Polycet

TS POLYCET 2023 Question Paper Solutions – Complete Maths Answers PDF Are you searching for TS POLYCET 2023 Question Paper Solutions? You are in the right place. Practising previous year question papers is one of the smartest ways to score high marks in the TS POLYCET exam. It helps students understand the exam pattern, important topics, and time management. In this post, we provide complete and easy-to-understand solutions for the TS POLYCET 2023 Maths Question Paper, with clear step-by-step explanations. The TS POLYCET 2023 question paper solutions are highly useful for every student preparing for the upcoming exams. Solve the paper sincerely and compare answers with detailed solutions to improve your score. Stay connected for more previous papers, mock tests, and chapter-wise maths solutions. Real Numbers   1. If ‘n’ is a prime number, then √n is (1) Prime number          (2) Composite number (3) Rational number      (4) irrational number     ‘n’ అనేది ఓకే ప్రధాన సంక్య అయిన √n   అనేది     (1)  ప్రధాన సంఖ్య                             (2) సంయుక్త  సంఖ్య      (3) అకరణీయ సంఖ్య                   (4)  కరణీయ సంఖ్య Answer: (4) Solution:   If ‘n’ is a prime number, then √n  is an irrational number 2.Among 1/2, 1/3, 1/4, 1/5 the non-terminating decimal is 1/2, 1/3, 1/4, 1/5 అనే సంఖ్యలలో అంతం కాని దశాంశం   (1) 1/2          (2) 1/3      (3) 1/4       (4) 1/5 Answer: (2) Solution: A fraction in its simplest form has a terminating decimal if the prime factors of its denominator are only 2, 5, or both. If the denominator has any other prime factor, it results in a non-terminating repeating decimal. 3. The value of log625(5) l og625(5) యొక్క విలువ (1) 1/2          (2) 1/4      (3) 1/3       (4) 1/5 Answer: (2) Solution: let log625(5) =  x 5 = 625x 5 = (54)x 5 = 54x 1 = 4x x = 1/4 4. √2 + √3 is (1) Rational number           (2) Irrational number (3) Prime number        (4) composite number √2 + √3 is అనునది ఒక (1) అకరణీయ సంఖ్య              (2) కరణీయ సంఖ్య (3) ప్రధాన సంఖ్య                    (4) సంయుక్త  సంఖ్య Answer: (2) Solution:  √2 + √3 is an irrational number 5. HCF of 7, 8, 9 is 7, 8, 9  ల గా.సా.భా. (1) 9             (2) 7                      (3) 1                  (4)  2 Answer: (3) Solution:  factors of 7 = 1, 7 factors of 8 = 1, 2, 4, 8 factors of 9 = 1, 3, 0039 HCF 0f 7, 8, 9 = 1     Sets 1.   If A={P, O, L, Y, T, E,C, H, N, I} and B = {E, X, A, M}then A∩B = A={P, O, L, Y, T, E,C, H, N, I} మరియు  B = {E, X, A, M}అయితే, A∩B = (1) {P}               (2) {E}                      (3) {X}                       (4) {T} Answer: (2) Solution:  Given A = {P, O, L, Y, T, E, C, H, N, I} and B = {E, X, A, M} A∩B = {P, O, L, Y, T, E, C, H, N, I}∩{E, X, A, M} = {E} 2.   If A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7} then A – B = A = {1, 2, 3, 4, 5} మరియు  B = {4, 5, 6, 7} అయితే, A – B = (1) {1, 2, 3}         (2) {3, 4, 5}         (3) {5, 6, 7}       (4) {2, 3, 4} Answer: (1) Solution:   Given A = {1, 2, 3, 4, 5} and B = {4, 5, 6, 7} A – B = {1, 2, 3, 4, 5} – {4, 5, 6, 7} = {1, 2, 3}     Polynomials 1. Product of zeroes of polynomial 5×2 – 1 is  5×2 – 1 అనే వర్గ బహుపదీ శూన్యాల లబ్దము     (1) 1        (2) ½         (3) 1/5    (4) – 1/5 Answer: (4) Solution:  Given polynomial is 5×2 – 1 Product of zeroes = c/a = – 1/5 2. (x + a) is a factor of f(x), if   (x + a)  అనేది f(x) యొక్క కారణాంకం అయినచో  (1) f(a) = 0            (2) f(–a) = 0         (3) f(1/a) = 0        (4) f(– 1/a) = 0   Answer: (2)   Solution:    Given (x + a) is a factor of f(x),then f(–a) = 0 3. If α, β are the zeroes of the quadratic polynomial ax2 + bx + c, a≠0, then α2 + β2 = ax2 + bx + c, a≠0 అనే వర్గ బహుపది యొక్క శూన్యాలు α, β అయిన α2 + β2 =     (1)   (b2 + 2ac)      (2) (c2 + 2ab)   (3) (b2 – 2ac)        (4) (c2 – 2ab)    Answer: (2)    Solution: Given polynomial is ax2 + bx + c, a≠0 α + β = – b/a αβ = c/a α2+ β2 = (α + β)2 – 2αβ α2+ β2 = (– b/a)2 – 2(c/a) α2+ β2 =  b2/a2 – 2c/a α2+ β2 =   (b2 – 2ac)   Linear equations in Two Variables   1. If 5x + py + 8 = 0 and 10x + 15y + 12 = 0 has no solution, then p = 5x + py + 8 = 0 మరియు 10x + 15y + 12 = 0 అను సమీకరణాలకు సాధన లేనిచో, p విలువ (1) 15/2      (2) 13/2          (3) 7/2        (4) 5/2 Answer: (1) Solution:   Given 5x + py + 8 = 0 and 10x + 15y + 12 = 0 have no solution a1 = 5; b1 = p; c1 = 8 a2 = 10; b2 = 15; c2 = 12              p = 15/2 2. If ax + b = 0 then x =  ax + b = 0 అయిన, x విలువ (1) – a       (2) a     (3) b/a    (4) – b/a Answer: (4) Solution:    Given ax + b = 0 ⟹ ax = – b ⟹ x = – b/a 3. The solution of system of equations and is మరియు  సమీకరణాల సాధన   (1) (1/4, 1/3)     (2)  (1/3, 1/4)        (3) (1/2, 1/3)       (4) (1/3, 1/2)   Answer: (3) Solution:  Given equations are  and Let  = a and  = b ⟹2a + 3b= 13 and 5a – 4b = – 2                          a

TS POLYCET 2022 Solutions – Complete Questions Explained Simply TS POLYCET 2022 Solutions-Preparing for TS POLYCET can feel overwhelming, especially when you’re unsure about the type of questions that might appear. The TS POLYCET 2022 paper gave students a balanced mix of easy, moderate, and a few tricky questions—testing not just knowledge, but confidence and time management. Why Solutions Matter Going through solutions is not just about checking answers; it’s about understanding how to approach a problem. Many students realise that even difficult questions become easy when broken into simple steps. Smart Preparation Tip Instead of memorising formulas blindly, focus on understanding concepts. Practice TS POLYCET 2022 to improve speed and accuracy. Start with easy questions in the exam, then move to tougher ones. Final Thought TS POLYCET is not about solving every question perfectly—it’s about staying calm, thinking clearly, and doing your best. With the right approach, even a challenging paper can turn into an opportunity. Real Numbers 1.  If the H.C.F. of any two numbers is equal to ‘1’ then those numbers are called as     (1) Coprime numbers        (2) Prime numbers            (3) Irrational numbers      (4) Rational numbers      రెండు సంఖ్యల యొక్క గ.సా.భా. ‘1’ అయిన, ఆ రెండు సంఖ్యలను ……. అంటారు.     (1) పరస్పర ప్రధాన సంఖ్యలు         (2) ప్రధాన సంఖ్యలు        (3) కరణీయ సంఖ్యలు                     (4) అకరణీయ సంఖ్యలు      Answer: (2)        Solution:   We know that the HCF of Prime numbers is always 1 2. The number ‘π’ is a      (1) Natural number     (2) Rational number           (3) Integer                (4) Irrational number       ‘π’ is అనునది ఒక       (1) సహజ సంఖ్య     (2) అకరణీయ సంఖ్య             (3) పూర్ణ సంఖ్య    (4) కరణీయ సంఖ్య         Answer: (2)        Solution:  π is an irrational number  3. The base of common logarithm is        సంవర్గమానాల ప్రామాణిక ఆధారం         (1) 2     (2) 5    (3) 10       (4) 1            Answer: (3)         Solution:    The base of the common logarithm is 10   4. √p + √q is an irrational number, where p and q are        (1) Even numbers       (2) Prime numbers                    (3) Rational numbers     (4) None       √p + √q కరణీయ సంఖ్య అయిన, P, qలు        (1) సరి సంఖ్యలు        (2) ప్రధాన సంఖ్యలు           (3) అకరణీయ సంఖ్యలు   (4) ఏది కాదు     Answer: (2)        Solution:  √p + √q is an irrational number, where p, q are Prime numbers 5. The value of  log2025(2025)      log2025(2025) యొక్క విలువ     (1) 0      (2) 1      (3) 2     (4) 3    Answer: (2)       Solution:    We know that loga(a)  = 1                    log2025(2025)= 1 TS POLYCET 2022 Solutions   Sets 1. If A={a, b, c, d} then number of subsets of A are A= {a,b,c, d} అయిన, A కు గల ఉపసమితుల సంఖ్య (1) 8        (2) 12           (3) 16          (4) 20     Answer: (3)    Solution:    Given A = {a, b, c, d}                    The number of elements in the set A are: n = 4                  Number of subsets of A = 2n                   = 24 = 16 2. Which of the following is true?     క్రింది వానిలో ఏది సత్యం ? (1) ф=0     (2) n(ф)=0        (3) ф={0}      (4)  n(ф’)= 0      Answer: (2)    Solution:   We know that the number of elements in an empty set = 0 ∴  n(ф)=0 Polynomials 1. The zeroes of the quadratic polynomial 4y2 + 8y 4y2 + 8y అనే వర్గ బహుపదీ శూన్యాలు (1) 0, 4       (2) 0, 2      (3) 0, 6        (4) 0, – 2    Answer: (4)  Solution:    Let p(y) = 4y2 + 8y For the zeroes of the polynomial p(y) = 0 4y2 + 8y = 0 4y(y + 2) = 0 ⟹ y = 0 or y + 2 = 0 y = 0 or y = – 2 2. If sum and product of zeroes of a Quadratic polynomial are 1, 1 respectively, then its corresponding quadratic polynomial is ఒక వర్గ బహుపది యొక్క శూన్యాల మొత్తం మరియు శూన్యాల లబ్ధం వరుసగా 1, 1 అయిన, ఆ వర్గ బహుపది ఏది ? (1) x2 – x + 1                       (2) x² + x + 1 (3) x2 + x – 2                        (4) x2 – x + 2     Answer: (1)    Solution:    Given α + β = 1 and αβ = 1 Quadratic polynomial is x2 – (α + β)x + αβ = x2 – (1)x + 1 = x2 – x + 1 TS POLYCET 2022 Solutions   Linear equations in Two Variables   1. The pair of equations x =0 and x=5 has (1) Unique solution        (2) Infinitely many solutions (3) Two solutions         (4) No solution    x = 0 మరియు x = 5 అను సమీకరణాల జత కలిగి ఉండే సాధనలు (1) ఏకైక సాధన కలిగి ఉంటాయి                (2) అనంతమైన సాధనలు కలిగి ఉంటాయి   (3) రెండు సాధనలను కలిగి ఉంటాయి    (4) ఎటువంటి సాధనలు కలిగి ఉండవు Answer: (4) Solution:  x = 0 is the equation of the Y–axis x = 5 is the line which is parallel to the Y–axis Given lines are parallel to each other ∴ They have no solution 2, The pair of equations x +  y = 7, 9x – 10y =12, represents the following (1) Parallel lines      (2) No solution 3) Infinitely many solutions    (4) One solution x +  y = 7, 9x – 10y = 12 రేఖా సమీకరణాల జత, క్రింది దానిని సూచించును. (1) సమాంతర రేఖలు       (2) సాధన లేదు (3) అనంతమైన సాధనలుంటాయి       (4) ఏకైక సాధన Answer: (4) Solution:   

POLYCET Real Numbers MCQs with Answers & Explanations 25   POLYCET Real Numbers MCQs – Preparing for the POLYCET exam requires a strong foundation in Real Numbers, one of the most important topics in Class 10 Mathematics. This set of 25 carefully designed MCQs covers key concepts such as HCF, LCM, Euclid’s Division Algorithm, irrational numbers, decimal expansions, and prime factorisation. These questions are crafted to match the latest POLYCET exam pattern, helping students improve accuracy, speed, and conceptual clarity. Whether you’re revising basics or testing your understanding, this practice set will boost your confidence and exam readiness. Each question includes a step-by-step explanation, making it ideal for self-study and quick revision. 1. The HCF of 12 and 18 is: A) 2B) 3C) 6D) 9 Answer: C Explanation:Factors of 12 = 1, 2, 3, 4, 6, 12Factors of 18 = 1, 2, 3, 6, 9, 18Common highest factor = 6 2. The LCM of 8 and 12 is: A) 12B) 24C) 36D) 48 Answer: B Explanation:Prime factors:8 = 2³, 12 = 2² × 3LCM = 2³ × 3 = 24 3. If HCF = 6 and LCM = 180 for two numbers, one number is 30. The other is: A) 36B) 42C) 48D) 60 Answer: A Explanation:Formula:Product of numbers = HCF × LCM= 6 × 180 = 1080Other number = 1080 ÷ 30 = 36 4. Euclid’s Division Algorithm states: A) a = bqB) a = bq + rC) a = brD) a = b + r Answer: B Explanation:Formula:a = bq + r, where 0 ≤ r < b 5. The decimal expansion of 1/4 is: A) Non-terminatingB) TerminatingC) RepeatingD) Irrational Answer: B Explanation:1/4 = 0.25 → finite decimal → terminating 6. Which is an irrational number? A) 2/3B) √4C) √5D) 0.75 Answer: C Explanation:√5 cannot be expressed as a fraction → irrational 7. The HCF of two co-prime numbers is: A) 0B) 1C) Equal numbersD) Product Answer: B Explanation:Co-prime numbers have only one common factor → 1 8. The decimal expansion of 2/11 is: A) TerminatingB) Non-terminating repeatingC) IrrationalD) Whole number Answer: B Explanation:2/11 = 0.1818… → repeating decimal 9. If a number has prime factorization 2³ × 3², then total factors are: A) 6B) 8C) 12D) 16 Answer: C Explanation:Number of factors = (3+1)(2+1) = 4×3 = 12 10. √49 is: A) 6B) 7C) 8D) 9 Answer: B Explanation:√49 = 7 11. Which of the following is rational? A) √7B) πC) 0.333…D) √2 Answer: C Explanation:0.333… = 1/3 → rational 12. The LCM of co-prime numbers is: A) 1B) SumC) ProductD) Difference Answer: C Explanation:LCM of co-primes = product of numbers 13. The decimal expansion of 7/8 is: A) TerminatingB) Non-terminatingC) IrrationalD) Whole Answer: A Explanation:7/8 = 0.875 → terminating 14. The smallest prime number is: A) 0B) 1C) 2D) 3 Answer: C Explanation:2 is the smallest and only even prime number 15. The product of HCF and LCM of two numbers is equal to: A) SumB) DifferenceC) Product of numbersD) Square Answer: C Explanation:Formula:HCF × LCM = Product of numbers 16. Which is not a real number? A) √2B) 5C) -3D) 1/0 Answer: D Explanation:1/0 is undefined → not a real number 17. The decimal expansion of 1/3 is: A) TerminatingB) Non-repeatingC) RepeatingD) Irrational Answer: C Explanation:1/3 = 0.333… repeating 18. A number is divisible by 3 if: A) Last digit is 3B) Sum of digits divisible by 3C) Even numberD) Prime Answer: B Explanation:Divisibility rule of 3 19. If LCM = HCF, then the numbers are: A) Co-primeB) EqualC) DifferentD) Prime Answer: B Explanation:LCM = HCF only when the numbers are equal 20. Which of the following is a terminating decimal? A) 3/7B) 5/6C) 9/20D) 2/11 Answer: C Explanation:Denominator = 2² × 5 → terminating 21. The prime factorisation of 36 is: A) 2 × 18B) 6 × 6C) 2² × 3²D) 3 × 12 Answer: C Explanation:36 = 2 × 2 × 3 × 3 22. √(2 × 8) = A) 2B) 4C) 6D) 8 Answer: B Explanation:√16 = 4 23. The number of irrational numbers between 1 and 2 is: A) 1B) 2C) FiniteD) Infinite Answer: D Explanation:Infinite irrational numbers exist between any two numbers 24. If a = bq + r and r = 0, then: A) a < bB) a is divisible by bC) a > bD) a is prime Answer: B Explanation:Remainder = 0 → exact division 25. Which of the following has a non-terminating, non-repeating decimal expansion? A) 4/5B) 7/9C) √3D) 2/8 Answer: C Explanation:√3 is irrational → non-terminating, non-repeating Conclusion & Student Tips Focus on formulas like HCF × LCM = Product Practice prime factorisation regularly Learn decimal expansion rules (terminating vs repeating) Revise divisibility rules Attempt mock tests for better speed Consistency and practice are key to scoring high in POLYCET Mathematics! YouTube

Polynomials Concepts and Practice Questions Guide Have you ever looked at an algebraic expression and felt confused about what it really means? You’re not alone. Imagine this: A student preparing for an exam keeps skipping polynomial questions because they “look complicated.” But once they understand just a few simple concepts, those same questions become the easiest marks on the paper. That’s the power of Polynomials. In this guide, I’ll break down polynomials in a super simple, friendly way—just like a teacher sitting next to you. By the end, you won’t just understand polynomials… you’ll actually enjoy solving them! What Are Polynomials? An algebraic expression becomes a polynomial if the powers of the variable(s) are whole numbers Example: 2x – 5, 3×2 + 5x – 3 , x3 + 3×2 – 6x + 3 Value of a polynomial p(a) is the value of a polynomial p(x) at x = a, whre a is any real number Ex:  let p (x) = 2x + 5                  Put x = 1 ⟹ p (1) =  2 (1) + 5 = 2 + 5 = 7 ∴ 7 is the value of the polynomial p(x) at x = 1 Zero of a polynomial Zero of a polynomial p(x) is any real number ‘k’ such that p(k) = 0. Ex:  let p (x) = x  + 5            Put x = 5 ⟹ p (– 5) =  – 5 + 5 = 0 ∴ – 5 is the zero of the polynomial p(x) Note:  For finding the zeroes of the polynomial p(x), let p(x) = 0 Degree of a polynomial The highest power of x in a polynomial p(x) is called the degree of the polynomial p(x) Example: Degree of the polynomial 3×2 – 4x is 2 Degree of the polynomial x3 – 4×4 – 5x + 6  is 4 Types of Polynomials According to Terms 1. Monomial:  If a polynomial has only one term, then it is called a monomial. Example: 2x, 3y, -5x, 9×3 2.  Binomial: If a polynomial has two terms, then it is called a Binomial. Example: 2x + 1, 3y – 7, -5x + 6, x5 + 5×3 3. Trinomial:  If a polynomial has three terms, then it is called a Trinomial. Example: x5 + 5×3+ 2x, 3y2 – 8y2 + 3 According to the degree 1. Linear Polynomial:  If a polynomial has a degree of one, then it is called a Linear Polynomial. Example: 2x + 1, 3y – 1, 2.  Quadratic Polynomial: If a polynomial has a degree of two, then it is called a Quadratic Polynomial. Example: 2×2  +  x + 1, y2  – 7, -x2  + 6, 3. Cubic Polynomial: If a polynomial has a degree of three, then it is called a Cubic Polynomial. Example: 5×3+ 2x, 9y3 – 8y2 + 3 Note: For any quadratic polynomial ax2 + bx + c, a ≠ 0, the graph of the corresponding equation y = ax2 + bx + c (a ≠ 0,) either opens upwards like ∪ or opens downwards ∩ as This depends on whether a > 0 or a< 0. The shape of these curves is called a parabola Real Numbers POLYCET Maths Guide for Top Rank – 2026 Graphical Representation of a Quadratic Polynomial The shape of the graph of y = ax2 + bx + c, (a ≠ 0), the following three cases arise. Case (i) : Here, the graph cuts X – axis at two distinct points. In this case, the x-coordinates of those two points are the two zeroes of the quadratic polynomial ax2 + bx + c. The parabola opens either upward or downward. Case (ii) : Here, the graph touches X – axis at exactly one point. In this case, the x-coordinate of that point is the only zero for the quadratic polynomial ax2 + bx + c. Case (iii) : Here, the graph is either completely above the X-axis or completely below the X – axis. So, it does not cut the X-axis at any point. The quadratic polynomial ax2 + bx + c has no zero in this case.   Relationship Between Zeros and Coefficients of the polynomial:  1. P(x) = ax + b is linear polynomial zero of the polynomial is x = −b/a = -(constant)/ x coefficient 2. P(x) = ax2 + bx + c (a ≠ 0) is the general form of a quadratic polynomial. Sum of the zeroes = α + β =  −b/a = -(x coefficient)/ x2 coefficient Product of the zeroes =−b/a = (constant)/ x2 coefficient  3. p(x) = ax3 + bx2 + cx + d ( a ≠ 0)is the general form of a cubic polynomial. α + β + γ = −b/a = -(x2 constant)/ x3 coefficient αβ + βγ + γα  = −b/a = (x constant)/ x3 coefficient α β γ = −−b/a = -(constant)/ x3 coefficient       If α and β are the zeroes of a quadratic polynomial, then its form is k [x2 – (α + β ) x + α β]      If α, β and γ are the zeroes of the cubic polynomial, then its form is k [x3 – (α + β + γ) x2 +( αβ + βγ +γα  )x – αβγ] Polynomials Concepts and Practice Questions Division Algorithm for the polynomials: If p(x) and g(x) are any two polynomials with g(x) ¹ 0, then we can find polynomials q(x) and r(x) such that p(x) = g(x) × q(x) + r(x), Where either r(x) = 0 or degree of r(x) < degree of g(x) if r(x) ≠ 0 We have the following results from the above discussions (i)  If g(x) is a linear polynomial then r(x) = r is a constant. (ii)  If degree of g(x) = 1, then degree of p(x) = 1 + degree of q(x). (iii)  If p(x) is divided by (x – a), then the remainder is p(a). (iv)  If r = 0, we say q(x) divides p(x) exactly or q(x) is a factor of p(x) Polynomials

Sets Explained for POLYCET: Master Concepts Fast & Score High (2026 Guide) Sets Explained for POLYCET—Imagine walking into your POLYCET exam hall and spotting a question from Sets… and instead of panic, you smile because you already know the answer in seconds. Sounds powerful, right? That’s the magic of understanding sets properly. Many students think sets is a small topic—but here’s the truth: it builds your logical thinking and helps you solve questions quickly with accuracy. In this guide, I’ll break down Sets Explained for POLYCET in the simplest way possible—like a friend teaching you before the exam. What Are Sets? (Simple Explanation) A set is a collection of well-defined objects. These objects are called elements. Example: Set of numbers: A = {1, 2, 3, 4} Set of vowels: B = {a, e, i, o, u} Important: A set should be clear and specific. Sets are typically represented using letters from the English alphabet. Elements in a set are written in a curly bracket { } separated by commas Roster Form of a Set In a ‘roster form’, we are writing a set by listing the elements in it. EX: A = {1, 2, 3, 4}; B = {a, e, i, o, u} Set Builder form of a set In a ‘Set builder form,’ we write a set by defining its elements with a “Common property“  Syntax for the set builder form Know about Belongs to The symbol ‘∈’ is used to denote membership of an element and read as ‘belongs to’ Ex: A = {1, 4, 5, 6} 4 ∈ A, 5 ∈ A, and 7 ∉ A Sets Explained for POLYCET Types of Sets You Must Know Empty Set (Null Set) A set with no elements Represented as: Ø or {} 👉 Example: Set of odd numbers divisible by 2 A = {x: 1 < x < 2, x is a natural number} Finite set:  A set that contains a finite number of elements is called a finite set Ex: A = {1, 2, 3, 6}; B = {x: x ∈ w, 0 ≤ x ≤ 6} Infinite set: A set that contains an infinite number of elements is called an infinite set Ex: N = {1, 2, 3, 4, …}; B = {x : x > 5, x ∈ W} Venn Diagrams: It is one method for representing relationships between sets. Venn diagrams are also known as “Venn–Euler diagrams. These diagrams consist of rectangles and closed curves, such as circles. μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} A = {1, 4, 5, 6}; B = {2, 8} Subset: For any two sets A and B, if every element of set A is in set B, then we can say that A is a subset of B. It is denoted by A ⊂ B.     Ex:  If A = {2, 3} and B = {1, 2, 3, 4}, then we say that ‘A is a subset of B’, and symbolically A ⊂ B. Note: If a set has n elements, then the number of subsets of that set = 2n The empty set is a subset of every set  Every set is a subset of itself If A ⊂ B, then A ∪ B = B A ∩ B = A  A – B = ∅ Power set: The collection of all possible subsets of a set A is called the power set of A, and it is represented by P(A). Ex: A = {a, b, c} Subsets of A are {a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}, ∅ P (A) = {{a}, {b}, {c}, {a, b}, {b, c}, {c, a}, {a, b, c}, ∅}  If a set A has n elements, then the number of elements of P (A) = 2n Universal set: A set that contains all the subsets of it under our consideration is called a universal set. The universal set is denoted by ‘𝛍’ or ‘U’ and represented by rectangles. μ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} A = {1, 4, 5, 9}         B = {7, 10} Union of sets: The union of two sets A and B is the set that contains all the elements of set A or set B, or both sets A and B. The symbol ∪ is used to denote the union The union of A and B is written as ‘A ∪ B’ and read as ‘A union B’ A∪B = {x: x ∈ A or x ∈ B}   Example A = {1, 3, 5}, B = {1, 2, 3, 4} A∪B = {1, 3, 5} ∪ {1, 2, 3, 4} = {1, 2, 3, 4, 5} Intersection of sets: The intersection of two sets A and B is the set that contains all the elements that are common to both sets A and B. The symbol ∩ is used to denote the union The intersection of A and B is written as ‘A ∩ B’ and read as ‘A intersection B’ A ∩ B = {x: x ∈ A and x ∈ B} Example A = {1, 3, 5}, B = {1, 2, 3, 4} A ∩ B = {1, 3, 5} ∩ {1, 2, 3, 4} = {1, 3} Disjoint sets: Two sets A and B are said to be disjoint sets if they have no common element ⟹ A ∩ B = ∅   Example A = {a, b, c}, B = {x, y, z} A ∩ B = ∅ Difference of sets: The difference set of sets A and B is the set of elements that belong to A but do not belong to B The Difference of A and B is Denoted by A – B  A – B = {x: x ∈ A and x ∉ B}     B – A = {x: x ∈ B and x ∉ A}   Sets Explained for POLYCET Cardinal number of a set: The