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This is a  Assertion Type Questions as classified in NCERT Exemplar

Option (ii)

 i.e., Both A and R are correct, but R is not the correct explanation of A is the answer the pH of rainwater is 5.6 because of the presence of hydronium ions produced due to the dissolution of carbon dioxide in rainwater from atmosphere and when the pH of rainwater drops from 5.6, it is being referred as acid rain. This can be shown as-

H₂O (l)+CO₂ (g)→H₂CO₃ (aq)

H₂CO₃ (aq)→H+ (aq)+HCO₃⁻ (aq)

The tuition fee for the BTech programmes at Shri Vishwakarma Skill University ranges from INR 1.8 Lacs to INR 2.7 lakh. Apart from the tuition fee, the total course fee includes various fee components, such as the hostel fee, admission fee, security charges, etc. Check out the following bifurcation of the SVSU BTech fee:

NOTE: The aforementioned fee is taken from the official website/sanctioning body. It is still subject to change and, hence, is indicative.

Let ‘x’ and ‘y’ be the two number

Then, x + y = 24 $\Rightarrow$ y = 24 - x

Let ‘P’ be their product then,

P = xy = x (24 - x) = 24x -x²

P (x) = 24x -x²

$\Rightarrow \frac{dp}{dx}=24-2x.$

$\Rightarrow \frac{d^{2}p}{d{x}^2}=-2.$

At $\frac{dp}{dx}=0$

24 - 2x = 0

$\Rightarrow x=\frac{24}{2}=12.$

So, P (12) $\frac{d^{2}p}{d{x}^2}=-2<0.$

x = 12 is a point of local maxima

Hence, y = 24 - 12 = 12.

The uqdtwno (x, y) is (12, 12).

Yes, candidates with an 80th percentile score on the CAT exam might be able to get admissions to the MBA course at Taxila Business School. However, it is not definite because the cutoff released by the institution of shortlisted candidates does not rely only on the secured entrance exam. The cutoffs are released after evaluating and calculating several parameters for the MBA course. One component is sure that candidates who have secured 80% in CAT will get 18 % weightage out of 20% weightage in the parameters of the qualifying test score. Check out the scaling of qualifying test weightage in the below table: 

Various companies visit Srusti Academy of Management and Technology for placements some of them are given below:

Shri Guru Ram Rai University BSc eligibility criteria differ from course to course. Interested students can check the below space to know the course-wise eligibility criteria for a few BSc courses:

• Nursing: Passed Class 12 with 45% aggregate marks in PCB and English. Moreover, the candidate must have attained 17 years of age.
• Biotechnology/PCM/PMD/PMG/PMS/ZBG/CBZ: Completed Class 12 PCM/PCB and a minimum of 45% marks
• Agriculture: Class 12 with Biology/Agriculture/Horticulture/Mathematics having a minimum of 45% marks in aggregate

This is a  Assertion Type Questions as classified in NCERT Exemplar

Option (iii)

i.e., Both A and R are not correct is the answer since in cold places, sunlight required to grow plants is less. Due to which plants are kept in a glass house so that sunlight enters in the greenhouse to heat up the soil and plants. The warm soil and plants emit infrared radiations which are partially absorbed and partially reflected by the glass. 

The average package for Srusti Academy of Management and Technology stood at INR 5.15 LPA. Check the below table to know more about the average package at Srusti Academy of Management and Technology:

We have, f(x) = x + sin 2x ,x ∈ [0, 2π].

f(x) = 1 + 2cos 2x

At f(x) = 0

1 + 2 cos2x = 0

$\Rightarrow cos2x=-\frac{1}{2}=-cos\frac{\pi }{3}=cos\pi -\frac{\pi }{3}=cos\frac{2\pi }{3}$

$\therefore 2x=2n\pi \pm \frac{2\pi }{3},n=1,2,3.$

$\Rightarrow x=n\pi \pm \frac{2\pi }{3}$

$n=0,x=\pm \frac{\pi }{3}\to x=\frac{\pi }{3}\in \left[0,2\pi \right].$

$n=1,x=\pi \pm \frac{\pi }{3}\to x=\pi +\frac{\pi }{3}and\pi -\frac{\pi }{3}$

$=\frac{4\pi }{3}ad\frac{2\pi }{3}\in [0,2\pi ]$

$n=2,x=2\pi \pm \frac{\pi }{3}\to x=2\pi +\frac{\pi }{3}ad2\pi -\frac{\pi }{3}.$

$\Rightarrow x=\frac{51}{3}\in [0,2\pi ].$

Hence, $x=\frac{\pi }{3},\frac{2\pi }{3},\frac{4\pi }{3}and\frac{5\pi }{3}$

Missing

At $x=\frac{\pi }{3},f\left(\frac{\pi }{3}\right)=\frac{\pi }{3}+sin\frac{2\pi }{3}=1.05+$ $sin\left(\pi -\frac{\pi }{3}\right)=1.05+sin\frac{\pi }{3}$

$=1.05+\surd 3/2$

= 1.05 + 0.87

= 1.92

At $x=\frac{2\pi }{3},f\left(\frac{2\pi }{3}\right)=\frac{2\pi }{3}+sin2\times \frac{2\pi }{3}$ $=2.10+sin\left(\pi +\frac{\pi }{3}\right)$

$=2.10-sin\frac{\pi }{3}=2,10-0.87$

= 1.23

At $x=\frac{4\pi }{3},f\left(\frac{4\pi }{3}\right)=\frac{4\pi }{3}+sin2\times \frac{4\pi }{3}=4\cdot 2+sin\left(3x-\frac{\pi }{3}\right)$

$=4.2+sin\frac{\pi }{3}=4.2+0.87.$

=5.07.

At $x=\frac{5\pi }{3},f\left(\frac{5\pi }{3}\right)=\frac{5\pi }{3}+sin2\times \frac{5\pi }{3}=5.25+sin\left(3x+\frac{\pi }{3}\right)$

$=5\cdot 25-sin\frac{1}{3}$

= 5.25 - 0.87 = 4.38

At and points,

f(0) = 0 + sin2 × 0 = 0

f(2π) = 2π + sin 2 × 2π = 6.2 + 0 = 6.28

∴Maximum value of f(x) = 6.28 at x = 2π and

minimum value of f(x) = 0 at x= 0

We have, f (x) = x⁴- 62x² + ax + 9, x∈  [0, 2].

$\Rightarrow$ f (x) = 4x³- 124x + a

∴f (x) active its maxⁿ value at x = 1∈ [0, 2]

∴f (1) = 0.

4 (1)³- 124 (1) + a = 0

$\Rightarrow$ a = 124 - 4 = 120.

∴a = 120

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

Excessive amount of sulphate (i.e., greater than 500 ppm) in drinking water causes laxative effect, otherwise at moderate levels it is harmless.

Yes, admission is currently open for the BA at MIT School of Vedic Sciences, MIT- ADT University for the academic year 2025. Students who meet the eligibility criteria can register and begin the admission process.

Srusti Academy of Management and Technology has an impressive placement record. The placement statistics for 2025 are given in the table below:

Yes,  BSc is available at Shri Guru Ram Rai University. It is an undergraduate programme. Moreover, the duration ranges from three to four years. BSc at SGRRU is spread across various specialisations, such as Nursing, Medical Microbiology, Yogic science,  and more. Students can choose the specialisations as per their interests, given that they fulfil the course-specific eligibility and selection criteria.

The deadline for applying to the BA programme at MIT School of Vedic Sciences, MIT-ADT University for 2025 is July 31. Applicants are advised to complete their registration before this date. Since eligibility is determined by Class 12 results, students should have their documents ready and submit their applications early to ensure they don’t miss the last date for MIT BA admission.

SCMS School of Architecture programme is offered for a duration of five years. The total tuition fee of the programme is INR 6.75 lakh. Students need to pay some part of the tuition fee and other components at the time of admission to finalise their seats.