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Number of total car owners of TATA = 30 + 20 + 24 + 42 + 23 + 33 + 26 + 50 = 251 lakh

Now, 13% of 251 = 32.63 lakh

Those states which enjoy more than 34.45 Lacs car owners of TATA are Pune and Guwahati.

$x^2+y^2+{\left(x-1\right)}^2+y^2+x^2+{\left(y-1\right)}^2+{\left(x-1\right)}^2+{\left(y-1\right)}^2=18$

$\Rightarrow x^2+y^2-x-y-\frac{7}{2}=0$

$r^2=\frac{1}{4}+\frac{1}{4}+\frac{7}{2}=4$

(x + y) = 4xy

$\Rightarrow \frac{dy}{dx}=\frac{4xy+4y^2-1}{1-4x^2-4xy},$

$\frac{d^{2}y}{d{x}^2}=\frac{\left(1-4x^2-4xy\right)\left(4y+4xy\text{'}+8yy\text{'}\right)-\left(4xy+4y^2-1\right)\left(-8x-4y-4xy\text{'}\right)}{{\left(1-4x^2-4xy\right)}^2}$

In the UPTET exam 2025, each paper will contain 150 multiple-choice questions (MCQs). There is no negative marking in the UPTET exam.

$B\left(1+2\lambda ,3+\lambda ,4+2\lambda \right)$

x – 2y – z = 3 => $\lambda =-6\Rightarrow B\left(-11,-3,-8\right)$

$N\left(1+t,3-2t,4-t\right)$  

$x-2y-z=3\Rightarrow t=2\Rightarrow N\left(3,-1,2\right)$  

Line NB : $\frac{x-3}{7}=\frac{y+1}{1}=\frac{3-2}{5}$

$d^2=P{M}^2=\frac{{\left|P\overrightarrow{Q}\times \overrightarrow{R}\right|}^2}{{\left|\overrightarrow{R}\right|}^2}$

${\left|\overrightarrow{R}\right|}^2=75$

$d^2=\frac{1950}{75}=26$  

$LHS={\displaystyle \sum _{r=1}^{15}r\left(r!\right)}$

$=\sum \left(r+1-1\right)r!={\displaystyle \sum _{r=1}^{15}\left(r+1\right)!-r!}$

$=\left(2!-1!\right)+\left(3!-2!\right)+....+\left(16!-15!\right)$

$\begin{array}{l}=16!-1\\ {=}^{16}{P}_{16}-1\end{array}$

The UPTET exam will be conducted in an offline (pen-and-paper-based) test. Candidates will be given a physical question paper and an OMR sheet to mark their answers. Candidates are waiting for the notification. 

$E_{C{\mathcal{l}}_2/C{\mathcal{l}}^{-}}^0=+1.36V$

$E_{l_2/l^{-}}^0=+0.54V$

$E_{A{g}^{+}/Ag}^0=+0.80V$

$E_{N{a}^{+}/Na}^0=-2.71V$

$E_{L{i}^{+}/Li}^0=-3.05V$

$\therefore E_{C{\mathcal{l}}_2/C{\mathcal{l}}^{-}}^0>E_{A{g}^{+}/Ag}^0>E_{N{a}^{+}/Na}^0>E_{L{i}^{+}/Li}^0$

KJ Somaiya College of Arts and Commerce provides good placements to its graduating students. The students are given excellent placement support every year placing them in top companies. Check out the table below to know the key highlights of the KJ Somaiya College of Arts and Commerce placements 2024:

NOTE: The above data is obtained from the NIRF report 2025

Required area

$={\displaystyle \underset{-2}{\overset{4}{\int }}\left(\frac{3x}{2}+6-\frac{3x^2}{4}\right)dx=27}$

$\frac{3x^2}{4}=\frac{3x}{2}+6\Rightarrow x=-2,4$

Yes, we often use transferred epithets in our daily conversation, knowingly or unknowingly. Though transferred epithets are more commonly used in poems and literature, they have become a natural part of our spoken and written English as they help give an emotional appeal to our thoughts.

Phrases like “Sleepless night”, “lucky pen”, “nervous cup of tea”, “lonely road” are some common examples of transferred epithets used in daily conversation.

The institution has not released the course-wise placement packages as of yet. Meanwhile the NIRF report has been released. Check out the table below to know more:

NOTE: The above data is obtained from the NIRF report 2025

Yes, KJ Somaiya College of Arts and Commerce has an impressive placement record. The table below provides the placement data for the past three years as per the NIRF Report 2025:

NOTE: The above data is obtained from the NIRF report 2025

Transferred Epithet Examples:

• She walked through the silent corridor.
• They shared a hopeful coffee before the interview.
• She clutched the guilty ticket as she snuck into the theater.
• I spent the afternoon under a melancholy tree.
• He stared at the troubled mirror, unsure of what he saw.

Equation : 2x² – (6 + k)x + 4 + 3k = 0

D < 0 => 6  $-4\sqrt[]{2}<k<6+4\sqrt[]{2}$

Sum of integral values of K is 1+2+3+.+11 = 66

The institution has not released the overall average package. The median package offered at KJ Somaiya College of Arts and Commerce placement in the past years are tabulated below:

A transferred epithet is a figure of speech in which an adjective is shifted from the person it logically describes to an object or idea closely associated with them. It is a poetic device that cleverly gives a dramatic or poetic effect to the sentence.

Transferred Epithet Examples:

• “He clung to the hopeful letter, re-reading her words under a dim lamp.”
• “Let's go for a walk. This peaceful breeze is too good to miss.”
• “Wrap yourself in a lazy weekend with the cozy blankets.”
• “Say goodbye to tired skin with our refreshing face wash.”

The average package at KJ Somaiya College of Arts and Commerce Placement  has not been made available yet. However the median package has been released and is given in the table below:

NOTE: The above data is obtained from the NIRF report 2025

Side of square = a

Radius of circle = r

Given : 4a + 2pr = 36

S = a² + pr²

^{$=\left(\frac{{\pi }^2}{4}+\pi \right)r^2-9\pi r+81$}

^{$\frac{ds}{dr}=0\Rightarrow r=\frac{18}{\pi +4}$}