Q48.During the detection of acidic radical present in a salt, a student gets a pale yellow precipitate soluble with difficulty in NH4OH solution when sodium carbonate extract was first acidified with dil. HNO3 and then AgNO3 solution was added. This indicates presence of : (1) Br− (2) I− (3) Cl− (4) CO32− JEE Main 2024 (06 Apr Shift 2) JEE Main Previous Year Paper
What This Question Tests
This question tests knowledge of the qualitative analysis for halide ions, specifically the characteristic precipitates formed with AgNO3 and their varying solubilities in ammonium hydroxide.
Concepts Tested
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6.22 — What Happens When
Chemistry Class 12 · Chapter 6
6.22 What happens when (i) n-butyl chloride is treated with alcoholic KOH, (ii) bromobenzene is treated with Mg in the presence of dry ether, (iii) chlorobenzene is subjected to hydrolysis, (iv) ethyl chloride is treated with aqueous KOH, (v) methyl bromide is treated with sodium in the presence of dry ether, (vi) methyl chloride is treated with KCN? Answers to Some Intext Questions 6.1 6.2 (i) H2SO4 cannot be used along with KI in the conversion of an alcohol to an alkyl iodide as it converts KI to corresponding acid, HI which is then oxidised by it to I2. 6.3 (i) ClCH2CH2CH2Cl (ii) ClCH2CHClCH3 (iii) Cl2CHCH2CH3 (iv) CH3CCl2CH3 191 Haloalkanes and Haloarenes Reprint 2025-26
6.10 — Acids, Bases And Salts A Very High Dielectric Constant Of 80. Thus,
Chemistry Class 11 · Chapter 6
6.10 ACIDS, BASES AND SALTS a very high dielectric constant of 80. Thus, Acids, bases and salts find widespread when sodium chloride is dissolved in water, occurrence in nature. Hydrochloric acid the electrostatic interactions are reduced by present in the gastric juice is secreted by the a factor of 80 and this facilitates the ions to lining of our stomach in a significant amount move freely in the solution. Also, they are of 1.2-1.5 L/day and is essential for digestive well-separated due to hydration with water processes. Acetic acid is known to be the main molecules. constituent of vinegar. Lemon and orange juices contain citric and ascorbic acids, and tartaric acid is found in tamarind paste. As most of the acids taste sour, the word “acid” has been derived from a latin word “acidus” meaning sour. Acids are known to turn blue litmus paper into red and liberate dihydrogen on reacting with some metals. Similarly, bases are known to turn red litmus paper blue, taste bitter and feel soapy. A common example of a base is washing soda used for washing purposes. When acids and bases are mixed in the right proportion they react with each Fig.6.10 Dissolution of sodium chloride in water.other to give salts. Some commonly known Na+ and Cl– ions are stablised by their examples of salts are sodium chloride, barium hydration with polar water molecules. sulphate, sodium nitrate. Sodium chloride (common salt) is an important component of Comparing, the ionization of hydrochloric our diet and is formed by reaction between acid with that of acetic acid in water we find hydrochloric acid and sodium hydroxide. It that though both of them are polar covalent Faraday was born near London into a family of very limited means. At the age of 14 he was an apprentice to a kind bookbinder who allowed Faraday to read the books he was binding. Through a fortunate chance he became laboratory assistant to Davy, and during 1813-4, Faraday accompanied him to the Continent. During this trip he gained much from the experience of coming into contact with many of the leading scientists of the time. In 1825, he succeeded Davy as Director of the Royal Institution laboratories, and in 1833 he also became the first Fullerian Professor of Chemistry. Faraday’s first important work was on analytical chemistry. After 1821 Michael Faraday much of his work was on electricity and magnetism and different electromagnetic (1791–1867) phenomena. His ideas have led to the establishment of modern field theory. He discovered his two laws of electrolysis in 1834. Faraday was a very modest and kind hearted person. He declined all honours and avoided scientific controversies. He preferred to work alone and never had any assistant. He disseminated science in a variety of ways including his Friday evening discourses, which he founded at the Royal Institution. He has been very famous for his Christmas lecture on the ‘Chemical History of a Candle’. He published nearly 450 scientific papers. Reprint 2025-26 190 chemistry molecules, former is completely ionized into its constituent ions, while the latter is only Hydronium and Hydroxyl Ions partially ionized (< 5%). The extent to which Hydrogen ion by itself is a bare proton with very ionization occurs depends upon the strength small size (~10–15 m radius) and intense electric of the bond and the extent of solvation field, binds itself with the water molecule at of ions produced. The terms dissociation one of the two available lone pairs on it giving and ionization have earlier been used with H3O+. This species has been detected in many different meaning. Dissociation refers to the compounds (e.g., H3O+Cl–) in the solid state. In process of separation of ions in water already aqueous solution the hydronium ion is further existing as such in the solid state of the solute, hydrated to give species like H5O2+, H7O3 + and as in sodium chloride. On the other hand, H9O4+. Similarly the hydroxyl ion is hydrated to give several ionic species like H3O2–, H5O3–ionization corresponds to a process in which – and H7O4 etc.a neutral molecule splits into charged ions in the solution. Here, we shall not distinguish between the two and use the two terms interchangeably. 6.10.1 Arrhenius Concept of Acids and Bases According to Arrhenius theory, acids are H9O4+ substances that dissociates in water to give hydrogen ions H+(aq) and bases are 6.10.2 The Brönsted-Lowry Acids and substances that produce hydroxyl ions Bases OH –(aq). The ionization of an acid HX (aq) can The Danish chemist, Johannes Brönsted and be represented by the following equations: the English chemist, Thomas M. Lowry gave HX (aq) → H+(aq) + X– (aq) a more general definition of acids and bases. or According to Brönsted-Lowry theory, acid HX(aq) + H2O(l) → H3O+(aq) + X –(aq) is a substance that is capable of donating a hydrogen ion H+ and bases are substances A bare proton, H+ is very reactive and capable of accepting a hydrogen ion, H+. Incannot exist freely in aqueous solutions. short, acids are proton donors and bases areThus, it bonds to the oxygen atom of a solvent proton acceptors.water molecule to give trigonal pyramidal Consider the example of dissolution of NH3hydronium ion, H3O+ {[H (H2O)]+} (see box). In in H2O represented by the following equation:this chapter we shall use H+(aq) and H3O+(aq) interchangeably to mean the same i.e., a hydrated proton. Similarly, a base molecule like MOH ionizes in aqueous solution according to the equation: MOH(aq) → M+(aq) + OH–(aq) The hydroxyl ion also exists in the hydrated form in the aqueous solution. Arrhenius concept of acid and base, however, suffers The basic solution is formed due to the from the limitation of being applicable only to presence of hydroxyl ions. In this reaction, aqueous solutions and also, does not account water molecule acts as proton donor and for the basicity of substances like, ammonia ammonia molecule acts as proton acceptor which do not possess a hydroxyl group. and are thus, called Lowry-Brönsted acid and Reprint 2025-26 EQUILIBRIUM 191 Arrhenius was born near Uppsala, Sweden. He presented his thesis, on the conductivities of electrolyte solutions, to the University of Uppsala in 1884. For the next five years he travelled extensively and visited a number of research centers in Europe. In 1895 he was appointed professor of physics at the newly formed University of Stockholm, serving its rector from 1897 to 1902. From 1905 until his death he was Director of physical chemistry at the Nobel Institute in Stockholm. He continued to work for many years on electrolytic solutions. In 1899 he discussed the temperature dependence of reaction rates on the basis of an equation, now usually known as Arrhenius equation. He worked in a variety of fields, and made important contributions to Svante Arrhenius immunochemistry, cosmology, the origin of life, and the causes of ice age. He was (1859-1927) the first to discuss the ‘green house effect’ calling by that name. He received Nobel Prize in Chemistry in 1903 for his theory of electrolytic dissociation and its use in the development of chemistry. base, respectively. In the reverse reaction, in case of ammonia it acts as an acid by H+ is transferred from NH4+ to OH–. In this donating a proton. case, NH4+ acts as a Bronsted acid while Problem 6.12OH– acted as a Brönsted base. The acid-base What will be the conjugate bases for thepair that differs only by one proton is called following Brönsted acids: HF, H2SO4 anda conjugate acid-base pair. Therefore, OH– – HCO3 ?is called the conjugate base of an acid H2O and NH4+ is called conjugate acid of the base Solution NH3. If Brönsted acid is a strong acid then The conjugate bases should have one its conjugate base is a weak base and vice- proton less in each case and therefore the versa. It may be noted that conjugate acid corresponding conjugate bases are: F –, has one extra proton and each conjugate base HSO4– and CO32– respectively. has one less proton. Problem 6.13 Consider the example of ionization of Write the conjugate acids for the following hydrochloric acid in water. HCl(aq) acts as Brönsted bases: NH2–, NH3 and HCOO–. an acid by donating a proton to H2O molecule which acts as a base. Solution The conjugate acid should have one extra proton in each case and therefore the corresponding conjugate acids are: NH3, NH4+ and HCOOH respectively. Problem 6.14 The species: H2O, HCO3–, HSO4– and NH3 can act both as Bronsted acids and bases. For each case give the corresponding conjugate It can be seen in the above equation, that acid and conjugate base. water acts as a base because it accepts the Solution proton. The species H3O+ is produced when The answer is given in the following Table:water accepts a proton from HCl. Therefore, Cl– is a conjugate base of HCl and HCl is the Species Conjugate Conjugate conjugate acid of base Cl –. Similarly, H2O is acid base a conjugate base of an acid H3O+ and H3O+ is H2O H3O+ OH–a conjugate acid of base H2O. – 2– HCO3 H2CO3 CO3 It is interesting to observe the dual role – 2– HSO4 H2SO4 SO4of water as an acid and a base. In case of + – reaction with HCl water acts as a base while NH3 NH4 NH2 Reprint 2025-26 192 chemistry 6.10.3 Lewis Acids and Bases (HClO4), hydrochloric acid (HCl), hydrobromic G.N. Lewis in 1923 defined an acid as a acid (HBr), hyrdoiodic acid (HI), nitric acid species which accepts electron pair and base (HNO3) and sulphuric acid (H2SO4) are termed which donates an electron pair. As far as bases strong because they are almost completely are concerned, there is not much difference dissociated into their constituent ions in an between Brönsted-Lowry and Lewis concepts, aqueous medium, thereby acting as proton as the base provides a lone pair in both the (H+) donors. Similarly, strong bases like cases. However, in Lewis concept many lithium hydroxide (LiOH), sodium hydroxide acids do not have proton. A typical example (NaOH), potassium hydroxide (KOH), caesium is reaction of electron deficient species BF3 hydroxide (CsOH) and barium hydroxide with NH3. Ba(OH)2 are almost completely dissociated into ions in an aqueous medium giving BF3 does not have a proton but still acts hydroxyl ions, OH–. According to Arrhenius as an acid and reacts with NH3 by accepting concept they are strong acids and bases asits lone pair of electrons. The reaction can be they are able to completely dissociate andrepresented by, produce H3O+ and OH– ions respectively in BF3 + :NH3 → BF3:NH3 the medium. Alternatively, the strength of an Electron deficient species like AlCl3, Co3+, acid or base may also be gauged in terms of Mg2+, etc. can act as Lewis acids while species Brönsted-Lowry concept of acids and bases, like H2O, NH3, OH– etc. which can donate a wherein a strong acid means a good proton pair of electrons, can act as Lewis bases. donor and a strong base implies a good proton acceptor. Consider, the acid-base dissociation Problem 6.15 equilibrium of a weak acid HA, Classify the following species into Lewis HA(aq) + H2O(l) H3O+(aq) + A–(aq) acids and Lewis bases and show how these conjugate conjugate act as such: acid base acid base (a) HO– (b) F – (c) H+ (d) BCl3 In section 6.10.2 we saw that acid (or Solution base) dissociation equilibrium is dynamic involving a transfer of proton in forward and (a) Hydroxyl ion is a Lewis base as it can reverse directions. Now, the question arises donate an electron lone pair (:OH– ). that if the equilibrium is dynamic then with (b) Flouride ion acts as a Lewis base passage of time which direction is favoured? as it can donate any one of its four What is the driving force behind it? In order electron lone pairs. to answer these questions we shall deal (c) A proton is a Lewis acid as it can into the issue of comparing the strengths accept a lone pair of electrons from of the two acids (or bases) involved in the bases like hydroxyl ion and fluoride dissociation equilibrium. Consider the two ion. acids HA and H3O+ present in the above mentioned acid-dissociation equilibrium. (d) BCl3 acts as a Lewis acid as it can We have to see which amongst them is a accept a lone pair of electrons from stronger proton donor. Whichever exceeds species like ammonia or amine in its tendency of donating a proton over the molecules. other shall be termed as the stronger acid
5.28 — How Many Ions Are Produced From The Complex Co(Nh3)6Cl2 In Solution?
Chemistry Class 11 · Chapter 5
5.28 How many ions are produced from the complex Co(NH3)6Cl2 in solution? (i) 6 (ii) 4 (iii) 3 (iv) 2 139 Coordination Compounds Reprint 2025-26
📋 Question Details
- Chapter
- Qualitative Analysis
- Topic
- Detection of Acidic Radicals
- Year
- 2024
- Shift
- 06 Apr Shift 2
- Q Number
- Q48
- Type
- MCQ
- NCERT Ref
- Class 11 Chemistry Ch 11: The p-Block Elements (for halide properties); JEE Practical Chemistry
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Q153.If α ≠β but α2 = 5α −3 and β2 = 5β −3 then the equation having α/β and β/α as its roots is (1) 3x2 −19x + 3 = 0 (2) 3x2 + 19x −3 = 0 (3) 3x2 −19x −3 = 0 (4) x2 −5x + 3 = 0 Q154.Difference between the corresponding roots of x2 + ax + b = 0 and x2 + bx + a = 0 is same and a ≠b, then (1) a + b + 4 = 0 (2) a + b - 4 = 0 (3) a - b - 4 = 0 (4) a - b + 4 = 0 Q155.Product of real roots of the equation t2x2 + |x| + 9 = 0 (1) is always positive (2) is always negative (3) does not exist (4) none of these Q156.If p and q are the roots of the equation x2 + px + q = 0, then (1) p =1, q = -2 (2) p = 0, q = 1 (3) p = -2, q = 0 (4) p = -2, q = 1 Q157.If 2a + 3b + 6c = 0(a, b, c ∈R) then the quadratic equation ax2 + bx + c = 0 has (1) at least one root in [0, 1] (2) at least one root in [2, 3] (3) at least one root in [4, 5] (4) none of these Q158. z and w are two non zero complex no.s such that |z| = |w| and Arg z + Arg w = π then z equals –– (1) W (2) - W (3) W (4) - W Q159.If |z −4| < |z −2|, its solution is given by (1) Re(z) > 0 (2) Re(z) < 0 (3) Re (z) > 3 (4) Re(z) > 2 Q160.The locus of the centre of a circle which touches the circle |z −z1| = a and |z −z2| = b externally ( z, z1 and z2 are complex numbers) will be (1) an ellipse (2) a hyperbola (3) a circle (4) none of these Q161.Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are (1) 216 (2) 375 (3) 400 (4) 720 Q162.Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed) is JEE Main 2002 JEE Main Previous Year Paper (1) 125 (2) 105 (3) 375 (4) 625 Q163.Five digit number divisible by 3 is formed using 0, 1, 2, 3, 4, 6 and 7 without repetition. Total number of such numbers are (1) 312 (2) 3125 (3) 120 (4) 216 Q164.If 1, log9 (31−x + 2), log3 (4.3x −1) are in A.P. then x equals (1) log3 4 (2) 1 + log3 4 (3) 1 - log3 4 (4) log4 3 Q165.The value of 21/4, 41/8, 81/6 + … … ∞ is (1) 1 (2) 2 (3) 3/2 (4) 4 Q166.Fifth term of a GP is 2, then the product of its 9 terms is (1) 256 (2) 512 (3) 1024 (4) none of these Q167.Sum of infinite number of terms of GP is 20 and sum of their square is 100. The common ratio of GP is (1) 5 (2) 3/5 (3) 8/5 (4) 1/5 Q168. 13 −23 + 33 −43 + … . +93 = (1) 425 (2) -425 (3) 475 (4) -475 Q169.The sum of integers from 1 to 100 that are divisible by 2 or 5 is (1) 3000 (2) 3050 (3) 3600 (4) 3250 Q170.If an = √7 + √7 + √7 + … . having n radical signs then by methods of mathematical induciton which is true (1) an > 7∀n ≥1 (2) an > 7∀n ≥1 (3) an < 4∀n ≥1 (4) an < 3∀n ≥1 Q171.The coefficients of xp and xq in the expansion of (1 + x)p+q are (1) equal (2) equal with opposite signs (3) reciprocals of each other (4) none of these Q172.If the sum of the coefficients in the expansion of (a + b)n is 4096 , then the greatest coefficient in the expansion is (1) 1594 (2) 792 (3) 924 (4) 2924 Q173.The positive integer just greater than (1 + 0.0001)10000 is JEE Main 2002 JEE Main Previous Year Paper (1) 4 (2) 5 (3) 2 (4) 3 Q174. r and n are positive integers r > 1, n > 2 and coefficient of (r + 2)th term and 3rth term in the expansion of (1 + x)2n are equal, then n equals (1) 3r (2) 3r + 1 (3) 2r (4) 2r + 1 Q175.The period of sin2 θ is (1) π2 (2) π (3) 2π (4) π/2 Q176.The number of solution of tan x + sec x = 2 cos x in [0, 2π) is (1) 2 (2) 3 (3) 0 (4) 1 Q177.A triangle with vertices (4, 0), (-1, -1), (3, 5) is (1) isosceles and right angled (2) isosceles but not right angled (3) right angled but not isosceles (4) neither right angled nor isoceles Q178.The sides of a triangle are 3x + 4y, 4x+37 and 5x + 57 where x, y > 0 then the triangle is (1) right angled (2) obtuse angled (3) equilateral (4) none of these Q179.If the pair of lines ax2 + 2hxy + by2 + 2gx + 2fy + c = 0 intersect on the y - axis then (1) 2fgh = bg2 + ch2 (2) bg2 ≠ch2 (3) abc = 2fgh (4) none of these Q180.The point of lines represented by 3ax2 + 5xy + (a2 −2)y2 = 0 and perpendicular to each other for (1) two values of a (2) ∀a (3) for one value of a (4) for no values of a Q181.Locus of mid point of the portion between the axes of x cos α + y sin α = p where p is constant is (1) x2 + y2 = 4 (2) x2 + y2 = 4p2 p2 (3) 1 + 1 = 2 (4) 1 + 1 = 4 x2 y2 p2 x2 y2 p2 Q182.If the chord y = mx + 1 of the circle x2 + y2 = 1 subtends an angle of measure 450 at the major segment of the circle then value of m is (1) 2 ± √2 (2) −2 ± √2 (3) −1 ± √2 (4) none of these Q183.The centres of a set of circles, each of radius 3 , lie on the circle x2 + y2 = 25. The locus of any point in the set is (1) 4 ≤x2 + y2 ≤64 (2) x2 + y2 ≤25 (3) x2 + y2 ≥25 (4) 3 ≤x2 + y2 ≤9 Q184.The centre of the circle passing through (0, 0) and (1, 0) and touching the circle x2 + y2 = 9 is JEE Main 2002 JEE Main Previous Year Paper , −√2) (1) ( 21 , 12 ) (2) ( 12 (3) ( 23 , 12 ) (4) ( 12 , 32 ) Q185.Two common tangents to the circle x2 + y2 = 2a2 and parabola y2 = 8ax are (1) x = ±(y + 2a) (2) y = ±(x + 2a) (3) x = ±(y + a) (4) y = ±(x + a) Q186. (1) 1 (2) -1 (3) zero (4) does not exist Q187. (1) e4 (2) e2 (3) e3 (4) 1 Q188.Let f(x) = 4 and f ′(x) = 4. Then Limx→2 xf(2)−2f(x)x−2 is given by (1) 2 (2) -2 (3) -4 (4) 3 Q189. 