Ask & Answer: India's Largest Education Community

We have, f (x) = sin x + cos x.

f (x) = cos x - sin x.

At f (x) = 0

cosx - sin x = 0

sinx = cos x

$\Rightarrow \frac{sinx}{cosx}=1.$

$\Rightarrow tanx=1=tan\frac{\pi }{4}$

$\Rightarrow x=\frac{\pi }{4}orx=n\pi +\frac{\pi }{4}.$

At $x=\frac{\pi }{4}+n\pi$ ,

$f\left(n\pi +\frac{\pi }{4}\right)=sin\left(n\pi +\frac{\pi }{4}\right)+cos\left(nx+\frac{\pi }{4}\right).$

$={(-1)}^{x}sin\frac{\pi }{4}+{(-1)}^{n}sin\frac{\pi }{4}.$

The mode of application is online and offline for PGDM course at Taxila Business School. Candidates need to pay an application fee of INR 1,200 to apply for PGDM admission. Check below the steps to apply for TBS Jaipur MBA admission:

Step 1: Visit the official website.

Step 2: Register with the basic details to generate login credentials.

Step 3: Login to fill out the application form.

Step 4: Upload the documents and pay the application fee.

Step 5: Submit the application form. 

Yes, Srusti Academy of Management and Technology has released its placement report. Refer to the table below to know more about the placement highlights given below:

We have, f(x) = sin 2x, x ∈ [0, 2π],

f(x) = 2cos 2x.

At f(x) = 0.

2 cos 2x = 0

cos 2x = 0

$\Rightarrow 2x=(2x+1)\frac{\pi }{2},x=0,1,2,3.$

$\Rightarrow x=(2x+1)\frac{\pi }{4}.$

$x=\frac{\pi }{4},\frac{3\pi }{4},\frac{5\pi }{4},\frac{7\pi }{4},\in \left[0,2\pi \right]$

$\therefore f\left(\frac{\pi }{4}\right)=sin\frac{2\pi }{4}=sin\frac{\pi }{2}=1$ .

$f\left(\frac{3\pi }{4}\right)=sin2\left(\frac{3\pi }{4}\right)=$ $sin\frac{3\pi }{2}$ $f\left(\frac{7\pi }{4}\right)$

$=sin\left(\pi +\frac{\pi }{2}\right)=$ $=sin2\times \frac{7\pi }{4}$

$=-sin\frac{\pi }{2}$ $=sin\frac{7\pi }{2}$

= 1. $=sin3\pi +\frac{\pi }{2}$

$f\left(\frac{5\pi }{4}\right)=sin2\times \left(\frac{5\pi }{4}\right)=sin\frac{5\pi }{2}=sin\left(2x+\frac{\pi }{4}\right)$ $=-sin\frac{\pi }{2}$

$=sin\frac{\pi }{4}=1$ = 1.

f(0) = sin 2(0) = sin 0 = 0

f(2π) = sin 2(2π) = sin 4π = 0

Hence, the points of maximum $xf\mathrm{x\; are.}$

$(\frac{\pi }{4},2)and\left(\frac{5\pi }{4},1\right).$

A total of 201 students were placed on campus at Srusti Academy of Management and Technology in 2025. Out of these 141 were from MBA and 60 belonged to MCA program.  Refer to the table below to know more:

SCMS School of Architecture offers BArch programme at the UG level. Students can pursue the programme after meeting the following eligibility criteria:

Pass in Class 12 or equivalent examination with Physics and Mathematics as compulsory subjects along with either Chemistry or Biology or Technical Vocational subject or Computer Science or Information Technology or Informatics Practices or Engineering Graphics or Business Studies with minimum 45% marks in aggregate.

We have, f (x) = 3x⁴- 8x³ + 12x²- 48x + 25, x ∈  [0, 3].

f (x) = 12x³- 24x² + 24x - 48.

At f (x) = 0.

12x³- 24x² + 24x - 48 = 0.

x³- 2x² + 2x - 4 = 0

x² (x - 2) + 2 (x - 2) = 0

(x - 2) + (x² + 2) = 0

x = 2 ∈ [0, 3] or x = $\pm \surd -2$ which is not possible as

∴f (x) = 3 (2)⁴- 8 (2)³ + 12 (2)²- 4 (2) + 25.

=48 - 64 + 48 - 96 + 25.

= -39.

f (0) =3 (0)⁴- 8 (0)³ + 12 (0)²- 48 (0) + 25.

= 25.

f (3) = 3 (3)⁴- 8 (3)³ + 12 (3)²- 48 (3) + 25.

= 243 - 216 + 108 - 144 + 25

= 16.

Maximum value of f (x) = 25 at x = 0.

and minimum value of f (x) = -39 at x = 2.

The placement package recorded at Srusti Academy of Management and Technology placements 2025 is given in the table below:

This is a  Short Answers Type Questions as classified in NCERT Exemplar

Ozone is found to be thermodynamically unstable and undergoes decomposition into molecular oxygen and a dynamic equilibrium exists between the production and decomposition of ozone. The reactions involved can be shown as- 

O₂ (g)  O (g) + O (g)

O (g) + O₂ (g) +M O₃ (g) + M

We have, p (x) = 41 -f2x - 18x².

P (x) = - 72 - 36x

P (x) = -36

At extreme point,

- 72 - 36x = 0

$\Rightarrow$ $x=\frac{-72}{36}=-2$ .

At x = - 2, p" (x) = - 36 < 0.

∴x = -2 is a point of local maximum and the value of local

Maximum is given by P (2) = 41 - 72 (- 2) - 18 (- 2)²

41 + 144 - 72 = 113 units.

To get admission to BArch at  SCMS School of Architecture, candidates must go through two levels of the selection process. First, fulfilling the basic educational requirements and second, qualifying the NATA entrance exam. Find below the detailed admission criteria for SCMS School of Architecture BArch admission:

Srusti Academy of Management and Technology provides great placements to its students. Check out the table below to know about the Srusti Academy of Management and Technology placement statistics 2025:

(i) We have, f (x) = e^x

$\Rightarrow$ f (x) = e^x.

$\Rightarrow f^{\prime }(x)=e^{x.}$

At, extreme points,

f (x) = 0

$\Rightarrow$ e^x = 0 which has no real ‘a’ value

∴f (x) has with maximum or minima

(ii) g (x) = log x

A (ii)

We have, g (x) = log x,

$\Rightarrow$ g (x) = $\frac{1}{x}$

At extreme points,

g (x) = 0

$\to \frac{1}{x}=0.$

$\Rightarrow$ 1 = 0 which is not true.

∴g (x) was value minima or maxima

(iii) h (x) = x³ + x² + x + 1.

A (iii)

We have, h (x) = x³ + x² + x + 1.

h (x) = 3x² + 2x + 1

At extreme points,

h (x) = 0

$\Rightarrow$ 3x² + 2x + 1 = 0

Uttarakhand University recognises different state and central boards like CBSE, ICSE, BIEAP etc. for its BSc course. Candidates looking to get admission into the BSc programme at Uttarakhand Open University should enrol for either a state or central board of education available in their state and apply for admissions.

Candidates who have a state or centrally recognised board can easily get admission into Uttarakhand Open University provided they meet the eligibility criteria for BSc at the university. The eligibility criteria for BSc is a passing grade in Class 12 exam.

The placement rate for Srusti Academy of Management and Technology stood at 80.9% in 2025. Check out the table below to know more: