11th
In this category students supposed to ask questions which belong to std 11th maharashtra board Science
- The centre and radius of the circle \(x^2+y^2-6x+8y=0\) are Answer: B. (3,-4) and 5 Centre (-g,-f)=(3,-4) , r=√(9+16)=5 . 1
- The eccentricity of the hyperbola \(\frac{x^2}{16}-\frac{y^2}{9}=1\) is Answer: D. 5/4 e=√(1+b²/a²)=sqrt1+frac916=5/4 . 1
- The length of the latus rectum of the ellipse \(\frac{x^2}{25}+\frac{y^2}{16}=1\) is Answer: A. 32/5 2b²/a=2×16/5=32/5 . 1
- The distance between the parallel lines \(3x+4y=5\) and \(6x+8y=25\) is Answer: B. 3/2 Write the second as 3x+4y=12.5 : d=|12.5-5|/5=1.5 . 1
- The value of \(\cos15^\circ-\sin15^\circ\) is Answer: A. 1/sqrt2 cos15^°-sin15^°=sqrt2cos(15^°+45^°)=sqrt2·1/2=frac1sqrt2 . 1
- The value of \((1+i)^8\) is Answer: C. 16 (1+i)²=2i⇒(1+i)⁸=(2i)⁴=16 . 1
- If \(\omega\) is a complex cube root of unity, then \((1+\omega-\omega^2)^3=\) Answer: D. −8 1+ω=-ω²⇒(-2ω²)³=-8ω⁶=-8 . 1
- \(\lim_{x\to0}\frac{1-\cos4x}{x^2}=\) Answer: B. 8 1-cos4x=2sin²2x ; lim2sin²2x/x²=2·4=8 . 1
- The number of distinct arrangements of the letters of the word BANANA is Answer: C. 60 6!/3! 2!=60 (A repeated 3 times, N twice). 1
- A committee of 5 is to be formed from 6 men and 4 women. The number of ways in which it contains at least 3 women is Answer: B. 66 binom43binom62+binom44binom61=60+6=66 . 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
- 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
- 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
- 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 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
- A wire of resistance R is stretched uniformly until its length is doubled. Its new resistance is Answer: C. 4R Volume constant: A→ A/2 . R=ρl/A→ρ2l/A/2=4R . 1
- A parallel plate capacitor has capacitance \(C\) with air between the plates. A dielectric slab of dielectric constant 4 and thickness equal to half the plate separation is inserted between the plates. The new capacitance is Answer: B. 1.6 C C'=ε₀A/d-t+t/K=ε₀A/d/2+d/8=8/5·ε₀A/d=1.6C . 1
- The energy stored in a 10 μF capacitor charged to 100 V is Answer: A. 0.05 J U=1/2CV²=1/2×10⁻⁵×10⁴=0.05 J. 1
- Capacitors of 3 μF and 6 μF are connected in series across a 90 V supply. The potential difference across the 3 μF capacitor is Answer: A. 60 V C_s=2 μF, Q=180 μC, V₃=180/3=60 V. 1