ACCORDING TO QUES, \[~\left( 1\text{ }+~{{y}^{2}} \right)\text{ }ta{{n}^{1}}x\text{ }dx~+\text{ }2y~\left( 1\text{ }+~{{x}^{2}} \right)~dy~=\text{ }0\] \[2y\text{ }\left( 1\text{ }+\text{ }{{x}^{2}}...
Form the differential equation by eliminating A and B in Ax2 + By2 = 1.
ACCORDING TO QUES, DIFFERENTIATING WITH RESPECT TO x ,
Solve the differential equation dy = cos x (2 – y cosec x) dx given that y = 2 when x = π/2.
according to ques,
(i) Assertion and reason both are correct statements but reason does not explain the assertion. (ii) Assertion and reason both are correct statements and reason explain the assertion. (iii) Both assertion and reason are the wrong statements. (iv) The assertion is correct statement and reason is the wrong statement. (v) The assertion is the wrong statement and reason is the correct statement. Assertion: Polytetrafluoroethene is used in making non-stick cookware. Reason: Fluorine has the highest electronegativity
Option (i) is correct Teflon is a chemically inert and thermally stable material that is used to make nonstick cookware.
(i) Assertion and reason both are correct statements but reason does not explain the assertion. (ii) Assertion and reason both are correct statements and reason explain the assertion. (iii) Both assertion and reason are the wrong statements. (iv) The assertion is correct statement and reason is the wrong statement. (v) The assertion is the wrong statement and reason is the correct statement. Assertion: Olefinic monomers undergo addition polymerisation. Reason: Polymerisation of vinyl chloride is initiated by peroxides/ persulphates.
Option (i) is correct Polymerization of olefins like ethene results in polymers like polythene.
(i) Assertion and reason both are correct statements but reason does not explain the assertion. (ii) Assertion and reason both are correct statements and reason explain the assertion. (iii) Both assertion and reason are the wrong statements. (iv) The assertion is correct statement and reason is the wrong statement. (v) The assertion is the wrong statement and reason is the correct statement. . Assertion: Rayon is a semi-synthetic polymer and is taken as a better choice than cotton fabric. Reason: Mechanical and aesthetic properties of cellulose can be improved by acetylation.
Option (ii) is correct. Rayon is a semi-synthetic polymer that is a better alternative than cotton because acetylation improves the characteristics of cellulose after processing.
Match materials are given in Column I with the polymers given in Column II.
(i) is f (ii) is e (iii) is a (iv) is c (v) is b (vi) is d
Match the polymers given in Column I with the type of linkage present in they have given in Column II.
(i) is b (ii) is d (iii) is a (iv) is d (v) is c
Match the polymer of column I with a correct monomer of column II.
(i) is e (ii) is c (iii) is a (iv) is b (v) is d
Why should the monomers use also polymerisation through free radical pathway be very pure?
Pure monomers are employed instead of polymerization through the free radical pathway because even little impurities serve as inhibitors, causing the chain reaction to abruptly stop and short length...
Which type of biomolecules has some structural similarity with synthetic polyamides? What is this similarity?
Proteins and synthetic polyamides share certain structural similarities. Polyamides, such as Nylon, are made up of Glycine and aminocaproic acid molecules linked together by an amide bond. A similar...
Name the polymers used in laminated sheets and give the name of monomeric units involved in its formation.
In laminated sheets, urea-formaldehyde resin is utilised. The monomeric components used to make laminated sheets are urea and formaldehyde.
What is the role of benzoyl peroxide also polymerisation of alkenes? Explain its mode of action with the help of an example.
By providing chain initiation, benzoyl peroxide functions as an initiator in free radical addition polymerisation of alkenes. The generated radical reacts with the carbon-carbon double bond of an...
To have practical applications why are cross-links required in rubber?
Cross-linking is used to increase these physical qualities by assisting in the binding of its planar polymer sheets, therefore improving elastomeric properties and thermal stability.
Can nucleic acids, proteins and starch be considered as step growth polymers?
Proteins, nucleic acids, and starch are all examples of step-growth polymers. Condensation polymers are step growth polymers. The loss of a simple molecule allows monomers with bifunctional or...
Identify the polymer given below :
This is polyisoprene or natural rubber. This polymer's monomeric unit is 2-methyl-1,3-butadiene.
Identify the type of polymer. —A—B—B—A—A—A—B—A—
In this polymer chain, the monomers A' and 'B' are randomly linked. As an example, this is a copolymer. A When a mixture of two or more unsaturated monomers reacts, a copolymer is formed.
Identify the type of polymer. —A—A—A—A—A—A—
The monomer in this case is –A-. This polymer is a homopolymer since the same or same monomer is repeated to make it.
A natural linear polymer of 2-methyl-1, 3-butadiene becomes hard on treatment with sulphur between 373 to 415 K and —S—S— bonds are formed between chains. Write the structure of the product of this treatment?
The structure of 2-methyl-1,3-butadiene is Rubber vulcanization is the term for this procedure. Sulphur works as a crosslinking agent in this case, stiffening the rubber and giving it better...
Vulcanisation makes rubber ______________. (i) more elastic (ii) soluble in inorganic solvent (iii) crystalline (iv) more stiff
Option (i) and (iv) are the answers. Rubber becomes more elastic and rigid after vulcanization. Sulphur produces cross connections at the reactive locations of double bonds or at their reactive...
