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- Important Questions
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- Important Questions
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- Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas
- MCQs or Short Questions
- Ch 01: Number Systems
- Ch 02: Functions and Groups
- Ch 03: Matrices and Determinants
- Ch 04: Quadratic Equations
- Ch 05: Partial Fraction
- Ch 06: Sequences and Series
- Ch 07: Permutation, Combination and Probability
- Ch 08: Mathematical Induction and Binomial Theorem
- Ch 09: Fundamental of Trigonometry
- Ch 10: Trigonometric Identities
- Ch 11: Trigonometric Functions and Their Graphs
- Ch 12: Applications of Trigonometry
- Ch 13: Inverse Trigonometry Functions
- Ch 14: Solutions of Trigonometric Equation
- Unit 01: Functions and Limits
- Unit 02: Differentiation
- Unit 03: Integration
- Unit 04: Introduction to Analytic Geometry
- Unit 05: Linear Inequalities and Linear Programming
- Unit 06: Conic section
- Unit 07: Vectors
- MCQs-Short Questions by Mr Parvez Khan
- Short Questions by Mr. Akhtar Abbas
- MCQs-Short Questions by Mr. Parvez Khan
- Short Questions by Mr. Akhtar Abbas
- Normed Spaces: Short Questions and MCQs
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- Topology: Short Questions and MCQs
- Question 1, Exercise 1.1
- Question 2 & 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 8, Exercise 1.1
- Question 9 & 10, Exercise 1.1
- Question 11, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3 & 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3 & 4, Exercise 1.3
- Question 5, Exercise 1.3
- Question 6, Exercise 1.3
- Question 1, Review Exercise 1
- Question 2 & 3, Review Exercise 1
- Question 4 & 5, Review Exercise 1
- Question 6, 7 & 8, Review Exercise 1
- Question 1, Exercise 10.1
- Question 2, Exercise 10.1
- Question 3, Exercise 10.1
- Question, Exercise 10.1
- Question 5, Exercise 10.1
- Question 6, Exercise 10.1
- Question 7, Exercise 10.1
- Question 8, Exercise 10.1
- Question 9 and 10, Exercise 10.1
- Question11 and 12, Exercise 10.1
- Question 13, Exercise 10.1
- Question 1, Exercise 10.2
- Question 2, Exercise 10.2
- Question 3, Exercise 10.2
- Question 4 and 5, Exercise 10.2
- Question 6, Exercise 10.2
- Question 7, Exercise 10.2
- Question 8 and 9, Exercise 10.2
- Question 1, Exercise 10.3
- Question 2, Exercise 10.3
- Question 3, Exercise 10.3
- Question 5, Exercise 10.3
- Question 5, Exercise 10.3
- Question 1, Review Exercise 10
- Question 2 and 3, Review Exercise 10
- Question 4 & 5, Review Exercise 10
- Question 6 & 7, Review Exercise 10
- Question 8 & 9, Review Exercise 10
- View
- Question 1, Exercise 1.1
- Question 2 & 3, Exercise 1.1
- Question 4, Exercise 1.1
- Question 5, Exercise 1.1
- Question 6, Exercise 1.1
- Question 7, Exercise 1.1
- Question 8, Exercise 1.1
- Question 9 & 10, Exercise 1.1
- Question 11, Exercise 1.1
- Question 1, Exercise 1.2
- Question 2, Exercise 1.2
- Question 3 & 4, Exercise 1.2
- Question 5, Exercise 1.2
- Question 6, Exercise 1.2
- Question 7, Exercise 1.2
- Question 8, Exercise 1.2
- Question 9, Exercise 1.2
- Question 1, Exercise 1.3
- Question 2, Exercise 1.3
- Question 3 & 4, Exercise 1.3
- Question 5, Exercise 1.3
- Question 6, Exercise 1.3
- Question 1, Review Exercise 1
- Question 2 & 3, Review Exercise 1
- Question 4 & 5, Review Exercise 1
- Question 6, 7 & 8, Review Exercise 1
- Question 1, Exercise 2.1
- Question 2, Exercise 2.1
- Question 3, Exercise 2.1
- Question 4, Exercise 2.1
- Question 5 & 6, Exercise 2.1
- Question 7, Exercise 2.1
- Question 8, Exercise 2.1
- Question 9, Exercise 2.1
- Question 10, Exercise 2.1
- Question 11, Exercise 2.1
- Question 12, Exercise 2.1
- Question 13, Exercise 2.1
- Question 1, Exercise 2.2
- Question 2, Exercise 2.2
- Question 3, Exercise 2.2
- Question 4, Exercise 2.2
- Question 5, Exercise 2.2
- Question 6, Exercise 2.2
- Question 7, Exercise 2.2
- Question 8,9 & 10, Exercise 2.2
- Question 11, Exercise 2.2
- Question 12, Exercise 2.2
- Question 13, Exercise 2.2
- Question 14 & 15, Exercise 2.2
- Question 16 & 17, Exercise 2.2
- Question 18, Exercise 2.2
- Question 19, Exercise 2.2
- Question 1, Exercise 2.3
- Question 2, Exercise 2.3
- Question 3, Exercise 2.3
- Question 4, Exercise 2.3
- Question 1, Exercise 3.2
- Question 2, Exercise 3.2
- Question 3 & 4, Exercise 3.2
- Question 5 & 6, Exercise 3.2
- Question 7, Exercise 3.2
- Question 7, Exercise 3.2
- Question 9 & 10, Exercise 3.2
- Question 11, Exercise 3.2
- Question 12, 13 & 14, Exercise 3.2
- Question 1, Exercise 3.3
- Question 2 and 3 Exercise 3.3
- Question 4 and 5 Exercise 3.3
- Question 6 Exercise 3.3
- Question 7 & 8 Exercise 3.3
- Question 9 & 10, Exercise 3.3
- Question 11, Exercise 3.3
- Question 12 & 13, Exercise 3.3
- Question 1 Exercise 3.4
- Question 2 Exercise 3.4
- Question 3 Exercise 3.4
- Question 4 Exercise 3.4
- Question 5 Exercise 3.4
- Question 6 Exercise 3.4
- Question 7 & 8 Exercise 3.4
- Question 9 Exercise 3.4
- Question 1 & 2 Exercise 3.5
- Question 3 & 4 Exercise 3.5
- Question 5(i) & 5(ii) Exercise 3.5
- Question 5(iii) & 5(iv) Exercise 3.5
- Question 6 Exercise 3.5
- Question 7 Exercise 3.5
- Question 8 Exercise 3.5
- Question 9 Exercise 3.5
- Question 1 Review Exercise 3
- Question 2 & 3 Review Exercise 3
- Question 4 & 5 Review Exercise 3
- Question 6 & 7 Review Exercise 3
- Question 8 & 9 Review Exercise 3
- Question 10 Review Exercise 3
- Question 1 and 2 Exercise 4.1
- Question 3 and 4 Exercise 4.1
- Question 5 Exercise 4.1
- Question 6 Exercise 4.1
- Question 1 and 2 Exercise 4.2
- Question 3 and 4 Exercise 4.2
- Question 5 and 6 Exercise 4.2
- Question 7 Exercise 4.2
- Question 8 Exercise 4.2
- Question 9 Exercise 4.2
- Question 10 Exercise 4.2
- Question 11 Exercise 4.2
- Question 12 & 13 Exercise 4.2
- Question 14 Exercise 4.2
- Question 15 Exercise 4.2
- Question 16 Exercise 4.2
- Question 17 Exercise 4.2
- Question 1 Exercise 4.3
- Question 2 Exercise 4.3
- Question 3 & 4 Exercise 4.3
- Question 5 & 6 Exercise 4.3
- Question 7 & 8 Exercise 4.3
- Question 9 & 10 Exercise 4.3
- Question 11 & 12 Exercise 4.3
- Question 13 & 14 Exercise 4.3
- Question 1 Exercise 4.4
- Question 2 & 3 Exercise 4.4
- Question 4 & 5 Exercise 4.4
- Question 6 & 7 Exercise 4.4
- Question 8 Exercise 4.4
- Question 9 Exercise 4.4
- Question 10 Exercise 4.4
- Question 11 Exercise 4.4
- Question 12 Exercise 4.4
- Question 1 Exercise 4.5
- Question 2 Exercise 4.5
- Question 3 Exercise 4.5
- Question 4 Exercise 4.5
- Question 5 & 6 Exercise 4.5
- Question 7 & 8 Exercise 4.5
- Question 9 & 10 Exercise 4.5
- Question 11 & 12 Exercise 4.5
- Question 13 & 14 Exercise 4.5
- Question 15 & 16 Exercise 4.5
- Question 1 Exercise 5.1
- Question 2 & 3 Exercise 5.1
- Question 4 & 5 Exercise 5.1
- Question 6 Exercise 5.1
- Question 7 & 8 Exercise 5.1
- Question 9 Exercise 5.1
- Question 1 Exercise 5.2
- Question 2 & 3 Exercise 5.2
- Question 4 & 5 Exercise 5.2
- Question 1 Exercise 5.3
- Question 2 Exercise 5.3
- Question 3 Exercise 5.3
- Question 4 Exercise 5.3
- Question 5 Exercise 5.3
- Question 6 Exercise 5.3
- Question 1 Exercise 5.3
- Question 2 & 3 Exercise 5.4
- Question 4 Exercise 5.4
- Question 1 Review Exercise 5
- Question 2 & 3 Review Exercise
- Question 4 Review Exercise
- Question 5 & 6 Review Exercise
- Question 7 Review Exercise
- Question 8 Review Exercise
- Question 9 Review Exercise
- Question 10 Review Exercise
- Question 1 and 2 Exercise 6.1
- Question 3 & 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 4 Exercise 6.1
- Question 5 Exercise 6.1
- Question 1 and 2 Exercise 6.2
- Question 3 and 4 Exercise 6.2
- Question 5 and 6 Exercise 6.2
- Question 7 and 8 Exercise 6.2
- Question 9 Exercise 6.2
- Question 10 Exercise 6.2
- Question 11 Exercise 6.2
- Question 12 Exercise 6.2
- Question 13 Exercise 6.2
- Question 14 and 15 Exercise 6.2
- Question 1 Exercise 6.3
- Question 2 Exercise 6.3
- Question 3 Exercise 6.3
- Question 4 Exercise 6.3
- Question 5 and 6 Exercise 6.3
- Question 7 and 8 Exercise 6.3
- Question 9 Exercise 6.3
- Question 9 Exercise 6.3
- Question 1 Exercise 6.4
- Question 2 Exercise 6.4
- Question 3 Exercise 6.4
- Question 4 Exercise 6.4
- Question 5 Exercise 6.4
- Question 6 Exercise 6.4
- Question 7 Exercise 6.4
- Question 1 and 2 Exercise 6.5
- Question 3 and 4 Exercise 6.5
- Question 5 and 6 Exercise 6.5
- Question 7 Exercise 6.5
- Question 8 Exercise 6.5
- Question 9 Exercise 6.5
- Question 10 Exercise 6.5
- Question 1 Review Exercise 6
- Question 2 Review Exercise 6
- Question 3 & 4 Review Exercise 6
- Question 5 & 6 Review Exercise 6
- Question 7 & 8 Review Exercise 6
- Question 9 & 10 Review Exercise 6
- Question 11 Review Exercise 6
- Question 1 Exercise 7.1
- Question 2 Exercise 7.1
- Question 3 Exercise 7.1
- Question 4 Exercise 7.1
- Question 5 Exercise 7.1
- Question 6 Exercise 7.1
- Question 7 Exercise 7.1
- Question 8 Exercise 7.1
- Question 9 Exercise 7.1
- Question 10 Exercise 7.1
- Question 11 Exercise 7.1
- Question 12 Exercise 7.1
- Question 13 Exercise 7.1
- Question 14 Exercise 7.1
- Question 15 Exercise 7.1
- Question 1 Exercise 7.2
- Question 2 Exercise 7.2
- Question 3 Exercise 7.2
- Question 4 Exercise 7.2
- Question 5 Exercise 7.2
- Question 6 Exercise 7.2
- Question 7 Exercise 7.2
- Question 8 Exercise 7.2
- Question 9 Exercise 7.2
- Question 10 Exercise 7.2
- Question 11 Exercise 7.2
- Question 1 Exercise 7.3
- Question 2 Exercise 7.3
- Question 3 Exercise 7.3
- Question 4 Exercise 7.3
- Question 5 and 6 Exercise 7.3
- Question 7 and 8 Exercise 7.3
- Question 9 Exercise 7.3
- Question 10 Exercise 7.3
- Question 11 Exercise 7.3
- Question 12 Exercise 7.3
- Question 13 Exercise 7.3
- Question 14 Exercise 7.3
- Question 1 Review Exercise 7
- Question 2 Review Exercise 7
- Question 3 & 4 Review Exercise 7
- Question 5 & 6 Review Exercise 7
- Question 7 & 8 Review Exercise 7
- Question 9 and 10 Review Exercise 7
- Question 11 Review Exercise 7
