All questions
- Nylon-6,6 is obtained by condensation polymerisation of Answer: D. hexamethylenediamine and adipic acid n H₂N(CH₂)₆NH₂+n HOOC(CH₂)₄COOH→ Nylon-6,6 + 2n H₂O . 1
- Which of the following reactions has 100% atom economy? Answer: B. CH2=CH2 + H2 → C2H6 In an addition reaction all reactant atoms end up in the product, so the atom economy is 100%. 1
- The number of molecules in 4.4 g of CO2 is Answer: A. 6.022×10²² n=4.4/44=0.1 mol ⇒0.1×6.022×10²³ molecules. 1
- A compound contains 40% C, 6.67% H and 53.3% O by mass. Its empirical formula is Answer: D. CH2O Mole ratio C : H : O =40/12:6.67/1:53.3/16=3.33:6.67:3.33=1:2:1 . 1
- The number of radial nodes in a 3p orbital is Answer: B. 1 Radial nodes =n-l-1=3-1-1=1 . 1
- The maximum number of electrons in an atom that can have \(n=3\) and \(m_s=+\frac12\) is Answer: B. 9 The n=3 shell has n²=9 orbitals, and each holds one electron with m_s=+1/2 . 1
- The bond order of the superoxide ion O2− is Answer: D. 1.5 O₂⁻ has 17 electrons: bonding 10, antibonding 7. Bond order =10-7/2=1.5 . 1
- The shape of the ClF3 molecule is Answer: B. T-shaped Cl has 3 bond pairs and 2 lone pairs (sp³d). The lone pairs occupy equatorial positions, giving a T-shape. 1
- The oxidation number of oxygen in OF2 is Answer: A. +2 F is always −1: x+2(-1)=0⇒ x=+2 . 1
- Under identical conditions, the ratio of the rates of effusion of H2 and O2 is Answer: B. 4 : 1 Graham's law: fracr_(H_2)r_(O_2)=√(32/2)=4 . 1
- Ozonolysis of but-2-ene followed by treatment with Zn/H2O gives Answer: A. two molecules of ethanal CH₃CH=CHCH₃ is cleaved at the C=C bond to give 2 CH₃CHO. 1
- The numbers of σ and π bonds in acrylonitrile (CH2=CH–C≡N) are Answer: C. 6 σ and 3 π σ: 3 C–H + 1 (C=C) + 1 (C–C) + 1 (C≡N) = 6. π: 1 (C=C) + 2 (C≡N) = 3. 1
- The negation of \(p\rightarrow q\) is Answer: B. pwedgesim q p→ qequivsim pvee q ; its negation is pwedgesim q . 1
- Which of the following statements is a tautology? Answer: A. (pwedge q)→ p If pwedge q is true then p is true, so the implication is always true. The others fail for (T,F), (F,T) and always,... 1
- If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) satisfies \(A^2-5A-2I=O\), then \(A^{-1}\) equals Answer: A. 1/2(A-5I) A(A-5I)=2I⇒ A⁻¹=1/2(A-5I) . 1
- If \(A\) is a square matrix of order 3 with \(|A|=4\), then \(|\operatorname{adj}(2A)|\) is Answer: B. 1024 |2A|=2³·4=32 ; |adjB|=|B|² for order 3, so 32²=1024 . 1
- The system \(x+y+z=1,\ x+2y+3z=2,\ x+3y+kz=3\) has infinitely many solutions when \(k=\) Answer: B. 5 Δ=k-5=0⇒ k=5 . Then E₂-E₁ and E₃-E₂ both give y+2z=1 , so the system is consistent. 1
- The general solution of \(2\cos^2\theta+3\sin\theta=0\) is Answer: D. θ=nπ+(-1)ⁿ(-π/6),\ ninmathbb Z 2-2sin²θ+3sinθ=0⇒(2sinθ+1)(sinθ-2)=0⇒sinθ=-1/2 . 1
- The value of \(\tan^{-1}2+\tan^{-1}3\) is Answer: D. 3π/4 Since 2·3>1 and both are positive, the sum =π+tan⁻¹2+3/1-6=π-fracπ4=3π/4 . 1
- In \(\triangle ABC\), \(a=3,\ b=5,\ c=7\). Then angle \(C\) is Answer: A. 2π/3 cos C=9+25-49/2·3·5=-1/2⇒ C=2π/3 . 1
- The acute angle between the lines represented by \(x^2-4xy+y^2=0\) is Answer: B. 60° tanθ=|2√(h²-ab)/a+b|=2√(4-1)/2=sqrt3⇒θ=60^° . 1
- If the lines represented by \(kx^2+6xy-7y^2=0\) are perpendicular, then \(k=\) Answer: A. 7 Perpendicular when a+b=0 : k-7=0⇒ k=7 . 1
- The joint equation of the lines through the origin perpendicular to the lines \(x^2-5xy+4y^2=0\) is Answer: A. 4x²+5xy+y²=0 Given lines (x-y)(x-4y)=0 have slopes 1,1/4 . Perpendicular slopes -1,-4 : (x+y)(4x+y)=0 . 1
- The area of the parallelogram whose diagonals are \(3\hat i+\hat j-2\hat k\) and \(\hat i-3\hat j+4\hat k\) is Answer: B. 5sqrt3 vec d₁×vec d₂=-2hat i-14hat j-10hat k , magnitude √(300)=10sqrt3 . Area =1/2|vec d₁×vec d₂|=5sqrt3 . 1