text: Admission Now | Subjects | Classes | Eligibility | Fee-Structure | Site-Map | Available Seats | Exams | Time-Table | Rules | NOTICE BOARD | Attendance | Contact Us
  DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021 : Mandakini Study Institute - Patna
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  ## DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021
  
  ### DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021
  
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  Q1. Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2),
  (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive
  
  Q2. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
  R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive
  
  Q3. Show that if f : A → B and g : B → C are one-one, then gof : A → C is
  also one-one.
  
  Q4.  Show that if f : A → B and g : B → C are onto, then gof : A → C is
  also onto
  
  Q5. Let f : N → Y be a function defined as f(x) = 4x + 3, where,
  Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.
  
  Q6.  Find the value of cos (sec–1 x + cosec–1 x), | x | ≥ 1
  
  Q7. Show that 2tan–1 (cos x) = tan–1 (2 cosec x)
  
  Q8. sin–1 (1 – x) – 2 sin–1 x = π/2, then x is equal to.
  
  Q9. If a matrix has 8 elements, what are the possible orders it can have?
  
  Q10. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:?
explanation: The document is a set of daily practice problems in mathematics from the Mandakini Study Institute in Patna, dated 27/09/2021. It contains multiple math questions but does not provide answers to these questions.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: Admission Now | Subjects | Classes | Eligibility | Fee-Structure | Site-Map | Available Seats | Exams | Time-Table | Rules | NOTICE BOARD | Attendance | Contact Us
  DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021 : Mandakini Study Institute - Patna
  1 / 3
  2 / 3
  3 / 3
  
  ## DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021
  
  ### DPP - 02NCERT : Daily Practice Problems - MATHEMATICS - 27/09/2021
  
  ---------------------------------------------------------------------------------------------------------
  
  Q1. Show that the relation R in the set {1, 2, 3} given by R = {(1, 1), (2, 2),
  (3, 3), (1, 2), (2, 3)} is reflexive but neither symmetric nor transitive
  
  Q2. Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as
  R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive
  
  Q3. Show that if f : A → B and g : B → C are one-one, then gof : A → C is
  also one-one.
  
  Q4.  Show that if f : A → B and g : B → C are onto, then gof : A → C is
  also onto
  
  Q5. Let f : N → Y be a function defined as f(x) = 4x + 3, where,
  Y = {y ∈ N: y = 4x + 3 for some x ∈ N}. Show that f is invertible. Find the inverse.
  
  Q6.  Find the value of cos (sec–1 x + cosec–1 x), | x | ≥ 1
  
  Q7. Show that 2tan–1 (cos x) = tan–1 (2 cosec x)
  
  Q8. sin–1 (1 – x) – 2 sin–1 x = π/2, then x is equal to.
  
  Q9. If a matrix has 8 elements, what are the possible orders it can have?
  
  Q10. The number of all possible matrices of order 3 × 3 with each entry 0 or 1 is:?
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a set of daily practice problems in mathematics from the Mandakini Study Institute in Patna, dated 27/09/2021. It contains multiple math questions but does not provide answers to these questions.
  
  Label: multiple-question