Which of the following polymers have vinylic monomer units? (i) Acrilan (ii) Polystyrene (iii) Nylon (iv) Teflon
Option (i), (ii) and (iv) are the answers. The vinylic monomer units of acrilan, polystyrene, and teflon are as follows:
Which of the following monomers form biodegradable polymers? (i) 3-hydroxybutyric acid + 3-hydroxypentanoic acid (ii) Glycine + aminocaproic acid (iii) Ethylene glycol + phthalic acid (iv) Caprolactam
Option (i) and (ii) are the answers. Biodegradable polymers are those that are quickly degraded and are not hazardous to the environment.
Which of the following polymers are condensation polymers? (i) Bakelite (ii) Teflon (iii) Butyl rubber (iv) Melamine formaldehyde resin
Option (i) and (iv) are the answers. Bakelite is a phenol and formaldehyde condensation polymer. Melamine formaldehyde resin is a melamine (2, 4, 6-triamino-1, 3, 5-triazine) and formaldehyde...
Which of the following are addition polymers? (i) Nylon (ii) Melamine formaldehyde resin (iii) Orlon (iv) Polystyrene
Option (iii) and (iv) are the answers. The addition polymers Orion and polystyrene are produced by polymerizing CH2 = CH – CN (acrylonitrile) and C6H5 – CH = CH2 styrene, respectively.
Which of the following polymers, need at least one diene monomer for their preparation? (i) Dacron (ii) Buna-S (iii) Neoprene (iv) Novolac
Option (ii) and (iii) are the answers. (b) (c)
Which of the following polymer can be formed by using the following monomer unit?
Option (iv) is the answer. Nylon -6 is a polymer made from caprolactam polymerization.
is a polymer having monomer units ____________.
Option (i) is the answer.
Which of the following statements is not true about low-density polythene? (i) Tough (ii) Hard (iii) Poor conductor of electricity (iv) Highly branched structure
Option (ii) is the answer. Low density polythene is a strong yet flexible (not too flexible) material with a weak electrical conductivity. Its structure is extremely branching.
In which of the following polymers ethylene glycol is one of the monomer units?
Option (i) is the answer. Condensation polymerization of ethylene glycol and phthalic acid with the removal of the water molecule yields the given polymer.
Which of the following polymer is biodegradable?
Option (C) is the answer. Biodegradable polymers are materials whose chemical and physical properties deteriorate and disintegrate entirely when exposed to microorganisms, aerobic, and anaerobic...
The commercial name of polyacrylonitrile is ______________. (i) Dacron (ii) Orlon (Acrilan) (iii) PVC (iv) Bakelite
Option (ii) is the answer.
Which of the following is not a semisynthetic polymer? (i) cis-polyisoprene (ii) Cellulose nitrate (iii) Cellulose acetate (iv) Vulcanised rubber
Option (i) is the answer M-polyisoprene is a polymer that comes from nature.
Which of the following polymers of glucose is stored by animals? (i) Cellulose (ii) Amylose (iii) Amylopectin (iv) Glycogen
Option (iv) is the answer. Glycogen is a glucose polymer present in animal livers, brains, and muscles. Amylase and amylopectin are structural components of starch, while cellulose is a polymer...
The stabilisation of coordination compounds due to chelation is called the chelate effect. Which of the following is the most stable complex species? (a) [Fe(CO)5] (b) [Fe(CN)6]3– (c) [Fe(C2O4)3]3– (d) [Fe(H2O)6]3+
Solution: (c) arrangement of cycle by linkage between metal particle and ligand balances out the coordination compound. The ligand which chelates the metal particle are known as chelating ligand....
Solve : 2 (y + 3) – xy dy/dx = 0, given that y(1) = -2.
according to ques,
Solve : (x + y) (dx – dy) = dx + dy. [Hint: Substitute x + y = z after separating dx and dy]
According to ques, or, \[\left( x~+~y \right)\text{ }\left( dx~~dy \right)\text{ }=~dx~+~dy\] \[\left( x\text{ }+\text{ }y \right)\text{ }dx\text{ }\text{ }\left( x\text{ }\text{ }y \right)\text{...
Find the general solution of y2dx + (x2 – xy + y2) dy = 0.
according to ques,
Find the general solution of the differential equation:(1+y^2)+(x-e^tan-1y)dy/dx=0.
according to ques,
Solve: x^2dy/dx=x^2+xy+y^2
according to ques,
Find the equation of a curve passing through origin and satisfying the differential equation: (1+x^2)dy/dx+2xy=4x^2
according to ques,
Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.
According to ques, Equation will be, \[{{\left( x\text{ }\text{ }0 \right)}^{2}}~+\text{ }{{\left( y\text{ }\text{ }a \right)}^{2}}~=\text{ }{{a}^{2}},\] where (0, a) is the centre...
Form the differential equation having y = (sin–1x)2 + A cos–1x + B, where A and B are arbitrary constants, as its general solution.
according to ques,
If y(t) is a solution of and y (0) = – 1, then show that y (1) = -1/2.
according to ques,
If y(x) is a solution of and y (0) = 1, then find the value of y(π/2).
according to ques,
Find the general solution of (x + 2y3) dy/dx = y.
according to ques,
Solve the differential equation dy/dx = 1 + x + y2 + xy2, when y = 0, x = 0.
according to ques, we can write,
Solve: ydx – xdy = x2ydx.
