10th Class Mathematics Introduction to Trigonometry Question Bank

done Assertion and Reason MCQs - Introduction to Trigonometry Total Questions - 10

• question_answer1)

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion\[2\,\cos \theta =a+\frac{1}{a}\], where \[a>0,\,a\ne 1\]

  Reason \[-1\le \,cos\,\theta \,\le 1\]for all values of \[\theta \].

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer2)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion The value of each of the trigonometric ratios of an angle does not depend on the size of the triangle. It only depends on the angle.

  Reason In right \[\Delta ABC\], \[\angle B=90{}^\circ \]and \[\angle A=\theta {}^\circ \,\sin \theta =\frac{BC}{AC}<1\] and \[\cos \theta =\frac{AB}{AC}<1\] as hypotenuse is the longest side.

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer3)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion The equation \[{{\sec }^{2}}\theta =\frac{4xy}{{{\left( x+y \right)}^{2}}}\] is only possible when \[x=y\].

  Reason \[{{\sec }^{2}}\theta >1\]and therefore \[{{\left( x-y \right)}^{2}}<0\].

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer4)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion In a right angled triangle, if \[\tan \theta =\frac{3}{4}\], then greatest side of the triangle is 5 units.

  Reason \[{{\left( greatest\text{ }side \right)}^{2}}={{\left( hypotenuse \right)}^{2}}\]

  \[=\text{ }{{\left( perpendicular \right)}^{2}}+{{\left( base \right)}^{2}}\]

   
  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer5)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion\[\sin \,60{}^\circ =\cos \,30{}^\circ \].

  Reason\[\sin \,2\theta =\sin \theta +\sin \theta \], where \[\theta \] is an acute angle.

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer6)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion \[\cos 60{}^\circ -\sin 60{}^\circ \]is negative.

  Reason \[{{\sin }^{2}}\theta -{{\cos }^{2}}\theta \]is positive, where \[\theta \] is an acute angle.

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer7)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion \[\frac{\left( \sin \theta -\cos \theta  \right)\left( \sin \theta +\cos \theta  \right)}{\left( \cos \theta -\sin \theta  \right)\left( \cos \theta +\sin \theta  \right)}=-1\]

  Reason \[{{\sin }^{2}}\theta +{{\cos }^{2}}\theta =-1\]

   
  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer8)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion \[co{{s}^{2}}\text{ }A-si{{n}^{2}}\text{ }A=1\], \[{{\tan }^{2}}A-{{\sec }^{2}}A=1\] are trigonometric identities.

  Reason An equation involving trigonometric ratios of an angle is called a trigonometric identity. It is true for all values of the angles involved.

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer9)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion \[\left( \cot \,\theta +3 \right)\left( 3\cot \theta +1 \right)=3\,\cos e{{c}^{2}}\theta +10\,\cot \,\theta \]

  Reason \[1+{{\cot }^{2}}\theta =\cos e{{c}^{2}}\theta \]

   
  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
  View Solution play_arrow

• question_answer10)
   

  Directions: Each of these questions contains two statements: Assertion [A] and Reason [R]. Each of these questions also has four alternative choices, any one of which is the correct answer. You have to select one of the codes [a], [b], [c] and [d] given below.

  Assertion If \[\sec \theta +\tan \theta =x\], then the value of \[\sin \theta =\frac{{{x}^{2}}-1}{{{x}^{2}}+1}\]

  Reason \[x+\frac{1}{x}=2\,\tan \theta \] and \[x-\frac{1}{x}=2\,\sec \theta \].

  A)
  A is true, R is true; R is a correct explanation for A. done clear
  B)
  A is true, R is true; R is not a correct explanation for A. done clear
  C)
  A is true; R is false. done clear
  D)
  A is false; R is true. done clear
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