.

Question: The 17th term of an AP exceeds its 10th term by 21. The common difference of the AP is(a) 3(b) 2(c) 3(d) 2 Solution: (a) 3T10=a+9d T17=a+16dAlso,a+16d= 21 + T10⇒ a+16d= 21 +a+9d⇒ 7d=21⇒ d= 3Hence, the common difference of the AP is 3....

The 2nd term of an AP is 13 and its 5th term is 25.

Question: The 2nd term of an AP is 13 and its 5th term is 25. What is its 17th term.(a) 69(b) 73(c) 77(d) 81 Solution: (b) 73T2=a+d = 13 ...(i)T5=a+4d = 25 ...(ii)On subtracting (i) from (ii), we get:⇒3d=12⇒d= 4On putting the value ofdin (i), we get:⇒a+ 4= 13⇒a= 9Now, T17=a+16d= 9 + 16 ⨯4 = 73Hence, the 17th term is 73....

Find the ratio in which the y-axis divides the line segment joining the points (5, −6)

Question: Find the ratio in which they-axis divides the line segment joining the points (5, 6) and (1,4). Also, find the coordinates of the point of division. Solution: The ratio in which the $\mathrm{y}$-axis divides two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ is $\lambda: 1$ The co-ordinates of the point dividing two points $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$ in the ratio $m: n$ is given as, $(x, y)=\left(\left(\frac{\lambda x_{2}+x_{1}}{\lamb...

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