According to ques we have, \[~ydx\text{ }\text{ }xdy\text{ }=\text{ }{{x}^{2}}ydx\] or, \[y\text{ }dx\text{ }\text{ }{{x}^{2}}y\text{ }dx\text{ }=\text{ }xdy\] \[y\text{ }\left( 1\text{ }\text{...
Solve the differential equation: dy/dx+1=e^x+y
ACCORDING TO QUES, \[dy/dx\text{ }+\text{ }1\text{ }=\text{ }{{e}^{x+y}}\] NOW PUTTING, \[x\text{ }+\text{ }y\text{ }=\text{ }t\] and differentiating w.r.t. x,
Find the general solution of: dy/dx+ay=e^mx
ACCORDING TO QUES, \[dy/dx\text{ }+\text{ }ay\text{ }=\text{ }{{e}^{mx}}\] for linear differential equation of first order, \[P\text{ }=\text{ }a\text{ }and\text{ }Q\text{ }=\text{...
Solve the differential equation: dy/dx+2xy=y
according to ques, \[dy/dx\text{ }+\text{ }2xy\text{ }=\text{ }y\]
Solve the differential equation: (x^2-1)dy/dx+2xy=1/x^2-1
according to ques,
Given that dy/dx=e^-2y and y = 0 when x = 5. Find the value of x when y = 3.
according to ques,
Find the differential equation of all non-vertical lines in a plane.
SINCE ,equation of all non-vertical lines is $$ \[~y\text{ }=\text{ }mx\text{ }+\text{ }c\] On differentiating w.r.t. x, \[dy/dx\text{ }=\text{ }m\] and, on differentiating w.r.t. x,...
Find the solution of : dy/dx = 2^y-x
ACCORDING TO QUES,
Find x, y, z if A = satisfies A¢ = A-1.
Ans:
If AB = BA for any two square matrices, prove by mathematical induction that (AB)n = An Bn.
Let \[~P\left( n \right)\text{ }:\text{ }{{\left( AB \right)}^{n}}~=\text{ }{{A}^{n}}{{B}^{n}}\] In this way, \[P\left( 1 \right)\text{ }:\text{ }{{\left( AB \right)}^{1}}~=\text{...
If A, B are square matrices of same order and B is a skew-symmetric matrix, show that A¢BA is skew symmetric.
Ans:
If A is square matrix such that A2 = A, show that (I + A)3 = 7A + I.
We realize that, \[A\text{ }.\text{ }I\text{ }=\text{ }I\text{ }.\text{ }A\] In this way, \[A\text{ }and\text{ }I\]are commutative. Subsequently, we can grow \[{{\left( I\text{ }+\text{ }A...
If P (x) = given matrix then show that P (x) . P (y) = P (x + y) = P (y) . P (x).
Ans:
If the matrix is a skew symmetric matrix, find the values of a, b and c.
Ans:
If A = and A-1 = A’, find value of a.
Ans: By utilizing equity of matrixs, we get \[co{{s}^{2}}~\alpha \text{ }+\text{ }si{{n}^{2~}}\alpha \text{ }=\text{ }1\], which is valid for all genuine upsides of \[\alpha .\]
If A = find A2 + 2A + 7I.
Ans:
Find the matrix A such that
Ans: Let, Presently, by equity of matrices, we get \[a\text{ }=\text{ }1,\text{ }b\text{ }=\text{ }-\text{ }2,\text{ }c\text{ }=\text{ }-\text{ }5\] Furthermore, \[2a\text{ }\text{ }d\text{ }=\text{...
Find the value of a, b, c and d, if
Ans: Presently, \[3a\text{ }=\text{ }a\text{ }+\text{ }4\Rightarrow a\text{ }=\text{ }2\] \[3b\text{ }=\text{ }6\text{ }+\text{ }a\text{ }+\text{ }b\] \[3b\text{ }-\text{ }b\text{ }=\text{ }8\]...
If , then find A2 – 5A – 14I. Hence, obtain A3.
Ans:
If find a matrix C such that 3A + 5B + 2C is a null matrix.
Ans: How about we think about a matrix C, with the end goal that Looking at the terms, \[\mathbf{2a}\text{ }+\text{ }\mathbf{48}\text{ }=\text{ }\mathbf{0}\text{ }\Rightarrow \text{...
If then find values of x, y, z and w.
Answer: In the given matrix condition, Looking at the comparing components, we get \[x\text{ }+\text{ }y\text{ }=\text{ }6,\] \[xy\text{ }=\text{ }8,\] \[z\text{ }+\text{ }6\text{ }=\text{ }0\]and...
Find inverse, by elementary row operations (if possible), of the following matrices
Ans: Since, we obtain all the zeroes in a row of the matrix A, L.H.S., A-1 does not exist.
Prove by Mathematical Induction that (A¢)n = (An) ¢, where n ∈ N for any square matrix A.
Ans:
Verify that A2 = I when A =
Ans:
If and x2 = –1, then show that (A + B)2 = A2 + B2
Answer: According to the given ques
Evaluate
Ans:
Let and a = 4, b = –2. Show that: (A – B)T = AT – BT
Answer: According to the given ques,
Let and a = 4, b = –2. Show that: (a) (AB)T = BT AT (b) (A –B)C = AC – BC
Answer: According to the given ques, (a) (b)
Let and a = 4, b = –2. Show that: (a) (AT)T = A (b) (bA)T = b AT
Answer: According to the given ques
Let and a = 4, b = –2. Show that: (a) (a + b)B = aB + bB (b) a (C–A) = aC – aA
Answer: (a) (b)
Let and a = 4, b = –2. Show that: (a) A + (B + C) = (A + B) + C (b) A (BC) = (AB) C
Answer: According to the given ques
Show that if A and B are square matrices such that AB = BA, then (A + B)2 = A2 + 2AB + B2.
Given, \[A\text{ }and\text{ }B\]are square matrices with the end goal that \[AB\text{ }=\text{ }BA.\] In this way, \[{{\left( A\text{ }+\text{ }B \right)}^{2}}~=\text{ }\left( A\text{ }+\text{ }B...
Let A and B be square matrices of the order 3 × 3. Is (AB)2 = A2 B2 ? Give reasons.
As, \[A\text{ }and\text{ }B\]be square matrixs of order \[3\text{ }x\text{ }3.\] We have, \[{{\left( AB \right)}^{2}}~=\text{ }AB\text{ }.\text{ }AB\] \[=\text{ }A\left( BA \right)B\] \[=\text{...
Show that A¢A and AA¢ are both symmetric matrices for any matrix A.
Answer: According to the given ques
If then verify that: (i) (2A + B)¢ = 2A¢ + B¢ (ii) (A – B)¢ = A¢ – B¢.
Answer: According to the given ques
Differentiate w.r.t tan-1 x when x ≠ 0.
according to ques,
If then verify that: (kA)¢ = (kA¢).
Answer: According to the given ques
Differentiate x/sinx w.r.t sin x.
according to ques,
If x = asin2t (1 + cos2t) and y = b cos2t (1–cos2t), show that
\[x~=~asin2t~(1\text{ }+\text{ }cos2t)~and~y~=~b~cos2t~(1cos2t)\]
If then verify that: (i) (A¢)¢ = A (ii) (AB)¢ = B¢A¢
Answer: According to the ques
If then verify that A2 + A = A (A + I), where I is 3 × 3 unit matrix.
Answer: According to the given matrix, the solution should be
Find dy/dx of each of the functions expressed in parametric: If x = ecos2t and y = esin2t, prove that dy/ dx = – y log x/ x log y.
\[x~=~{{e}^{cos2t}}~and~y~=~{{e}^{sin2t}}\] So, \[cos\text{ }2t\text{ }=\text{ }log\text{ }x\] and \[sin\text{ }2t\text{ }=\text{ }log\text{ }y\]
If verify that A (B + C) = (AB + AC).
Answer: According to the given matrix, the solution should be
Find dy/dx of each of the functions expressed in parametric:
according to ques,
If: = A, find A.
Answer: According to the given matrix, the should be
Solve the matrix:
Answer: According to the given matrix, the solution should be
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Find dy/dx of each of the functions expressed in parametric: x = 3cosq – 2cos3q, y = 3sinq – 2sin3q.
\[x\text{ }=~3cosq\text{ }\text{ }2co{{s}^{3}}q,~y~=\text{ }3sinq\text{ }\text{ }2si{{n}^{3}}q.\]
If (i) (AB) C = A (BC) (ii) A (B + C) = AB + AC.
Answer: According to the given matix, the solution should be
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Give an example of matrices A, B and C such that AB = AC, where A is non-zero matrix, but B ≠ C.
Answer: From (I) and (ii), Thus, \[AB\text{ }=\text{ }AC\]however \[B\text{ }\ne \text{ }C.\]
If A = [3 5], B = [7 3], then find a non-zero matrix C such that AB = AC.
Answer: Given, \[A\text{ }=\text{ }{{\left[ 3\text{ }5 \right]}_{1\times 2}}~\]and \[B\text{ }=\text{ }{{\left[ 7\text{ }3 \right]}_{1\times 2}}\] For \[AC\text{ }=\text{ }BC\] We have order of...
Find dy/dx of each of the functions expressed in parametric:
according to ques,
Differentiate :
according to ques,
If X and Y are 2 x 2 matrices, then solve the following matrix equations for X and Y
Answer: According to the given matix, the solution should be
Differentiate :
according to ques,
Solve for x and y:
Answer: Presently, we have \[2x\text{ }+\text{ }3y\text{ }\text{ }8\text{ }=\text{ }0\text{ }\ldots ..\text{ }\left( 1 \right)~\]and \[x\text{ }+\text{ }5y\text{ }\text{ }11\text{ }=\text{ }0\text{...
Differentiate :
according to ques,
Given Is (AB)’ = B’ A’ ?
Answer: From (I) and (ii), we have \[\left( AB \right)\text{ }=\text{ }B\text{ }A\]
Differentiate :
according to ques,
Differentiate :
according to ques,
Show by an example that for A ≠ 0, B ≠ 0, AB = 0.
Answer: According to the given matrix, the solution should be – Hence Proved
If possible, find BA and AB where
Answer: According to question, the solutions should be
Differentiate :
according to ques,
Differentiate :
according to ques,
If then verify (BA)2 ≠ B2 A2
Answer: The provided matrixs \[A\]has order \[3\text{ }x\text{ }2\]and B has order 2 x 3. Thus, \[BA\] is characterized and will have order 3 x 3. Be that as it may, \[{{A}^{2}}~and\text{...
