BA programme at PK University is a three-year undergraduate course, divided into six equal semesters. It is designed for students interested in pursuing a degree in the field of humanities. The curriculum is structured to offer a balanced academic experience throughout the programme duration.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

The value of tan 3A -tan2A-tanA is equal to

(a) tan3Atan2AtanA

(b) -tan3Atan2AtanA

(c) tanAtan2A-tan2Atan3A-tan3AtanA

(d) None of these

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alok kumar singh

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n expression i s t a n 3 A - t a n 2 A - t a n A \\ t a n 3 A = t a n (2 A + A) \\ \Rightarrow t a n 3 A = \frac{t a n 2 A + t a n A}{1 - t a n 2 A . t a n A} \\ \Rightarrow t a n 3 A (1 - t a n 2 A . t a n A) = t a n 2 A + t a n A \\ \Rightarrow t a n 3 A - t a n 3 A t a n 2 A t a n A = t a n 2 A + t a n A \\ \Rightarrow t a n 3 A - t a n 2 A - t a n A = t a n 3 A t a n 2 A t a n A \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Five Exemplar Solution

Evaluate $\sum_{n = 1} {(1 + i)}^{3}$ , where $n \in ?$ .

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Payal Gupta

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l} W e h a v e \sum_{n = 1}^{13} (i^{n} + i^{n + 1}) \\ = (i + i^{2}) + (i^{2} + i^{3}) + (i^{3} + i^{4}) + (i^{4} + i^{5}) + (i^{5} + i^{6}) + (i^{6} + i^{7}) + (i^{7} + i^{8}) + (i^{8} + i^{9}) + (i^{9} + i^{10}) \\ (i^{10} + i^{11}) + (i^{11} + i^{12}) + (i^{12} + i^{13}) + (i^{13} + i^{14}) \\ = i + 2 (i^{2} + i^{3} + i^{4} + i^{5} + i^{6} + i^{7} + i^{8} + i^{9} + i^{10} + i^{11} + i^{12} + i^{13}) + i^{14} \\ = i + 2 [- 1 - i + 1 + i - 1 - i + 1 + i - 1 - i + 1 + i] + (- 1) \\ = i + 2 (0) - 1 \Rightarrow - 1 + i \\ H e n c e, \sum_{n = 1}^{13} (i^{n} + i^{n + 1}) = - 1 + i . \end{array}$

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Five Exemplar Solution

For a positive integer $n$ , find the value of ${(1 - i)}^{n} \frac{1}{1 - i^{n}}$ .

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Payal Gupta

Contributor-Level 10

This is a short answer type question as classified in NCERT Exemplar

$\begin{array}{l} W e h a v e {(1 - i)}^{n} {(1 - \frac{1}{i})}^{n} \\ = {[(1 - i) (1 - \frac{1}{i})]}^{n} = {[(1 - i) (1 - \frac{1}{i} \times \frac{i}{i})]}^{n} = {[(1 - i) (1 - \frac{i}{i^{2}})]}^{n} \\ = {[(1 - i) (1 + i)]}^{n} [? i^{2} = - 1] \\ = {[1 - i^{2}]}^{n} = {[1 + 1]}^{n} = 2^{n} \\ H e n c e, {(1 - i)}^{n} {(1 - \frac{1}{i})}^{n} = 2^{n} . \end{array}$

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

The minimum value of $3 c o s x + 4 s i n x + 8$ is:

(a) 5

(b) 9

(c) 7

(d) 3

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alok kumar singh

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n expression i s 3 c o s x + 4 s i n x + 8 \\ L e t y = 3 c o s x + 4 s i n x + 8 \\ \Rightarrow y - 8 = 3 c o s x + 4 s i n x \\ M i n i m u m v a l u e o f y - 8 = - \sqrt[]{{(3)}^{2} + {(4)}^{2}} \\ y - 8 = - \sqrt[]{9 + 16} = - 5 \\ y = 8 - 5 = 3 \\ S o, t h e m i n i m u m v a l u e o f t h e g i v e n expression i s 3 . \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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9 months ago

Ohio University Study Abroad

What is the application fee for Ohio University?

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Shreya Basu

Contributor-Level 10

International applicants must make sure to meet the admission requirements as per their programs and submit the documents during teh applicants process. Before the final submission of the application process applicants must make sure to pay an Ohio University application fee of USD 55, which is non-refundable. Failing to pay the application fee would result in unsuccessful submission of the application.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

If $t a n α = \frac{m}{m + 1}$ and $t a n β = \frac{1}{m + 2}$ , then $α + β$ is equal to:

(a) $\frac{π}{2}$

(b) $\frac{π}{3}$

(c) $\frac{π}{6}$

(d) $\frac{π}{4}$

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alok kumar singh

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t t a n α = \frac{m}{m + 1} a n d t a n β = \frac{1}{2 m + 1} \\ t a n (α + β) = \frac{t a n α + t a n β}{1 - t a n α . t a n β} = \frac{\frac{m}{m + 1} + \frac{1}{2 m + 1}}{1 - \frac{m}{m + 1} \times \frac{1}{2 m + 1}} \\ = \frac{\frac{2 m^{2} + m + m + 1}{(m + 1) (2 m + 1)}}{\frac{(m + 1) (2 m + 1) - m}{(m + 1) (2 m + 1)}} = \frac{2 m^{2} + 2 m + 1}{2 m^{2} + 2 m + m + 1 - m} \\ = \frac{2 m^{2} + 2 m + 1}{2 m^{2} + 2 m + 1} = 1 \\ t a n (α + β) = t a n \frac{π}{4} ∴ α + β = \frac{π}{4} \\ H e n c e, t h e c o r r e c t o p t i o n i s (d) . \end{array}$

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9 months ago

Ohio University Study Abroad

How do I apply to Ohio University?

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Shreya Basu

Contributor-Level 10

Applicants willing to apply to the Ohio University admissions must meet the admission eligibility and submit the necessary documents as per the programme requirements. Students can apply via Common App or University portal as per their level of program. Applicants would then be required to pay the Ohio University application fee for UG and PG respectively before the Ohio University admission deadlines. The steps for the application process are as follows:

Students applying for undergraduate programs must make an acocunt inthe Common App and search for Ohio University to start the application process. Applicants applying for postgraduate

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

Which of the following is correct?

(a) $s i n 1^{\circ} > s i n 1$

(b) $s i n 1^{\circ} < s i n 1$

(c) $s i n 1^{\circ} = s i n 1$

(d) $s i n 1^{\circ} = \frac{π}{1 8^{0}}$

Hint 1 radian = $\frac{π}{18 0^{0}} = 5 7^{0} 3 0^{'} a p p r o x$

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alok kumar singh

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} W e k n o w t h a t i f θ i n c r e a s e s t h e n t h e v a l u e o f s i n θ a l s o i n c r e a s e s . \\ S o, s i n 1^{0} < s i n 1 [? 1 r a d i a n = \frac{π}{180} s i n 1] \\ H e n c e, t h e c o r r e c t o p t i o n i s (b) . \end{array}$

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9 months ago

Science Biology Spl

I scored low marks in 12th and want admission into a central university for BSc Biology. Is that possible?

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Ankita Jha

Contributor-Level 7

If you scored low marks in 12th but want to join a central university, it's still possible through CUET, as many central universities focus mainly on CUET scores rather than Class 12 marks alone. However some courses or universities may set a minimum eligibility percentage, often around 40–50%, so check the specific requirements of the university and course you're interested in. Choose courses with lower competition to improve your chances of getting admission.

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9 months ago

DIT University Colleges in Dehradun

Who can enroll for course admission at DIT University?

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Liyansha Gaurav

Contributor-Level 10

The university shortlists candidates based on their merit or entrance exam scores. DIT University Dehradun also conducts DUET for shortlisting aspirants for MPharm, M.Tech and PhD courses. The university conducts other selection rounds like GDPI or PI rounds for some of the specific courses. However, for PhD who have a valid score GATE / SET / SLET will be selected based on PI. Students can check the table below to know course-wise eligibility:

Course Name	Eligibility Criteria
BTech	Class 12 with 4 subjects-Physics, Mathematics, English and best one of the remaining subjects with at least 50%-60% aggregate in Class 10 and Class 12
MBA	Graduation with 50% aggregate
MCA	Graduate (e.g. BE/BTech/BSC/Bcom/BA/BVoc/BCA/BBA etc.) with 50% aggregate preferably with Mathematics at Class 12 level or at graduation level
MTech	BE/ BTech in relevant specialisations with at least 55% aggregate
MPharm	BPharm with at least 55% aggregate
BCA	Class 12 with Mathematics or its equivalent examination in any stream with at least 50% aggregate

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

The value of $t a n 7 5^{\circ} - c o t 7 5^{\circ}$ is equal to:

