The more positive the value of Eᶱ,
Question: The more positive the value of Eᶱ, the greater is the tendency of the species to get reduced. Using the standard electrode potential of redox couples given below to find out which of the following is the strongest oxidising agent. Eᶱ Values : Fe3+/Fe2+ = + 0.77; I2(s)/I = + 0.54; Cu2+/Cu = + 0.34; Ag+/Ag = + 0.80V (i) Fe3+ (ii) I2(s) (iii) Cu2+ (iv) Ag Solution: Option (iv)Ag is the answer....
Read More →The angle between the curves
Question: The angle between the curves $y^{2}=x$ and $x^{2}=y$ at $(1,1)$ is A. $\tan ^{-1} \frac{4}{3}$ B. $\tan ^{-1} \frac{3}{4}$ C. $90^{\circ}$ D. $45^{\circ}$ Solution: Given two curves $y^{2}=x$ and $x^{2}=y$ Differentiating both the equations w.r.t. $x$, $\Rightarrow 2 y \frac{d y}{d x}=1$ and $2 x=\frac{d y}{d x}$ $\Rightarrow \frac{d y}{d x}=\frac{1}{2 y}$ and $\frac{d y}{d x}=2 x$ For $(1,1)$ : $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{1}{2}$ and $\frac{\mathrm{dy}}{\mathrm{d...
Read More →Which of the following is not an
Question: Which of the following is not an example of redox reaction? (i). CuO + H2 Cu + H2O (ii) Fe2O3 + 3CO 2Fe + 3CO2 (iii) 2K + F2 2KF (iv) BaCl2 + H2SO4 BaSO4 + 2HCl Solution: Option (iv) BaCl2 + H2SO4 BaSO4 + 2HClis the answer....
Read More →A line passes through the points A
Question: A line passes through the points A(4, -6) and B(-2, -5). Show that the line AB makes an obtuse angle with the x-axis. Solution: For the line to make an obtuse angle with X-axis, the angle of the line should be greater than 90 For the angle to be greater than $90^{\circ}$, $\tan \theta$ must be negative Where tan is the slope of the line. Given points are A(4, -6) and B(-2, -5) slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ The slope of line $A B$ is $\left(\frac{-5+6}{-2-4}\righ...
Read More →The point on the curve
Question: The point on the curve $y=12 x-x^{2}$ where the slope of the tangent is zero will be A. $(0,0)$ B. $(2,16)$ C. $(3,9)$ D. $(6,36)$ Solution: Given that the curve $y=12 x-x^{2}$ The slope of the curve $\frac{d y}{d x}=12-2 x$ Given that the slope of the tangent $=0$ $\Rightarrow 12-2 x=0$ $\Rightarrow x=6$ So, $y=72-36$ $\Rightarrow y=36$ So, the correct option is $D$....
Read More →Assertion (A): In the dissociation
Question: Assertion (A): In the dissociation of PCl5 at constant pressure and temperature addition of helium at equilibrium increases the dissociation of PCl5. Reason (R): Helium removes Cl2 from the field of action. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (iv)Both A and R are false is the answer....
Read More →The point on the curve
Question: The point on the curve $y^{2}=x$ where tangent makes $45^{\circ}$ angle with $x$-axis is A. $\left(\frac{1}{2}, \frac{1}{4}\right)$ B. $\left(\frac{1}{4}, \frac{1}{2}\right)$ C. $(4,2)$ D. $(1,1)$ Solution: Given that $y^{2}=x$ The tangent makes $45^{\circ}$ angle with $x$-axis. So, slope of tangent $=\tan 45^{\circ}=1$ $\because$ the point lies on the curve $\therefore$ Slope of the curve at that point must be 1 $2 y \frac{d y}{d x}=1$ $\Rightarrow \frac{d y}{d x}=\frac{1}{2 y}$ $\Rig...
