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Let B? be the event where Box-I is selected and B? →where box-II selected
P (B? )=P (B? )=1/2
Let E be the event where selected card is non prime.
For B? : Prime numbers: {2,3,5,7,11,13,17,19,23,29}
For B? : Prime numbers: {31,37,41,43,47}
P (E)=P (B? )×P (E/B? )+P (B? )P (E/B? )
= 1/2×20/30+1/2×15/20
Required probability:
P (B? /E) = (P (E/B? )P (B? )/P (E) = (1/2×20/30)/ (1/2×20/30+1/2×15/20) = (2/3)/ (2/3+3/4) = 8/17

Candidates seeking admission to the Ambalika Institute of Professional Studies must fulfil the college's eligibility criteria. The institute offers Diploma in Electrical Engineering, Diploma in Computer Science and Diploma in Mechanical Engineering Automobile courses. However, the institute also offers direct admission under Management Quota/ Vacant Seats after counselling of BTE (JEECUP).

With weak field ligands Mn (II) will be of high spin and with strong field ligands it will be of low spin.
Ni (II) tetrahedral complexes will be generally of high spin due to sp³ hybridisation. Mn (II) is of light pink color in aqueous solution.

Slope of tangent is 2, Tangent of hyperbola
x²/4-y²/2=1 at the point (x? , y? ) is xx? /4-yy? /2=1 (T=0)
Slope: x? /2y? =2 ⇒ x? =4y?
(x? , y? ) lies on hyperbola
⇒ x? ²/4-y? ²/2=1
From (1) and (2)
(4y? )²/4-y? ²/2=1 ⇒ 4y? ²-y? ²/2=1
⇒ 7y? ²=2 ⇒ y? ²=2/7
Now x? ²+5y? ² = (4y? )²+5y? ² = 21y? ² = 21×2/7=6

f? = 1/ (2l) √ (T? /µ)
f? = 1/ (2l) √ (T? /µ)
f? /f? = 450/300 = √ (T? /T? )
⇒ T? /T? = 9/4 = 2.25

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2x-y+2z=2
x-2y+λz=-4
x+λy+z=4
For no solution:
D=|2, -1,2; 1, -2, λ 1,1,1|=0
⇒ 2 (-2-λ²)+1 (1-λ)+2 (λ+2)=0
⇒ -2λ²+λ+1=0
⇒ λ=1, -1/2
D? =|2, -1,2; -4, -2, λ 4,1,1|
=2 (-2-λ)+1 (-4-4λ)+2 (-4+8)
=2 (1+λ) which is not equal to zero for λ=1, -1/2

On moving Left to Right along a period.
Atomic Radius → decreases.
Electronegativity → Increases.
Electron gain enthalpy → Increases.
Ionisation Enthalpy → Increases

No, once the IPU CET admit card is issued, the exam centre allotted cannot be changed. The centres are assigned based on the choices filled during the application process and the availability of seats at each centre. Candidates are expected to appear at the centre mentioned on their admit card, as requests for changes are generally not entertained under any circumstances.

Based on theory.

Let three terms of G.P. are a/r, a, ar product=27
⇒ a³=27 ⇒ a=3
S=3/r+3r+3
For r>0
(3/r+3r)/2 ≥ √9 = 3
⇒ 3/r+3r≥6
For r<0, 3/r+3r≤-6
From (1) and (2)
S∈ (-∞, -3]∪ [9, ∞)

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Energy Density = 1/2 B²/µ?
B = √ (2 × µ? × Energy density)
B = √ (2 × 4π × 10? × 1.02 × 10? ) = 160 × 10? = 160nT

f (x) = {ae? +be? , -1For continuity at x=1
Lim (x→1? )f (x) = Lim (x→1? )f (x)
⇒ ae+be? ¹=c ⇒ b=ce-ae²
For continuity at x=3
Lim (x→3? )f (x) = Lim (x→3? )f (x)
⇒ 9c=9a+6c ⇒ c=3a
f' (0)+f' (2)=e
(ae? -be? ) at x=0 + (2cx) at x=2 = e
⇒ a-b+4c=e
From (1), (2) and (3)
a-3ae+ae²+12a=e
⇒ a (e²+13-3e)=e
⇒ a=e/ (e²-3e+13)

The vapour pressure of solution will be less than vapour pressure of pure solvent, so some vapour molecules will get condensed to maintain new equilibrium.

The primary eligibility requirement for admission to the BSc course at Sabarmati University is that applicants must complete their Class 12 from a Science stream with decent scores. Moreover, for admissions to the BSc course, the university releases the merit list of shortlisted candidates after evaluating their Class 12 scores. 

There is no concise placements report for BPharm released by GJUST. However, as per the data available online, the average salary of BPharm graduates ranges from INR 2.6 LPA to INR 5.8 LPA. Some of the job profiles along with the salary packages are:

NOTE: The average salary has been taken from Ambitionbox.com.

Executive PGDM admission dates have not been revealed by PBS at this point of time. The admissions are decided through an admission interview conducted by PBS itself. It appears that candidates can apply for admissions at any point of time and the institute officials will call them for the admission interview at the appropriate time. For more information, candidates are advised to visit the official website.