1p + 2p + 3p + … + np Limn→∞ np+1 is (1) 1 (2) 1 p+1 1−p (3) p 1 − p−11 (4) p+21 denotes greatest integer less than or equal to x) Q190. Limx→0 log xn−[x][x] , n ∈N([x] (1) has value -1 (2) has value 0 (3) has value 1 (4) does not exist Q191.If f(1) = 1, f ′(1) = 2, then Limx→1 √f(x)−1 is √x−1 (1) 2 (2) 4 (3) 1 (4) 1/2 Q192.In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average of the girls? (1) 73 (2) 65 (3) 68 (4) 74 Q193.The equation of a circle with origin as a centre and passing through equilateral triangle whose median is of length 3a is JEE Main 2002 JEE Main Previous Year Paper (1) x2 + y2 = 9a2 (2) x2 + y2 = 16a2 (3) x2 + y2 = 4a2 (4) x2 + y2 = a2 Q194.In a triangle with sides a, b, c, r1 > r2 > r3 (which are the ex-radii) then (1) a > b > c (2) a < b < c (3) a > b and b < c (4) a < b and b > c Q195. log l p 1 l, m, n are the pth , qth and rth term of a G.P. all positive, then log m q 1 equals log n r 1 (1) -1 (2) 2 (3) 1 (4) 0 Q196. a b ax + b If a > 0 discriminant of ax2 + 2bx + c is -ve, then b c bx + c is ax + b bx + c 0 (1) +ve (2) (ac −b2) (ax2 + 2bx + c) (3) -ve (4) 0 Q197. cot−1(√cos α) = tan−1(√cos α) = x, then sin x = (1) tan2 ( α2 ) (2) cot2 ( α2 ) (3) tan α (4) cot ( α2 ) Q198.The domain of sin−1 [log3(x/3)] is (1) [1, 9] (2) [-1,9] (3) [-9, 1] (4) [-9, -1] Q199.Which one is not periodic (1) |sin 3x| + sin2 x (2) cos √x + cos2 x (3) cos 4x + tan2 x (4) cos 2x + sin x Q200.If f(x + y) = f(x) ⋅f(y)∀x ⋅y and f(5) = 2, f ′(0) = 3 then f ′(5) is (1) 0 (2) 1 (3) 6 (4) 2 Q201.f is defined in [-5, 5] as f(x) = x if x is rational and = -x is irrational. Then (1) f(x) is continuous at every x, except x = 0 (2) f(x) is discontinuous at every x, except x = 0 (3) f(x) is continuous everywhere (4) f(x) is discontinuous everywhere n d2y dy (1 + x2) dx2 + x dx is Q202.If y = (x + √1 + x2) , then (1) n2y (2) −n2y (3) −y (4) 2x2y Q203.The maximum distance from origin of a point on the curve x = a sin t −b sin ( atb ) y = a cos t −b cos ( atb ), both a, b > 0 is (1) a - b (2) a + b (3) √a2 + b2 (4) √a2 −b2 JEE Main 2002 JEE Main Previous Year Paper Q204. ∫10π0 | sin x|dx is (1) 20 (2) 8 (3) 10 (4) 18 xdx then Limn→∞n [In + In−2] equals Q205. In = ∫π/40 tann (1) 1/2 (2) 1 (3) ∞ (4) zero is Q206. ∫ 0√2 [x2]dx (1) 2 −√2 (2) 2 + √2 (3) √2 −1 (4) √2 −2 Q207. ∫π−π 2x(1+sin1+cos2 xx) dx is (1) π2 (2) π2 4 (3) zero (4) π 2 Q208.If y = f(x) makes +ve intercept of 2 and 0 unit on x and y axes and encloses an area of 3/4 square unit with the axes then ∫20 xf ′(x)dx is (1) 3/2 (2) 1 (3) 5/4 (4) -3/4 Q209.The area bounded by the curves y = ln x, y = ln |x|, y = | ln x| and y = | ln ||x| is (1) 4 sq. units (2) 6 sq. units (3) 10 sq. units (4) none of these d3y Q210.The order and degree of the differential equation 2/3 are + 3 dx = 4 dx3 (1 dy ) (1) (1, 32 ) (2) (3, 1) (3) (3, 3) (4) (1, 2) Q211.The solution of the equation d2y = e−2x dx2 (1) e−2x (2) e−2x 4 4 + cx + d (3) 4 1 e−2x + cx2 + d (4) 14 e−4x + cx + d Q212. f(x) and g(x) are two differentiable functions on [0, 2] such that f ′′(x) −g′′(x) = 0 f ′(1) = 2g′(1) = 4f(2) = 3g(2) = 9 then f(x) −g(x) at x = 3/2 is (1) 0 (2) 2 (3) 10 (4) 5 Q213.If |→a| = 4, |→b| = 2 and the angle between →a and →b is π/6 then (→a × →b)2 = 2 is equal to (1) 48 (2) 16 (3) →a (4) none of these Q214. If →a,→b, →c are vectors such that |→a→b→c| = 4 then (1) 16 (2) 64 (3) 4 (4) 8 JEE Main 2002 JEE Main Previous Year Paper Q215.If →a,→b, →c are vectors such that →a + →b + →c = 0 and |→a| = 7, |→b| = 5, |→c| = 3 then angle between vector →b and →c is (1) 60∘ (2) 30∘ (3) 45∘ (4) 90∘ Q216.If |a| = 5, |b| = 4, |c| = 3 thus what will be the value of |a ⋅b + b. c + c. a| , given that →a + →b + →c = 0 (1) 25 (2) 50 (3) -25 (4) -50 Q217. 3λ→c + 2μ(→a × →b) = 0 then (1) 3λ + 2μ = 0 (2) 3λ = 2μ (3) λ = μ (4) λ + μ = 0 Q218. →a = 3^i −5^j and →b = 6^i + 3^j are two vectors and →c is a vector such that →c = →a × →b then |→a| : |→b| : |→c| (1) √34 : √45 : √39 (2) √34 : √45 : 39 (3) 34 : 39 : 45 (4) 39 : 35 : 34 Q219.If →a × →b = →b × →c = →c × →a then →a + →b + →c = (1) abc (2) -1 (3) 0 (4) 2 Q220.The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12 N. The magnitude of the two forces are (1) 13, 5 (2) 12, 6 (3) 14, 4 (4) 11, 7 Q221.A plane which passes through the point (3, 2, 0) and the line x−41 = y−75 = z−44 is (1) x - y + z = 1 (2) x + y + z = 5 (3) x + 2y - z = 1 (4) 2x - y + z = 5 Q222.The d.r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x + y = 3 are (1) 1, √2, 1 (2) 1, 1, √2 (3) 1, 1, 2 (4) √2, 1, 1 Q223.A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is 2 1 , 13 and 14 . Probability that the problem is solved is (1) 3 (2) 1 4 2 (3) 2 (4) 1 3 3 Q224. A and B are events such that P(A ∪B) = 3/4, P(A ∩B) = 1/4, P(¯A) = 2/3 then P(¯A ∩B) is (1) 5/12 (2) 3/8 (3) 5/8 (4) 1/4 Q225.A die is tossed 5 times. Getting an odd number is considered a success. Then the variance of distribution of success is JEE Main 2002 JEE Main Previous Year Paper (1) 8/3 (2) 3/8 (3) 4/5 (4) 5/4 JEE Main 2002 JEE Main Previous Year Paper
Q40.The correct order of increasing basicity of the given conjugate bases (R = CH3) is –––––– (1) RCOO < HC = C < R < NH2 (2) R < HC ≡C < RCOO < NH2 ––––– (3) RCOO < NH2 < HC ≡C < R (4) RCOO < HC ≡C < NH2 < R
Q43.Copper wire test for halogens is known as (1) Duma's Test (2) Beilstein's Test (3) Liebig's Test (4) Lassigne's Test
Q45.Beilstein test is used for the estimation of which one of the following elements? (1) S (2) Cl (3) C and H (4) N