📘 Mathematics
Q1.
Let f(x)=x³+x²f′(1)+2xf″(2)+f‴(3), x∈R. Then f′(5) is:
(1)117/5
(2)62/5
(3)65/5
(4)2/5
Correct Answer: (1)
Q2.
One end of a focal chord of y²=16x is (16,16). If P(α,β) divides it in ratio 5:2, minimum α+β is:
Correct Answer: (1)
Q3.
Largest n∈N for which 7ⁿ divides 10! is:
Correct Answer: (1)
Q4.
If area of region {(x,y):1−2x≤y≤4−x²,x≥0,y≥0} is α/β, gcd(α,β)=7. Find α+β.
Correct Answer: (2)
Q5.
Maximum of [(cos⁻¹x)²+(sin⁻¹x)²]=m²π²/n², x∈[−√3/2,1/√2]. Find m+n.
Correct Answer: (3)
Q6.
If α,β are roots of x²+2ax+(3a+10)=0 and α<1<β, possible values of a are:
(1)(−∞,−11/5)
(2)(−∞,−3)
(3)(−∞,−8)∪(5,∞)
(4)(−∞,−11/5)
Correct Answer: (4)
Q7.
∫₀¹ 4cot⁻¹(1−2x+4x²)dx = atan⁻¹(2) − b loge5. Find 2a+b.
Correct Answer: (3)
Q8.
Let A={2,3,4,5,9}. Relation R={(x,y):2x≤3y}. If m elements in R and n to be added to make symmetric, m+n is:
Correct Answer: (3)
📗 Physics
Q1.
Battery of emf e and internal resistance r gives maximum power when:
(1)R=r
(2)R=2r
(3)R=√2r
(4)R=r/2
Correct Answer: (1)
Q2.
Sum of 52.01 m, 153.2 m and 0.123 m (significant figures) is:
(1)205.3
(2)205
(3)205.333
(4)205.33
Correct Answer: (1)
Q3.
Energy of electron in orbit is −0.04E. If L angular momentum, then 2πL/h is:
Correct Answer: (1)
Q4.
A diatomic gas (γ=1.4) does 100J work in isobaric expansion. Heat given is:
(1)350J
(2)100J
(3)250J
(4)150J
Correct Answer: (1)
Q5.
Mass 2kg, x=αt²+βt+γ. Work done from t=2s to 3s is:
Correct Answer: (3)
Q6.
De-Broglie wavelength of particle with m=6×10⁻²⁷kg, q=3×10⁻¹⁹C, V=1.21V is:
(1)10⁻¹¹m
(2)10⁻¹⁰m
(3)10⁻⁹m
(4)10⁻¹²m
Correct Answer: (1)
Q7.
Two spheres of equal mass and charge approach. Minimum speed to touch is:
(1)q²/16πϵ₀mR
(2)q²/8πϵ₀mR
(3)q²/4πϵ₀mR
(4)q²/πϵ₀mR
Correct Answer: (1)
Q8.
Terminal velocity of ball radius 6mm is 20cm/s. For 3mm it is:
(1)2cm/s
(2)5m/s
(3)4m/s
(4)5cm/s
Correct Answer: (4)
📙 Chemistry
Q1.
1g organic compound gives 1.49g Mg₂P₂O₇. % of P is:
(1)41.6
(2)38.2
(3)35.4
(4)29.8
Correct Answer: (1)
Q2.
Correct nucleophilicity order: CH₃COO⁻, PhO⁻, OH⁻, ClO₄⁻
(1)3>2>1>4
(2)2>3>1>4
(3)1>2>3>4
(4)4>3>2>1
Correct Answer: (1)
Q3.
Mn₂O₇ related correct statements are:
(1)A,B,C
(2)A,B,C,D
(3)B,C,D
(4)A,C,D
Correct Answer: (3)
Q4.
Which is optically active?
(1)n-propyl chloride
(2)iso-propyl chloride
(3)iso-butyl chloride
(4)sec-butyl chloride
Correct Answer: (4)
Q5.
When 8.74g MnO₂ reacts with HCl, Cl₂ formed is:
(1)7.1g
(2)17.1g
(3)14.2g
(4)3.55g
Correct Answer: (1)
Q6.
Central atom oxidation state in compound formed when K₂Cr₂O₇ reacts with H₂O₂:
Correct Answer: (4)
Q7.
Correct bond length order C–H, C–O, C=O, C≡N is:
(1)C–H>C–O>C=O>C≡N
(2)C–O>C=O>C≡N>C–H
(3)C–H>C–O>C≡N>C=O
(4)C≡N>C–O>C–H>C=O
Correct Answer: (2)
Q8.
Correct order of SN2 reactivity:
(1)D>C>B>A
(2)A>B>D>C
(3)A>B>C>D
(4)D>A>C>B
Correct Answer: (2)