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  $\left|\overline{a}\times \left(\overline{a}\times \overline{c}\right)\right|=\left|3\overline{b}\right|=3\left|\overline{b}\right|$

$\Rightarrow 3=3.2sin\theta \Rightarrow sin\theta =\frac{1}{2}\Rightarrow co{s}^2\theta =\frac{3}{4}$  

While filling the GATE application form 2026, candidates have to enter their personal, communication, educational qualification, and documents (photo, signature and ID proof). Reserved category had to submit their caste certificate and PwD applicants had to submit their disability certificate.

$\underset{x\to 0}{lim}{\left[si{n}^2\left(\frac{\pi }{2-3x}\right)\right]}^{se{c}^2\left(\frac{\pi }{2-5x}\right)}$

$e^{\underset{x\to 0}{lim}\left[si{n}^2\left(\frac{\pi }{2-3x}\right)-1\right]se{c}^2\left(\frac{\pi }{2-5x}\right)}$

$=e^{\underset{x\to 0}{lim}\frac{-si{n}^2\left(\frac{-3\pi x}{2\left(2-3x\right)}\right)}{si{n}^2\left(\frac{-5\pi x}{2\left(2-5x\right)}\right)}}=e^{-\frac{9}{25}}$

Any point on x + y = 1 can be taken as (t, 1 – t) The equation of chord with this as mid-point is y (1 – t) -2a (x + t) = (1 – t)² – 4at

It passes through (a, 2a)

So, t² – 2t + 2a² – 2a + 1 = 0

This should have two distinct real roots.

So D > 0

$\begin{array}{l}\Rightarrow a^2-a<0\\ \Rightarrow 0<a<1\end{array}$          

So, length of latus rectum < 4 and 0 < a < 1

$\Rightarrow LR=1,2,3$            

Candidates have to go through the following points to appear for the OUAT entrance exam.

• Check and confirm the fulfilment of the eligibility criteria
• Complete the registration process
• Submit the application fee after registration
• Select the nearest exam centre
• Upload all the required documents
• Download the Admit Card
• Submit the application form after filling all the details
• Download the admit card to appear for the OUAT exam.

The OUAT entrance exam will be conducted in computer-based mode for two hours. The exam centres will be located in Odisha and New Delhi.

The eligible GATE paper codes (for two paper combinations) in GATE computer Science and engineering are -

• Data Science and Artificial Intelligence (DA)
• Electronics and Communication (EC)
• Geomatics Engineering (GE)
• Mathematics (MA)
• Physics (PH) and 
• Statistics (ST)

Candidates must be careful with the GATE paper codes while filling out the application form. 

$v=\frac{fu}{u-f}=\frac{(-10)(-15)}{-15+10}\mathrm{c}\mathrm{m}=-30\mathrm{c}\mathrm{m}$

$v_{\text{image}}=\frac{dv}{dt}=-{\left(\frac{v}{u}\right)}^2\frac{du}{dt}=-{\left(\frac{-30}{-15}\right)}^2\left(10\right)\mathrm{c}\mathrm{m}{\mathrm{s}}^{-1}=-40\mathrm{c}\mathrm{m}{\mathrm{s}}^{-1}$

$V_{\text{object}}=\frac{du}{dt}=+10\mathrm{c}\mathrm{m}{\mathrm{s}}^{-1}$

Relative velocity $=v_{\text{object}}-v_{\text{image}}$

$=10-(-40)=50\mathrm{c}\mathrm{m}{\mathrm{s}}^{-1}$

For UG admission, Humboldt University of Berlin does not require submission of ACT or SAT marks are necessity. You have to provide a German University Entrance Qualification which can be obtained through the German Abitur or equivalent qualification.

But the university also looks into other factors for admissions like -

• Strong academic background
• English language proficiency requirements
• LORs
• Personal essays 
• Extracurricular activities 

Key point: Fehling solution do not oxidise aromatic aldehydes, except when EWG present 
at O/P position So (I), (III), (IV) not show this test

You can use the position vector to find the real displacement of a point from a reference point.

No need to get disheartened. If by chance you couldn't crack the NIMCET, you can apply for other MCA programs from other private colleges, or take up other MCA entrance exams, or even prepare well to retake the NIMCET the next year. Good thing is that there is no limit on the number of attempts for NIMCET. Additionally, there is no age limit as well.

The Graduate Aptitude Test in Engineering is conducted once a year, and the admission process will be held in the following way -

• First, the candidate has to qualify GATE paper
• Then opt for either COAP/CCMT counselling
• Select colleges based on their GATE scores
• Accept seat and report to the allotted college to confirm admission

GATE- qualified students can also apply for PSU recruitment. 

According to VSEPR theory:
For the species which contain
Has square pyramidal shape

These are BrF? , ClF? , XeOF?

Two vectors which are parallel to each other, irrespective of direction, are called parallel vectors.

Types are given below

• Collinear vectors
• Parallel vectors
• Antiparallel vectors

Out of numbers $\frac{1}{2},\frac{2}{4},\frac{3}{6},\frac{1}{3},\frac{2}{6},\frac{2}{3},\frac{4}{6}$ will result only 3 distinct rational numbers.

Total numbers =   

Total number of electron in Ti = 22
Total number of electron in Ti? = 22 – 4 = 18 So EAN value of Ti = 18 + 12 + 4 = 34

Factual
⇒ leaching methods is used for those metal in which metal is more soluble than impurities and these are Al, Au, Ag, low grade Cu

For GATE registration help, contact the organizing institute IIT Roorkee helpline: 01332-284531 (Mon–Fri, 9:30 AM–5:30 PM).