Q84.If limx→1 (5x+1)1/3−(x+5)1/3 = m√5 , where gcd(m, n) = 1, then 8 m + 12n is equal to______ (2x+3)1/2−(x+4)1/2 n(2n)2/3
What This Question Tests
This question requires evaluating a limit of an indeterminate form (0/0) by applying L'Hopital's Rule or by rationalization techniques involving fractional powers, followed by algebraic simplification to find the values of m and n.
Concepts Tested
Formulas Used
lim (f(x)/g(x)) = lim (f'(x)/g'(x)) if 0/0 form
d/dx(u^n) = n u^(n-1) du/dx
📚 NCERT Sections This Tests
13.5 — The Q Value Of A Nuclear Reaction A + B ® C + D Is Defined By
Physics Class 12 · Chapter 13
13.5 The Q value of a nuclear reaction A + b ® C + d is defined by Q = [ mA + mb – mC – md]c2 where the masses refer to the respective nuclei. Determine from the given data the Q-value of the following reactions and state whether the reactions are exothermic or endothermic. (i) 11 H+13 H →12 H+12 H (ii) 126 C+126 C →1020 Ne+ 24 He Atomic masses are given to be m ( 12 H ) = 2.014102 u m ( 13 H) = 3.016049 u m ( 126 C ) = 12.000000 u m ( 1020 Ne ) = 19.992439 u
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Limits & Continuity
- Topic
- Evaluation of limits using L'Hopital's Rule
- Year
- 2024
- Shift
- 04 Apr Shift 1
- Q Number
- Q84
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 5: Continuity and Differentiability
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