(a) $2 \sqrt[]{3}$

(b) $2 + \sqrt[]{3}$

(c) $2 - \sqrt[]{3}$

(d) 1

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alok kumar singh

Contributor-Level 10

This is an Objective Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n expression is t a n 7 5^{0} - c o t 7 5^{0} \\ t a n 7 5^{0} - c o t 7 5^{0} = t a n 7 5^{0} - c o t {(90 - 15)}^{0} \\ = t a n 7 5^{0} - t a n 1 5^{0} = \frac{s i n 7 5^{0}}{c o s 7 5^{0}} - \frac{s i n 1 5^{0}}{c o s 1 5^{0}} \\ = \frac{s i n 7 5^{0} c o s 1 5^{0} - c o s 7 5^{0} s i n 1 5^{0}}{c o s 7 5^{0} c o s 1 5^{0}} \\ = \frac{s i n (7 5^{0} - 1 5^{0})}{\frac{1}{2} \times 2 c o s 7 5^{0} c o s 1 5^{0}} \\ = \frac{2 s i n 6 0^{0}}{c o s (7 5^{0} + 1 5^{0}) + c o s (7 5^{0} - 1 5^{0})} \\ = \frac{2 \times \frac{\sqrt[]{3}}{2}}{c o s 9 0^{0} c o s 6 0^{0}} = \frac{\sqrt[]{3}}{0 + \frac{1}{2}} = 2 \sqrt[]{3} \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) . \end{array}$

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9 months ago

Leiden University Study Abroad

What are the requirements to get into Leiden University?

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Taru Bhandari

Contributor-Level 9

Indian students must fulfill the basic criteria and submit all the important documents such as LORs, academic transcripts, CV, motivation letter and the English test scores. Indian students who want to study at Leiden University must fulfill the requirements mentioned below:

UG requirements:

Diploma equivalent to a Dutch pre-university diploma
Academic records of secondary and higher education
Letter of motivation
CV
SATor ACT scores
Program-specific requirements
Transcripts with IB grades
English language scores

PG requirements:

Relevant UG degree or equivalent from a recognised university with good scores
Academic transcripts
LOR
Letter of m

...more

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9 months ago

Leiden University Study Abroad

How long does Leiden University take to provide an offer letter to international students?

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Gunjan Aggrawal

Contributor-Level 9

Leiden University receives thousands of applications from over 100 countries. The university has over 6,000 international students. Choosing a deserving applicant for the courses is quite a time-consuming process as it involves receiving applications, identifying eligible candidates, and sending a response. The university considers students based on their aa strong academic record, relevant work experience, demonstrated motivation, English language proficiency, and more. The whole process can take 4-6 weeks to send a response via email.

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9 months ago

Leiden University Study Abroad

How much is the application fee for Leiden University?

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Jasleen Shukla

Contributor-Level 9

The Leiden University application fee is EUR 100 for UG and PG students. Students must pay the application fee after filling the application. International students must fulfill the eligibility criteria by holding a Diploma equivalent Dutch pre-university diploma. They must submit mandatory documents, including LORs, academic transcripts, a letter of motivation, CV or resume, motivation letter, along with English language scores.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Four Exemplar Solution

Let $P (n)$ be a statement and let P(k + 1) for some natural number $k$ . Then $P (n)$ is true for all $n \in ℕ$ .

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Vishal Baghel

Contributor-Level 10

This is a Objective Type Questions as classified in NCERT Exemplar
Sol:

$\begin{array}{l} G i v e n t h a t : P (k) \Rightarrow P (k + 1) \\ P (1) \Rightarrow P (2) w h i c h i s n o t t r u e . \\ H e n c e, t h e s t a t e m e n t i s' F a l s e' . \end{array}$

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9 months ago

Leiden University Study Abroad

Does Leiden University give scholarships for international students?

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Piyush Pandey

Contributor-Level 9

Leiden University offers various scholarships to international students. One of most popular scholarships for Indians is Leiden University Excellence Scholarship. To avail this scholarship, students must be international and apply for it in February every year. Some other popular scholarships for international students at Leiden are mentioned below-

Minerva Scholarship Fund
Faculty-Specific Scholarships
Erasmus+ Grants

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9 months ago

Leiden University Study Abroad

Is Leiden good for international students?

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Akansha katariya

Contributor-Level 10

Leiden University is one of best universities in Netherlands for international students. Along with top rankings and global recognitions, the university is popular for good academic, research and teaching and student community. It offers various programs in fields like Archaeology, Humanities, Law, Medicine, Science and Social and Behavioral Science. The programs include practical learning, in depth knowledge, research opportunities, etc.

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9 months ago

Maths NCERT Exemplar Solutions Class 11th Chapter Three Exemplar Solution

If $t a n θ = 3$ and $θ$ lies in the third quadrant, then the value of $s i n θ$ is: