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You can check the Pearson PTE Academic Practice Test Plus - Volume 1 and 2 books to access the PTE sample papers. These books include 4 complete practice tests with authentic questions, each of which comes with a tip to answer that question. The books also come with a CD in which you can listen to the audio recordings of specific tasks. 

To go beyond the conventional practice methods, you can find the Scored Practice Tests offered by Pearson. These tests simulate the real PTE test and your responses are scored by the similar AI algorithm as is used in exam.

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

Sol:

$\begin{array}{l}LetredmarblesberepresentedwithRandblackmarblesberepresentedwithB.\\ Thefollowingthreeconditionsarepossible,ifatleastoneofthethreemarbles\\ drawnbeblackandfirstmarbleisred.\\ \left(i\right)E_1=IIballisblackandIIIisred\\ \left(ii\right)E_2=IIballisblackandIIIisalsoblack\\ \left(iii\right)E_3=IIballisredandIIIisblack\\ \therefore P\left(E_1\right)=P\left(R_1\right).P\left(B_1/R_1\right).P\left(R_2/R_1{B}_1\right)=\frac{5}{8}.\frac{3}{7}.\frac{4}{6}=\frac{60}{336}=\frac{5}{28}\\ P\left(E_2\right)=P\left(R_1\right).P\left(B_1/R_1\right).P\left(B_2/R_1{B}_1\right)=\frac{5}{8}.\frac{3}{7}.\frac{2}{6}=\frac{30}{336}=\frac{5}{56}\\ andP\left(E_3\right)=P\left(R_1\right).P\left(R_2/R_1\right).P\left(B_1/R_1{R}_2\right)=\frac{5}{8}.\frac{4}{7}.\frac{3}{6}=\frac{60}{336}=\frac{5}{28}\\ \therefore P\left(E\right)=P\left(E_1\right)+P\left(E_2\right)+P\left(E_3\right)=\frac{5}{28}+\frac{5}{56}+\frac{5}{28}=\frac{25}{56}\\ Hence,therequiredprobabilityis\frac{25}{56}.\end{array}$

MBA programme at Nehru Gram Bharati University Kotwa is a full-time postgraduate course spread over two years. The course is divided into four semesters, ensuring a balanced academic structure with continuous learning, projects, and assessments each term.  

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

Sol:

$\begin{array}{l}Weknowthat:\\ A\cup Bdenotesthatatleastoneoftheeventsoccursand\\ A\cap Bdenotesthatthetwoeventsoccurssimultaneously.\\ So,P\left(A\cup B\right)=P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)\\ \Rightarrow 0.6=P\left(A\right)+P\left(B\right)-0.3\\ \Rightarrow 0.9=P\left(A\right)+P\left(B\right)\\ \Rightarrow 0.9=1-P\left(\overline{A}\right)+1-P\left(\overline{B}\right)\\ \Rightarrow P\left(\overline{A}\right)+P\left(\overline{B}\right)=2-0.9=1.1\\ Hence,therequiredansweris1.1\end{array}$

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There are many affordable Cyber Security colleges in Pune. Here is a categorization of the best Cyber Security colleges in Pune, based on their average course fees:

Disclaimer: This info. is sourced from the official website and may vary.

According to the 2025 placement report, IIIT Nagpur graduates received an average package that stood at 14.2 LPA. The average package offered between the years 2024 and 2025 are tabulated below:

Hello!

No, Cyber Security courses in Mumbai are not necessarily expensive. Here is a fee-wise bifurcation of the best Cyber Security colleges in Mumbai:

Disclaimer: This info. is taken from the official website and may differ.

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

Sol:

$\begin{array}{l}AccordingtothesolutionofQ.1,wehave\\ A=\left\{\left(1,1\right),\left(2,2\right),\left(3,3\right),\left(4,4\right),\left(5,5\right),\left(6,6\right)\right\}\\ \therefore n\left(A\right)=6andn\left(S\right)=6\times 6=36\\ So,P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{6}{36}=\frac{1}{6}\\ andB=\left\{\left(4,6\right),\left(6,4\right),\left(5,5\right),\left(5,6\right),\left(6,5\right),\left(6,6\right)\right\}\\ n\left(B\right)=6andn\left(S\right)=6\times 6=36\\ \therefore P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{6}{36}=\frac{1}{6}\\ A\cap B=\left\{\left(5,5\right),\left(6,6\right)\right\}\\ \therefore P\left(A\cap B\right)=\frac{2}{36}=\frac{1}{18}\\ Therefore,ifAandBareindependent,then\\ P\left(A\cap B\right)=P\left(A\right).P\left(B\right)\\ \Rightarrow \frac{1}{18}\ne \frac{1}{6}\times \frac{1}{6}=\frac{1}{36}\\ \Rightarrow \frac{1}{18}\ne \frac{1}{36}\\ Hence,AandBarenotindependentevents.\end{array}$

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

Check the reviews first. You want a book that uses real test questions, covers all the math and reading sections, and explains the answers simply so you can understand exactly how to fix your errors for a better score. Trust the official GRE books.

This is a Long Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Here,SamplespaceS=\left\{\begin{array}{l}\left(1,2\right),\left(2,1\right),\left(1,3\right),\left(3,1\right),\left(2,3\right),\left(3,2\right),\left(1,4\right),\left(4,1\right),\left(1,5\right),\left(5,1\right),\left(2,4\right)\\ \left(4,2\right),\left(2,5\right),\left(5,2\right),\left(3,4\right),\left(4,3\right),\left(3,5\right),\left(5,3\right),\left(5,4\right),\left(4,5\right)\end{array}\right\}\\ \therefore n\left(S\right)=20\\ LetXbetherandomvariabledenotingthesumofthenumbersontwocardsdrawn.\\ \therefore X=3,4,5,6,7,8,9\\ So,P\left(X=3\right)=\frac{2}{20}P\left(X=4\right)=\frac{2}{20}\\ P\left(X=5\right)=\frac{4}{20}P\left(X=6\right)=\frac{4}{20}\\ P\left(X=7\right)=\frac{4}{20}P\left(X=8\right)=\frac{2}{20}\\ P\left(X=9\right)=\frac{2}{20}\\ \therefore themeanE\left(X\right)={\displaystyle \sum _{i=1}^n{X}_i{P}_i}\\ =3\times \frac{2}{20}+4\times \frac{2}{20}+5\times \frac{4}{20}+6\times \frac{4}{20}+7\times \frac{4}{20}+8\times \frac{2}{20}+9\times \frac{2}{20}\\ =\frac{6}{20}+\frac{8}{20}+\frac{20}{20}+\frac{24}{20}+\frac{28}{20}+\frac{16}{20}+\frac{18}{20}=\frac{120}{20}=6\\ \therefore E\left(X^2\right)={\displaystyle \sum _{i=1}^n{P}_i}{X}_i^2\\ =9\times \frac{2}{20}+16\times \frac{2}{20}+25\times \frac{4}{20}+36\times \frac{4}{20}+49\times \frac{4}{20}+64\times \frac{2}{20}+81\times \frac{2}{20}\\ =\frac{18}{20}+\frac{32}{20}+\frac{100}{20}+\frac{144}{20}+\frac{196}{20}+\frac{128}{20}+\frac{162}{20}=\frac{780}{20}=39\\ \therefore Variance\left(X\right)=E\left(X^2\right)-{\left[E\left(X\right)\right]}^2\\ =39-{\left(6\right)}^2=39-36=3\end{array}$

The COMEDK UGET round 1 counselling registration and document uploading started on June 9, and the last date to register is June 18 (2:00 pm). The last date for document verification is July 12. Candidates must go through the instructions and complete the registration before the due date. The seat allotment list will be published based on the documents submitted and merit scores. 

This is a Long Answer Type Questions as classified in NCERT Exemplar

Sol:$\begin{array}{l}\end{array}$

IMD is one of best universities for MBA program in Switzerland. It has certain minimum requirements for admission of international students, along with submission of mandatory documents. Following are minimum requirements for admission-

• UG degree from recognised university or equivalent
• Minimum 2 years of documented employment history
• English language scores
• GMAT score of 585-805
• One page CV
• LOR
• Academic records
• Completed application form and payment receipt

In order to get admission at NIMT candidates must keep certain documents ready. Student can check the list of documents below:

• Scanned Class 10, Class 12 and graduation marksheet
• Leaving Certificate
• Aadhaar Card
• Passport-size photograph
• Signature

Note: The list of documents mentioned above are the general documents. For more details visit the official website.

In the BTech Dairy Technology course, you get to learn about the scientific and technological fundamentals behind the processing and production of milk products and how technology and engineering principles ensure the quality and safety of the products with enhanced shelf life to make sure they are safe for human consumption.

If you're somebody who has a deep interest and passion for the concepts behind the production and processing of milk and its by-products, you can definitely opt for this course after completing Class 12, which usually spans 4 years.