DIFFERENCIATE: (x + 1)2 + (x + 2)3 + (x + 3)4
ACCORDING TO QUES,
Find A, if:
Answer: On looking at components of the two sides, we have \[4x\text{ }=\text{ }-4\text{ }\Rightarrow x\text{ }=\text{ }-1\] \[4y\text{ }=\text{ }8\text{ }\Rightarrow \text{ }y\text{ }=\text{ }2\]...
DIFFERENCIATE: sinm x . cosn x
ACCORDING TO QUES,
DIFFERENCIATE: (sin x)cos x
ACCORDING TO QUES,
Find the matrix A satisfying the matrix equation:
ANSWER: Presently, \[{{P}^{-1}}~PAQ\text{ }=\text{ }{{P}^{-1~}}I\] Thus, \[IAQ\text{ }=\text{ }{{P}^{-1}}\] \[AQ\text{ }=\text{ }{{P}^{-1}}\] \[AQ{{Q}^{-1}}~=\text{ }{{P}^{-1}}~{{Q}^{-1}}\]...
DIFFERENCIATE:
ACCORDING TO QUES,
Explain why ozone is thermodynamically less stable than oxygen.
Ozone is less thermodynamically stable because it decomposes into oxygen and this decay leads to heat release, so its entropy is positive whereas the free energy is negative for this ozone.
DIFFERENCIATE: sin x2 + sin2 x + sin2 (x2)
ACCORDING TO QUES,
Explain why the stability of oxoacids of chlorine increases in the order given below: HClO< HClO2< HClO3< HClO4
As the decrease in the electronegativity of the halogen, the tendency of the XO3 group (X = halogens) to withdraw the electrons of the O-H bond has decreased so the perhalic acid strength also...
In the ring test of NO3– ion, Fe2+ ion reduces nitrate ion to nitric oxide, which combines with Fe2+ (aq) ion to form the brown complex. Write the reactions involved in the formation of a brown ring.
Reaction Involved: NO3- + 3Fe2+ + 4H+ → NO + 3Fe2 + 2H2O [Fe(H2O) 6]SO4 + NO → [Fe(H2O) 5NO]SO4 (brown coloured complex)
On reaction with Cl2, phosphorus forms two types of halides ‘A’ and ‘B’. Halide A is a yellowish-white powder but halide ‘B’ is a colourless oily liquid. Identify A and B and write the formulas of their hydrolysis products.
Identification: Halide A - PCl5 (yellowish-white powder) Halide B - PCl3 (colourless oily liquid) Reaction Involved: PCl3 + 3H2O H3PO3 + 3HCl (Hydrolysis of PCl5) PCl5 + H2O POCl3+ 2HCl PCl5 +...
DIFFERENCIATE:
ACCORDING TO QUES,
Show that satisfies the equation A2 – 3A – 7I = 0 and hence find A-1.
Answer: According to question, the matrix can be solved as Given, Presently, \[{{A}^{2}}-\text{ }3A\text{ }-\text{ }7I\text{ }=\text{ }0\] Increasing the two sides with\[A-1\], we get...
Differentiate: sin (ax2 + bx + c)
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
Differentiate:
ACCORDING TO QUES,
SF6 is known but SCl6 is not. Why?
Fluorine is the most potent oxidizing agent and can oxidize sulfur in its high oxidation state (+6) to form SF6. Chlorine is not a good oxidizing agent, it cannot oxidize sulfur in its high...
Out of H2O and H2S, which one has a higher bond angle and why?
H2O has a higher bond angle than H2S because as we move from oxygen to sulfur the size of the central atom increases and electronegativity decreases due to which bond moving from the central atom...
Give the reason to explain why ClF3 exists but FCl3 does not exist.
Chlorine has some empty area in the d orbital which is why it can show an oxidation state of +3. Fluorine has no vacancy in the d orbital, it cannot show a good oxidation state. Fluorine shows only...
Why is nitric oxide paramagnetic in gaseous state but the solid obtained on cooling it is diamagnetic?
The nitric acid in the form of a gas is present in the form of a monomer. It contains only one unpaired electron and is therefore paramagnetic. In the solid state, it exists as a dimer (N2O2). There...
In PCl5, phosphorus is in sp3d hybridised state but all its five bonds are not equivalent. Justify your answer with reason.
The size of the axial bond is greater than the size of the equatorial bond to endure repulsion because the three equatorial bonds create more repulsion. The two axial P-Cl bonds are therefore longer...
Differentiate:
ACCORDING TO QUES,
Find the value of x if
Answer: According to given matrix, the solution should be \[[16\text{ }+\text{ }2x\text{ }+\text{ }10(x)\text{ }+\text{ }12\text{ }+\text{ }{{x}^{2}}~+\text{ }4x]\text{ }=\text{ }0\]...
PH3 forms bubbles when passed slowly in water but NH3 dissolves. Explain why?
With water, the PH3 does not form any hydrogen bond. It therefore does not dissolve in water and evaporates as a gas and forms bubbles while the ammonia forms the hydrogen bond and dissolves in water.
Write the structure of pyrophosphoric acid.
Write a balanced chemical equation for the reaction showing catalytic oxidation of NH3 by atmospheric oxygen.
Reaction Involved: NH3 + O2 → 4NO + 6H2O The platinum gauze acts as a catalyst to speed up the reaction.
In the preparation of H2SO4 by Contact Process, why is SO3 not absorbed directly in water to form H2SO4?
The dissolution of SO3 in water is very exothermic. This leads to the formation of tiny droplets that are corrosive and can even attack the lead pipes used to cover the tower in the communication...
Differentiate:
ACCORDING TO QUES,
A function f : R ® R satisfies the equation f ( x + y) = f (x) f (y) for all x, y ÎR, f (x) ¹ 0. Suppose that the function is differentiable at x = 0 and f ¢ (0) = 2. Prove that f ¢(x) = 2 f (x).
\[f\left( x \right)\text{ }=\text{ }2f\left( x \right).\]
Show that f (x) = |x – 5| is continuous but not differentiable at x = 5.
ACCORDING TO QUES, Therefore, f(x) is not differentiable at \[x\text{ }=\text{ }5.\]
If show that (A + B) (A – B) ≠ A2 – B2
Answer: Thus, from (I) and (ii), \[\left( A\text{ }+\text{ }B \right)\text{ }\left( A\text{ }-\text{ }B \right)\text{ }\ne \text{ }{{A}^{2}}-\text{ }{{B}^{2}}\]
Which of the following statements are true?
(i) The only type of interactions between particles of noble gases is due to weak dispersion forces. (ii) Ionisation enthalpy of molecular oxygen is very close to that of xenon. (iii) Hydrolysis of...
In which of the following reactions conc. H2SO4 is used as an oxidising reagent?
(i) CaF2+ H2SO4 → CaSO4+ 2HF (ii) 2HI + H2SO4 → I2 + SO2+ 2H2O (iii) Cu + 2H2SO4 → CuSO4 + SO2 + 2H2O (iv) NaCl + H2SO4 → NaHSO4 + HCl Correct Answers: (ii) 2HI + H2SO4 → I2 + SO2+ 2H2O...
Which of the following statements are correct?
(i) S–S bond is present in H2S2O6 (ii) In peroxosulphuric acid (H2SO5) sulphur is in +6 oxidation state. (iii) Iron powder along with Al2O3 and K2O is used as a catalyst in the preparation of NH3 by...
Which of the following orders are correct as per the properties mentioned against each?
(i) As2O3< SiO2< P2O3< SO2 Acid strength. (ii) AsH3< PH3< NH3 Enthalpy of vaporization. (iii) S < O < Cl < F More negative electron gain enthalpy. (iv) H2O > H2S > H2Se...
SOLVE:
According to ques, FUNCTION is differentiable at \[x\text{ }=\text{ }2.\]
Which of the following statements are correct?
(i) All three N—O bond lengths in HNO3 are equal. (ii) All P—Cl bond lengths in PCl5 molecule in the gaseous state are equal. (iii) P4 molecule in white phosphorus have angular strain therefore...
Which of the following statements are correct for SO2 gas?
(i) It acts as a bleaching agent in moist conditions. (ii) Its molecule has linear geometry. (iii) It’s dilute solution is used as a disinfectant. (iv) It can be prepared by the reaction of dilute...
Which of the following statements are correct?
(i) Among halogens, radius ratio between iodine and fluorine is maximum. (ii) Leaving F—F bond, all halogens have weaker X—X bond than X—X’ bond in interhalogens. (iii) Among interhalogen compounds,...
Which of the following is correct for P4 the molecule of white phosphorus?
(i) It has 6 lone pairs of electrons. (ii) It has six P–P single bonds. (iii) It has three P–P single bonds. (iv) It has four lone pairs of electrons. Correct Answers: (ii) It has six P–P...
Which of the following options are not in accordance with the property mentioned against them?
(i) F2 > Cl2 > Br2 > I2 - Oxidising power. (ii) MI > MBr > MCl > MF - Ionic character of metal halide. (iii) F2 > Cl2 > Br2 > I2 - Bond dissociation enthalpy. (iv) HI <...
If chlorine gas is passed through a hot NaOH solution, two changes are observed in the oxidation number of chlorine during the reaction. These are ________ and _________.
(i) 0 to +5 (ii) 0 to +3 (iii) 0 to –1 (iv) 0 to +1 Correct Answers: (i) 0 to +5 (iii) 0 to –1 Explanation:
SOLVE:
NOW ACCORDING TO QUES, AND, HENCE DIFFERENTIABILITY AT \[x\text{ }=\text{ }0.\]
SOLVE:
SO, f(x) is not differentiable at \[x\text{ }=\text{ }2.\]
Find non-zero values of x satisfying the matrix equation:
Answer: Given, On looking at the relating components, we get \[2x\text{ }+\text{ }10x\text{ }=\text{ }48\] \[12x\text{ }=\text{ }48\] In this manner, \[x\text{ }=\text{ }4\] It's additionally seen...
Show that the function f (x) = |sin x + cos x| is continuous at x = p. Examine the differentiability of f, where f is defined by
Given, \[f\left( x \right)\text{ }=\text{ }\left| sin\text{ }x\text{ }+\text{ }cos\text{ }x \right|\text{ }at\text{ }x\text{ }=\text{ }\pi \] Presently, put \[g\left( x \right)\text{ }=\text{...
Find values of a and b if A = B, where
Answer: Given, \[matrix\text{ }A\text{ }=\text{ }matrix\text{ }B\] Then, at that point, their comparing components are equivalent. Thus, we have \[{{a}_{11}}~=\text{ }{{b}_{11}};\]\[a\text{ }+\text{...
Find all points of discontinuity of the function:
Now, if f(t) is discontinuous, then \[2-\text{ }\text{ }x\text{ }=\text{ }0\Rightarrow x\text{ }=\text{ }2\] And, \[2x-\text{ }\text{ }1\text{ }=\text{ }0\Rightarrow x\text{ }=\text{...
Given the function f (x) = 1/(x + 2) . Find the points of discontinuity of the composite function y = f (f (x)).
fun wont be define and continuous \[2x\text{ }+\text{ }5\text{ }=\text{ }0\Rightarrow x\text{ }=\text{ }-5/2\] hence,\[x\text{ }=\text{ }-5/2\] is the point of discontinuity.
In the preparation of HNO3, we get NO gas by catalytic oxidation of ammonia. The moles of NO produced by the oxidation of two moles of NH3 will be ______.
(i) 2 (ii) 3 (iii) 4 (iv) 6 Correct Answer: (i) 2 Explanation: In the preparation of HNO3, we get NO gas by catalytic oxidation of ammonia. The moles of NO produced by the oxidation of two...
The oxidation state of a central atom in the anion of compound NaH2PO2 will be ______.
(i) +3 (ii) +5 (iii) +1 (iv) –3 Correct Answer: (iii) +1 Explanation: NaH2PO2 = 1 + (2x+1) + x + 2(−2) =0 x−1 = 0 x = +1
Which of the following is not tetrahedral in shape?
(i) NH4+ (ii) SiCl4 (iii) SF4 (iv) SO42- Correct Answer: (iii) SF4 Explanation: The shape of SF4 is not tetrahedral.
Which of the following are peroxoacids of sulphur?
(i) H2SO5 and H2S2O8 (ii) H2SO5 and H2S2O7 (iii) H2S2O7 and H2S2O8 (iv) H2S2O6 and H2S2O7 Correct Answer: (i) H2SO5 and H2S2O8 Explanation: Peroxides of Sulphur - H2SO5 and...
Hot conc. H2SO4 acts as a moderately strong oxidising agent. It oxidises both metals and nonmetals. Which of the following element is oxidised by conc H2SO4 into two gaseous products?
(i) Cu (ii) S (iii) C (iv) Zn Correct Answer: (iii) C Explanation: When hot conc. H2SO4 acts as a moderately strong oxidising agent, it oxidises both metals and nonmetals. The element Carbon...
A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When an excess of this gas reacts with NH3 an unstable trihalide is formed. In this process the oxidation state of nitrogen changes from _________.
(i) –3 to +3 (ii) –3 to 0 (iii) –3 to +5 (iv) 0 to –3 Correct Answer: (i) –3 to +3 Explanation: A black compound of manganese reacts with a halogen acid to give greenish yellow gas. When an...
In the preparation of compounds of Xe, Bartlett had taken O2+Pt F6– as a base compound. This is because
(i) both O2 and Xe has the same size. (ii) both O2 and Xe has the same electron gain enthalpy. (iii) both O2 and Xe has almost same ionisation enthalpy. (iv) both Xe and O2 are gases Correct...
In solid state PCl5 is a _________.
(i) covalent solid (ii) octahedral structure (iii) ionic solid with [PCl6]+ octahedral and [PCl4]– tetrahedra (iv) ionic solid with [PCl4]+tetrahedral and [PCl6]– octahedral Correct Answer:...
Reduction potentials of some ions are given below. Arrange them in decreasing order of oxidising power.
IonReduction potential Eᶱ/V ClO4–Eᶱ = 1.19V IO4–Eᶱ = 1.65V BrO4 –Eᶱ = 1.74V (i) ClO4–> IO4– > BrO4– (ii) IO4– > BrO4– > ClO4– (iii) BrO4– > IO4– > ClO4– (iv) BrO4– > ClO4– >...
Which of the following is isoelectronic pair?
(i) ICl2, ClO2 (ii) BrO2-, BrF2+ (iii) ClO2, BrF (iv) CN-, O3 Correct Answer: (ii) BrO2-, BrF2+ Explanation: BrO2- = 35 + 2 * 8 + 1 => 52 BrF2+ = 35 + 2 * 9 - 1 =>...
Find the values of a and b such that the function f defined by following function is a continuous function at x = 4.
So, \[-1\text{ }+\text{ }a\text{ }=\text{ }a\text{ }+\text{ }b\text{ }=\text{ }1\text{ }+\text{ }b\] \[-1\text{ }+\text{ }a\text{ }=\text{ }a\text{ }+\text{ }b\text{ }and\text{ }1\text{ }+\text{...
If A matrix Z such that X + Y + Z is a zero matrix.
Answer: According to the given ques
Write the negation of the following simple statements
(i) All similar triangles are congruent.
(ii) Area of a circle is same as the perimeter of the circle.
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is...
Prove that the function f defined by following equation remains discontinuous at x = 0, regardless the choice of k
Since the left hand limit is not equal to the right hand limit and both have constant values. so the given function remains discontinuous at \[x\text{ }=\text{ }0.\] ...
Write the negation of the following simple statements
(i) 2 is not a prime number.
(ii) Every real number is an irrational number.
(i) "Not p" is the negation of the assertion p. The negation of p is represented by $\sim p$. The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement is “2...
If (i) X + Y (ii) 2X – 3Y
Answer: According to the question, the matrix can be solved as
Write the negation of the following simple statements
(i) The number 17 is prime.
(ii) 2 + 7 = 6.
