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Direction ratio of line (1, -1, -6)
Equation of line (x−3)/1 = (y+4)/-1 = (z+5)/-6 =k
x=k+3, y=−k−4, z=−6k−5
Solving with plane k=−2
⇒x=1, y=−2, z=7
⇒Distance=√ (3−1)²+6²+3²=√49=7

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• Airline tickets
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• Academic history
• University transcripts

N=2¹? 5¹? 11¹¹ 13¹¹
5→4n+1 type→number of choice=11
11→4n+3 type→number of choice=6
13→4n+1 type→number of choice=12
. Number of divisor of 4n+1 type=11×6×12=792

Z = (3+2icosθ)/ (1-3icosθ) = (3−6cos²θ)+i (11cosθ) / (1+9cos²θ)
Real part = 0
⇒3−6cos²θ=0
⇒θ=45?
⇒sin²3θ+cos²θ=1/2+1/2=1

e? +e³? −4e²? −e? +1=0
Divide by e²?
⇒ (e²? +e? ²? )− (e? +e? )−4=0
Put e? +e? =t>0
e²? +e? ²? +2=t²
t²−2−t−4=0
⇒t²−t−6=0
⇒t=3, t=−2 but t≠−2
⇒t=3
⇒e? +e? =3
Number of solution=2

$\overrightarrow{A}\times \overrightarrow{A}=AAsin\theta \widehat{n}$

$=AAsin0°\widehat{n}$

= 0 [since Angle between the vectors are zero degree]

$\overrightarrow{A}\times \overrightarrow{A}=0$

f' (x)=g (x)
f" (x)=g' (x)
⇒g (x).g' (x)=f' (x).f" (x)
f (x) has five roots
⇒f' (x) has atleast 4 roots.
And f" (x) has atleast of 3 roots
⇒g (x).g' (x)=0 has atleast 7 roots in (a, b)

General form Σ? ? C? (1/2)? < 1/2
Σ? ? C? < 2?
⇒? C? +? C? +.? C? < 128
⇒256− (? C? +? C? +.? C? ) < 128
⇒? C? +? C? +.? C? > 128
n≥5

Future tense follows a simple rule: Subject + will/ shall + base form of the verb. For example, take a look at the following sentences:

• I will eat dinner at 11 PM.
• He will visit his grandma next week.

p: there exist M>0
Such that x≥M for all x∈S
Obviously ~p: M>0 such that x. Negation of 'there exists' is 'for all'.

The BTech scholarships at IIT Guwahati have different eligibility criteria. Some of them are merit based scholarships where, the candidates are offered BTech scholarships due totheir high score in either the JEE Advanced exam or their last qualifying exam. Candidates who belong to the SC/ST groups are also awarded scholarships if they can prove that they belong tosuch categories.

In English grammar, there are mainly four types of future tense. Have a look at the types of future tenses:

• Simple Future Tense
• Future Continuous Tense
• Future Perfect Tense
• Future Perfect Continuous Tense

Any point on line (1)
x=α+k
y=1+2k
z=1+3k
Any point on line (2)
x=4+Kβ
y=6+3K
Z=7+3K?
⇒1+2k=6+3K, as the intersect
∴1+3k=7+3K?
⇒K=1, K? =−1
x=α+1; x=4−β
⇒y=3; y=3
z=4; z=4
Equation of plane
x+2y−z=8
⇒α+1+6−4=8 . (i)
and 4−β+6−4=8 . (ii)
Adding (i) and (ii)
α+5−β+12−8=16
α−β+17=24
⇒α−β=7

Lt? →? x/ (1−sinx)¹/? − (1+sinx)¹/? )
= 2x/ (1−sinx)¹/? − (1+sinx)¹/? ) Multiply by conjugate
= 4x/ (1−sinx)¹/²− (1+sinx)¹/²) Multiply by conjugate
= 8x/ (1−sinx−1−sinx) Multiply by conjugate
= 4x/sinx = −4

Yes, SRM Valliammai Engineering College, Chengalpattu also provides management-oriented concessions. These include reimbursement of tuition fees for economically backward students, staff wards, and victims of natural calamities. Such schemes provide financial assistance in addition to the scholarships offered by the government.

The college offers BPharma and DPharma courses. The selection criteria are a mix of entrance exams and merit-based as per the respective courses. The mode of GNIT College of Pharmacy course admissions is online. Admission to various courses is based on merit and entrance exam scores. The accepted entrance exam is JEECUP.

Yes, SRM Valliammai Engineering College, Chengalpattu offers scholarships under government schemes. BC, MBC, SC, ST, and minority students eligible as per annual income criteria can apply. First graduate fee concession and merit-based central sector scholarships are the benefits.

In English grammar, the future tense is a verb form that is used to denote actions take will take place after the present time. It offers clarity on what is planned, assumed, or predicted to occur in the future.

Examples of future tense:

• He will go to the Church on Sunday.
• Shea will remove her makeup after she is done with the next act.
• I will eat ice cream for dessert.