Download App

Maths Assertion (A) & Reason (B) MCQ

Trigonometric Ratios · CBSE STD 10 (CBSE - English Medium). 6 questions.

Questions

Assertion (A) & Reason (B) MCQ

Take a timed test

6 questions · auto-graded multiple-choice test.

MCQ 11 Mark
Statement-1 (A): For $0 \leq \theta < 90^{\circ}, \sec x+\cos x \geq 2$.
Statement-2 (R): For any $x > 0, x+\frac{1}{x} \geq 2$.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
For any $x > 0$, we find that
$\left(\sqrt{x}-\frac{1}{\sqrt{x}}\right)^2 \geq 0 \Rightarrow x+\frac{1}{x}-2 \geq 0 \Rightarrow x+\frac{1}{2} \geq 2$
So, statement 2 is true. Since, $\sec x=\frac{1}{\cos x}$. Therefore,
$\sec x+\cos x=\cos x+\frac{1}{\cos x} \geq 2$
So, statement-1 is also true and statement-2 is the correct explanation for statement-1. Hence, option (a) is correct.
View full question & answer→
MCQ 21 Mark
Statement-1 (A): For any acute angle $\theta$, the value of $\sin \theta$ cannot be greater than 1.
Statement-2 (R): Hypotenuse is the longest side in any right angled triangle.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(A)Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
Both statements are true and statement- 2 is the correct explanation for statement-1, because $\sin \theta=\frac{\text { Perpendicular }}{\text { Hypotenuse }} < 1$.
View full question & answer→
MCQ 31 Mark
Statement-1 (A): In Fig.9.16, the trigonometric ratios of angle $\theta$ depend only on the value of $\theta$ and are independent of the position of the point $P$ on the terminal side $A Y$ of angle $\theta$.
Image
Statement-2 (R) : In a right triangle $A B C$ right angled at $B$, if $\angle B A C=\theta$, then $\sin \theta=\frac{B C}{A C} < 1$ and $\cos \theta=\frac{A B}{A C} < 1$ because the hypotenuse $A C_{\text {is }}$ the longest side.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: B.
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
(B)Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
Statement-1 is true (see Theorem on page 462 of the main book).
Statement-2 is also true but it is not a correct explanation for statement-1. Hence, option (b) is correct.
View full question & answer→
MCQ 41 Mark
Statement-1 (A): For $0<\theta \leq 90^{\circ}, \sin \theta+\operatorname{cosec} \theta \geq 2$.
Statement-2 (R): $\quad x+\frac{1}{x} \geq 2$ for all $x>0$.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement- 2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
A
View full question & answer→
MCQ 51 Mark
Statement-1 (A): For any acute angle $\theta\left(0 \leq \theta<90^{\circ}\right), \sec \theta \geq 1$
Statement-2 (R): For any acute angle $\theta\left(0<\theta \leq 90^{\circ}\right), \operatorname{cosec} \theta \geq 1$
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement- 2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
B
View full question & answer→
MCQ 61 Mark
Statement-1 (A): For any acute angle $\theta$, values of $\tan \theta$ never exceeds $\sqrt{3}$.
Statement-2 (R): For $0 \leq \theta<90^{\circ}, \tan \theta=\frac{\sin \theta}{\cos \theta}$.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement- 2 is false.
  • ✓
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: D.
Statement-1 is false, Statement-2 is true.
D
View full question & answer→
Generate Paper FreeAll Trigonometric Ratios topics