Read More →Assertion (A): An aqueous solution of ammonium
Question: Assertion (A): An aqueous solution of ammonium acetate can act as a buffer. Reason (R): Acetic acid is a weak acid and NH4OH is a weak base. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is false but R is true. (iv) Both A and R are false. Solution: Option (iii) A is false but R is trueis the answer....
Read More →Solve this
Question: If the points $A(a, 0), B(0, b)$ and $P(x, y)$ are collinear, using slopes, prove that $\frac{x}{a}+\frac{y}{b}=1$ Solution: Given points are A(a,0),B(0,b) and P(x,y) For three points to be collinear, the slope of all pairs must be equal, that is the slope of AB = slope of BP = slope of PA. slope $=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}_{1}}\right)$ Slope of $A B=\left(\frac{b-0}{0-a}\right)=\frac{b}{-a}$ Slope of BP $=\left(\frac{y-b}{x-0}\right)=\frac{y-...
Read More →Assertion (A): Aqueous solution of ammonium carbonate
Question: Assertion (A): Aqueous solution of ammonium carbonate is basic. Reason (R): Acidic/basic nature of a salt solution of a salt of a weak acid and weak base depends on Ka and Kb value of the acid and the base forming it. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (i)Both A and R are true and R is the correct explanation o...
Read More →The point on the curve
Question: The point on the curve $y=x^{2}-3 x+2$ where tangent is perpendicular to $y=x$ is A. $(0,2)$ B. $(1,0)$ C. $(-1,6)$ D. $(2,-2)$ Solution: Given that the curve $y=x^{2}-3 x+2$ where tangent is perpendicular to $y=x$ Differentiating both w.r.t. $\mathrm{x}$, $\frac{\mathrm{dy}}{\mathrm{dx}}=1$ and $\frac{\mathrm{dy}}{\mathrm{dx}}=2 \mathrm{x}-3$ $\because$ the point lies on the curve and line both Slope of the tangent $=-1$ $\Rightarrow 2 x-3=-1$ $\Rightarrow x=1$ And $y=1-3+2$ $\Rightar...
Read More →Assertion (A): For any chemical reaction at
Question: Assertion (A): For any chemical reaction at a particular temperature, the equilibrium constant is fixed and is a characteristic property. Reason (R): Equilibrium constant is independent of temperature. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution: Option (iii) is correct....
Read More →If the three points A
Question: If the three points $A(h, k), B\left(x_{1}, y_{1}\right)$ and $C\left(x_{2}, y_{2}\right)$ lie on a line then show that $\left(h-x_{1}\right)\left(y_{2}-y_{1}\right)=\left(k-y_{1}\right)\left(x_{2}-x\right)$ Solution: For the lines to be in a line, the slope of the adjacent lines should be the same. Given points are $A(h, k), B\left(x_{1}, y_{1}\right)$ and $C\left(x_{2}, y_{2}\right)$ So slope of AB = BC = CA slope $=\left(\frac{\mathrm{y}_{2}-\mathrm{y}_{1}}{\mathrm{x}_{2}-\mathrm{x}...
Read More →Assertion (A): The ionisation of hydrogen
Question: Assertion (A): The ionisation of hydrogen sulphide in water is low in the presence of hydrochloric acid. Reason (R): Hydrogen sulphide is a weak acid. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false (iv) Both A and R are false Solution: Option (ii) is the answer....
Read More →Assertion (A): A solution containing a mixture
Question: Assertion (A): A solution containing a mixture of acetic acid and sodium acetate maintains a constant value of pH on the addition of small amounts of acid or alkali. Reason (R): A solution containing a mixture of acetic acid and sodium acetate acts as a buffer solution around pH 4.75. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R are false. Solution...
Read More →Assertion (A): Increasing order of acidity
Question: Assertion (A): Increasing order of acidity of hydrogen halides is HF HCl HBr HI Reason (R): While comparing acids formed by the elements belonging to the same group of the periodic table, HA bond strength is a more an important factor in determining the acidity of acid than the polar nature of the bond. (i) Both A and R are true and R is the correct explanation of A. (ii) Both A and R are true but R is not the correct explanation of A. (iii) A is true but R is false. (iv) Both A and R ...
Read More →If the tangent to the curve
Question: If the tangent to the curve $x=a t^{2}, y=2 a t$ is perpendicular to $x$-axis, then its point of contact is A. $(a, a)$ B. $(0, a)$ C. $(0,0)$ D. $(a, 0)$ Solution: Given that the tangent to the curve $x=a t^{2}, y=2 a t$ is perpendicular to $x$-axis. Differentiating both w.r.t. $t$, $\frac{\mathrm{dx}}{\mathrm{dt}}=2 \mathrm{at}, \frac{\mathrm{dy}}{\mathrm{dt}}=2 \mathrm{a}$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\frac{\mathrm{dy}}{\mathrm{dt}}}{\frac{\mathrm{dx}}{\mathrm{...
Read More →Using slopes. Prove that the points A
Question: Using slopes. Prove that the points A(-2, -1), B(1,0), C(4, 3) and D(1, 2) are the vertices of a parallelogram. Solution: The property of parallelogram states that opposite sides are equal. We have 4 sides as AB,BC,CD,DA Given points are A(-2,-1),B(1,0),C(4,3) and D(1,2) AB and CD are opposite sides, and BC and DA are the other two opposite sides. So slopes of AB = CD and slopes BC = DA slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ Slope of $A B=\left(\frac{0+1}{1+2}\right)=\fr...
Read More →Match Column (I) with Column (II).
Question: Match Column (I) with Column (II). Solution: (i) are b and c (ii) is d (iii) is a...
Read More →Match the following species
Question: Match the following species with the corresponding conjugate acid Species Conjugate acid Solution: (i) is b (ii) is e (iii) is c (iv) is d...
Read More →The point on the curve
Question: The point on the curve $y^{2}=x$ where tangent makes $45^{\circ}$ angle with $x$-axis is A. $\left(\frac{1}{2}, \frac{1}{4}\right)$ B. $\left(\frac{1}{4}, \frac{1}{2}\right)$ C. $(4,2)$ D. $(1,1)$ Solution: Given that $\mathrm{y}^{2}=\mathrm{x}$ The tangent makes $45^{\circ}$ angle with $\mathrm{x}$-axis. So, slope of tangent $=\tan 45^{\circ}=1$ $\because$ the point lies on the curve $\therefore$ Slope of the curve at that point must be 1 $2 \mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}=...
Read More →Match standard free energy
Question: Match standard free energy of the reaction with the corresponding Equilibrium constant Solution: (i) is d (ii) is a (iii) is b...
Read More →Using slopes show that the points A
Question: Using slopes show that the points A(-4, -1), B(-2, -4), C(4, 0) and D(2, 3) taken in order, are the vertices of a rectangle. Solution: A rectangle has all sides perpendicular to each other, so the product of slope of every adjacent line is equal to -1. Given point in order are $A(-4,-1), B(-2,-4), C(4,0)$ and $D(2,3)$ slope $=\left(\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\right)$ Slope of $A B=\left(\frac{-4+1}{-2+4}\right)=\frac{-3}{2}$ Slope of $B C=\left(\frac{0+4}{4+2}\right)=\frac{4}{6}=\f...
Read More →For the reaction : N2 (g) + 3H2(g) → 2NH3(g)
Question: For the reaction : N2 (g) + 3H2(g) 2NH3(g) Equilibrium constant Kc= [NH3]2/[N2][H2]3 Some reactions are written below in Column I and their equilibrium constants in terms of Kc are written in Column II. Match the following reactions with the corresponding equilibrium constant Solution: (i) is d (ii) is c (iii) is b...
Read More →Match the following equilibria
Question: Match the following equilibria with the corresponding condition Solution: (i) is b (ii) is d (iii) is c (iv) is a...
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