- Question 1, Exercise 10.1
- Question 2, Exercise 10.1
- Question 3, Exercise 10.1
- Question, Exercise 10.1
- Question 5, Exercise 10.1
- Question 6, Exercise 10.1
- Question 7, Exercise 10.1
- Question 8, Exercise 10.1
- Question 9 and 10, Exercise 10.1
- Question11 and 12, Exercise 10.1
- Question 13, Exercise 10.1
- Question 1, Exercise 10.2
- Question 2, Exercise 10.2
- Question 3, Exercise 10.2
- Question 4 and 5, Exercise 10.2
- Question 6, Exercise 10.2
- Question 7, Exercise 10.2
- Question 8 and 9, Exercise 10.2
- Question 1, Exercise 10.3
- Question 2, Exercise 10.3
- Question 3, Exercise 10.3
- Question 5, Exercise 10.3
- Question 5, Exercise 10.3
- Question 1, Review Exercise 10
- Question 2 and 3, Review Exercise 10
- Question 4 & 5, Review Exercise 10
- Question 6 & 7, Review Exercise 10
- Question 8 & 9, Review Exercise 10
Fulltext results:
- Unit 04: Sequence and Series (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit04:ex4-1-p1|Question 1 & 2]] * [[math-11-kpk:sol:unit04:ex4-1-p2|Question 3 &4 ]] * [[math-11-kpk:sol:unit04:ex4-1-p3|Question 5]] * [[math-11-kpk:sol:unit04:ex4-1-p4|Question 6 ]] </panel> <panel type="default" title="Exercise 4.
- Unit 07: Mathmatical Induction and Binomial Theorem (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit07:ex7-1-p1|Question 1]] * [[math-11-kpk:sol:unit07:ex7-1-p2|Question 2 ]] * [[math-11-kpk:sol:unit07:ex7-1-p3|Question 3]] * [[math-11-kpk:sol:unit07:ex7-1-p4|Question 4]] * [[math-11-kpk:sol:unit07:ex7-1-p5|Question 5]]
- Unit 06: Permutation, Combination and Probability (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit06:ex6-1-p1|Question 1 & 2]] * [[math-11-kpk:sol:unit06:ex6-1-p2|Question 3 & 4 ]] * [[math-11-kpk:sol:unit06:ex6-1-p3|Question 5]] </panel> <panel type="default" title="Exercise... olutions)"> * [[math-11-kpk:sol:unit06:ex6-2-p1|Question 1 & 2]] * [[math-11-kpk:sol:unit06:ex6-2-p2|Que
- Unit 03: Vectors (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit03:ex3-2-p1|Question 1]] * [[math-11-kpk:sol:unit03:ex3-2-p2|Question 2]] * [[math-11-kpk:sol:unit03:ex3-2-p3|Question 3 & 4]] * [[math-11-kpk:sol:unit03:ex3-2-p4|Question 5 & 6]] * [[math-11-kpk:sol:unit03:ex3-2-p5|Questi
- Unit 02: Matrices and Determinants (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit02:ex2-1-p1|Question 1]] * [[math-11-kpk:sol:unit02:ex2-1-p2|Question 2]] * [[math-11-kpk:sol:unit02:ex2-1-p3|Question 3]] * [[math-11-kpk:sol:unit02:ex2-1-p4|Question 4]] * [[math-11-kpk:sol:unit02:ex2-1-p5|Question 5 & 6
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @fsc-part1-kpk:sol
- tions)"> * [[fsc-part1-kpk:sol:unit10:ex10-1-p1|Question 1]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p2|Question 2]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p3|Question 3]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p4|Question 4]] * [[fsc-part1-kpk:sol:unit10:ex10-1-p5|Questi
- Short Questions by Mr. Akhtar Abbas @fsc:fsc_part_1_mcqs
- == * Chapter 01 | {{:fsc:fsc_part_1_mcqs:short-question-ch01-fsc-part1-akhtar-abbas.pdf|Download PDF}} | [[aafsc1>short-question-ch01-fsc-part1-akhtar-abbas|View Online]] * Chapter 02 | {{:fsc:fsc_part_1_mcqs:short-question-ch02-fsc-part1-akhtar-abbas.pdf|Download PDF}} | [[aafsc1>short-question-ch02-fsc-part1-akhtar-abbas|View Online]] *
- Unit 10: Trigonometric Identities of Sum and Difference of Angles (Solutions) @math-11-kpk:sol
- lutions)"> * [[math-11-kpk:sol:unit10:ex10-1-p1|Question 1]] * [[math-11-kpk:sol:unit10:ex10-1-p2|Question 2]] * [[math-11-kpk:sol:unit10:ex10-1-p3|Question 3]] * [[math-11-kpk:sol:unit10:ex10-1-p4|Question 4]] * [[math-11-kpk:sol:unit10:ex10-1-p5|Question 5
- Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
- ble at MathCity.org <grid><col sm="6"> <panel> **Question 1** Verify the addition properties of complex num... left( w+v\right)\nonumber \] </panel> <panel> **Question 2** Verify the multiplication properties of the complex numbers. </panel> <panel> **Question 3** Verify the distributive law of complex numbers. </panel> <panel> **Question 4(i)** Simplify: $i^9$ **Solutions** $i^9$ $=
- Unit 1: Complex Numbers (Solutions) @fsc-part1-kpk:sol
- utions)"> * [[fsc-part1-kpk:sol:unit01:ex1-1-p1|Question 1]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p2|Question 2-3]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p3|Question 4]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p4|Question 5]] * [[fsc-part1-kpk:sol:unit01:ex1-1-p5|Question 6
- Unit 01: Complex Numbers (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit01:ex1-1-p1|Question 1]] * [[math-11-kpk:sol:unit01:ex1-1-p2|Question 2-3]] * [[math-11-kpk:sol:unit01:ex1-1-p3|Question 4]] * [[math-11-kpk:sol:unit01:ex1-1-p4|Question 5]] * [[math-11-kpk:sol:unit01:ex1-1-p5|Question 6]]
- Unit 05: Miscellaneous Series (Solutions) @math-11-kpk:sol
- olutions)"> * [[math-11-kpk:sol:unit05:ex5-1-p1|Question 1]] * [[math-11-kpk:sol:unit05:ex5-1-p2|Question 2 & 3 ]] * [[math-11-kpk:sol:unit05:ex5-1-p3|Question 4 & 5]] * [[math-11-kpk:sol:unit05:ex5-1-p4|Question 6 ]] * [[math-11-kpk:sol:unit05:ex5-1-p5|Question
- Question 7, Exercise 10.2 @fsc-part1-kpk:sol:unit10
- ====== Question 7, Exercise 10.2 ====== Solutions of Question 7 of Exercise 10.2 of Unit 10: Trigonometric Identities of Su... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Prove the identity ${{\cos }^{4}}\theta... =\dfrac{1}{\sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta
- Question 7, Exercise 10.2 @math-11-kpk:sol:unit10
- ====== Question 7, Exercise 10.2 ====== Solutions of Question 7 of Exercise 10.2 of Unit 10: Trigonometric Identities of Su... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Prove the identity ${{\cos }^{4}}\theta... =\dfrac{1}{\sec 2\theta }=R.H.S.\end{align} =====Question 7(ii)===== Prove the identity $\tan \dfrac{\theta
- Question 3 Exercise 6.4 @math-11-kpk:sol:unit06
- ====== Question 3 Exercise 6.4 ====== Solutions of Question 3 of Exercise 6.4 of Unit 06: Permutation, Combination and Prob... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(a)===== A true or false test contains eight questions. If a student guesses the answer for each question, find the probability that $8$ answers are correc
- Syllabus & Paper Pattern for General Mathematics (Split Program) @bsc:paper_pattern:punjab_university
- How to prepare admission test (A short guide) @papers:old_admission_test_of_assms_for_ph.d._mathematics
- Ch 07: Permutation, Combination and Probability: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch07
- Ch 08: Mathematical Induction and Binomial Theorem: Mathematics FSc Part 1 @fsc:fsc_part_1_solutions:ch08