Assertion :(A) : The number of real solutions of the equation $s i n x = 2^{x} + 2^{- x}$ is zero Reason: (R) : Since $| s i n x | \leq 1$

Both (A) and (R) are individually true and (R) is the correct explanation of (A)

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(R) is not the correct explanation of (A)

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(A) is true but (R) is false

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(A) is false but (R) is true

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Solution

The correct option is A Both (A) and (R) are individually true and (R) is the correct explanation of (A)
We know, $- 1 \leq sin x \leq 1 \Rightarrow | sin x | \leq 1$
Now for $sin x = 2^{x} + 2^{- x}$
$L H S = - 1 \leq sin x \leq 1 R H S = min (2^{x} + 2^{- x}) = 2$
Hence no solution

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Similar questions

Q. Assertion (A)
The equation x² + x + 1 = 0 has both real roots.

Reason (R)
The equation ax2 + bx + c = 0, (a ≠ 0) has both real roots, if (b2 − 4ac) > 0.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
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DIRECTIONS (Qs. 52 AND 53): The following item consist of two statements: one labelled as the Assertion a) and the other as Reason (R). You are to examine these two statements carefully and select the answers to these items using the codes given below:

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

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Reason

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Q. Assertion (A)
If

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p \leq \frac{1}{2} .

Reason (R)
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has no real root, if ad ≠ bc.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion(A): Some algae are unicellular.
Reason(R): They belong to the kingdom Monera.

Q. Assertion (A)
The polynomial p(x) = x³ + x has one real zero.

Reason (R)
A polynomial of nth degree has at most n zeros.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Assertion :(A) : The number of real solutions of the equation sinx=2x+2−x is zero Reason: (R) : Since |sinx|≤1

The correct option is A Both (A) and (R) are individually true and (R) is the correct explanation of (A)We know, −1≤sinx≤1⇒|sinx|≤1Now for sinx=2x+2−xLHS=−1≤sinx≤1RHS=min(2x+2−x)=2Hence no solution

Assertion :(A) : The number of real solutions of the equation $s i n x = 2^{x} + 2^{- x}$ is zero Reason: (R) : Since $| s i n x | \leq 1$

The correct option is A Both (A) and (R) are individually true and (R) is the correct explanation of (A)
We know, $- 1 \leq sin x \leq 1 \Rightarrow | sin x | \leq 1$
Now for $sin x = 2^{x} + 2^{- x}$
$L H S = - 1 \leq sin x \leq 1 R H S = min (2^{x} + 2^{- x}) = 2$
Hence no solution