(i) "Not p" is the negation of the statement p. The negation of p is represented by the "$\sim p$." The truth value of $\sim p$ is the opposite of the truth value of p. The negation of the statement...
If possible, find the sum of the matrices A and B,
where A = And B = Answer: The given two matrixs \[A\text{ }and\text{ }B\]are of various orders. Two matrices can be added provided that order for both the matrixs is same. So, the sum of matrices...
Find values of a and b if A = B, where
Answer: Given, \[matrix\text{ }A\text{ }=\text{ }matrix\text{ }B\] Then, at that point, their comparing components are equivalent. Thus, we have \[{{a}_{11}}~=\text{ }{{b}_{11}};\]\[a\text{ }+\text{...
Construct a 3 × 2 matrix whose elements are given by aij = ei.xsin jx
Leave A alone a \[3\text{ }x\text{ }2\] matrix With the end goal that, \[{{a}_{ij}}~=\text{ }{{e}^{i.x}}sin\text{ }jx;\]where \[1\text{ }\le \text{ }i\text{ }\le \text{ }3;\text{ }1\text{ }\le...
Find the value of k so that the function f is continuous at the indicated point:
ACCORDING TO QUES,
Find the value of k so that the function f is continuous at the indicated point:
HENCE K IS \[1\]
Construct a2 × 2 matrix where (i) aij = (i – 2j)2/ 2 (ii) aij = |-2i + 3j|
We have, \[A\text{ }=\text{ }{{[{{a}_{ij}}]}_{2\times 2}}\] (I) Such that,\[~{{a}_{ij}}~=\text{ }{{\left( i\text{ }\text{ }2j \right)}^{2}}/\text{ }2;\] \[where\text{ }1\text{ }\le \text{ }i\text{...
Find the value of k so that the function f is continuous at the indicated point:
\[~k\text{ }=\text{ }{\scriptscriptstyle 1\!/\!{ }_2}\]
In the matrix A = , write : Write elements a23, a31, a12
For the given matrix, Elements: \[{{a}_{23}}~=\text{ }{{x}^{2}}~\text{ }y,\text{ }{{a}_{31}}~=\text{ }0,\text{ }{{a}_{12}}~=\text{ }1\]
Find the value of k so that the function f is continuous at the indicated point:
So, \[7\text{ }=\text{ }2k\] \[k\text{ }=\text{ }7/2\text{ }=\text{ }3.5\] SO VALUE OF K IS \[3.5\]
In the matrix A = , write : (i) The order of the matrix A (ii) The number of elements
For the given matrix, (I) The order for the matrix \[A\text{ }is\text{ }3\text{ }x\text{ }3.\] (ii) The number of elements of the matrix \[~=\text{ }3\text{ }x\text{ }3\text{ }=\text{ }9\]
If a matrix has 28 elements, what are the possible orders it can have? What if it has 13 elements?
For a provided matrix of order \[m\text{ }x\text{ }n,\]it has \[mn\]components, where \[m\text{ }and\text{ }n\]are normal numbers. Here we have, \[m\text{ }x\text{ }n\text{ }=\text{ }28\] \[\left(...
Find which of the functions if is continuous or discontinuous at the indicated points: f (x) = |x| + |x – 1| at x = 1
And hence, f(x) is continuous at \[x\text{ }=\text{ }1.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }1.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is discontinuous at \[x\text{ }=\text{ }0.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }0.\]
Find which of the functions if is continuous or discontinuous at the indicated points:
And hence, f(x) is continuous at \[x\text{ }=\text{ }0.\]
On addition of conc. H2SO4 to a chloride salt, colourless fumes are evolved but in case of an iodide salt, violet fumes come out. This is because
(i) H2SO4 reduces HI to I2 (ii) HI is of violet colour (iii) HI gets oxidised to I2 (iv) HI changes to HIO3 Correct Answer: (iii) HI gets oxidised to I2 Explanation: Reaction...
In qualitative analysis when H2S is passed through an aqueous solution of salt acidified with dil. HCl, a black precipitate is obtained. On boiling the precipitate with dil. HNO3, it forms a solution of blue colour. Addition of excess of aqueous solution of ammonia to this solution gives _________.
(i) a deep blue precipitate of Cu (OH)2 (ii) a deep blue solution of [Cu (NH3)4]2+ (iii) a deep blue solution of Cu(NO3)2 (iv) a deep blue solution of Cu(OH)2.Cu(NO3)2 Correct Answer: (ii) a...
In a cyclotrimetaphosphoric acid molecule, how many single and double bonds are present?
(i) 3 double bonds; 9 single bonds (ii) 6 double bonds; 6 single bonds (iii) 3 double bonds; 12 single bonds (iv) Zero double bonds; 12 single bonds Correct Answer: (ii) 6 double bonds; 6...
Which of the following elements can be involved in pπ–dπ bonding?
(i) Carbon (ii) Nitrogen (iii) Phosphorus (iv) Boron Correct Answer: (iii) Phosphorus Explanation: The element which is involved in the pπ–dπ bonding is Phosphorus.
Which of the following pairs of ions are isoelectronic and isostructural?
(i) CO32-, NO3- (ii) ClO3- , CO32- (iii) SO32-, NO3- (iv) ClO3- , SO32– Correct Answer: (i) CO32-, NO3- Explanation: CO32- and NO3- are the pairs of ions that are isoelectronic and...