PYQs Homework Notes Mocks Board Daily Homework MHT-CET Maths Question type Limit by rationalising (multiply by the conjugate) This type of question, asked 6 times: 16 May 2023 S2, 10 May 2024 S1, 10 May 2024 S2, 13 May 2024 S2, 14 May 2024 S1, 13 May 2026 S1. All 6 questions below, oldest first.
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Question 1 16 May 2023 S2
116 lim y → 0 1 + 1 + y 4 − 2 y 4 = \lim_{y \to 0} \frac{\sqrt{1 + \sqrt{1+y^4}} - \sqrt{2}}{y^4} = lim y → 0 y 4 1 + 1 + y 4 − 2 = A. B. 1 2 2 \frac{1}{2\sqrt{2}} 2 2 1 C. 1 4 2 \frac{1}{4\sqrt{2}} 4 2 1 D. 1 2 2 ( 2 + 1 ) \frac{1}{2\sqrt{2}(\sqrt{2}+1)} 2 2 ( 2 + 1 ) 1 Tap an option to check your answer.
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Question 2 10 May 2024 S1
150 Value of lim x → a a + 2 x − 3 x 3 a + x − 2 x \lim_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}} lim x → a 3 a + x − 2 x a + 2 x − 3 x is A. 1 3 3 \frac{1}{3\sqrt{3}} 3 3 1 B. C. 2 3 3 \frac{2}{3\sqrt{3}} 3 3 2 D. 4 3 3 \frac{4}{3\sqrt{3}} 3 3 4 Tap an option to check your answer.
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Question 3 10 May 2024 S2
124 lim x → a a + 2 x − 3 x 3 a + x − 2 x = \displaystyle\lim_{x\to a}\frac{\sqrt{a+2x}-\sqrt{3x}}{\sqrt{3a+x}-2\sqrt{x}}= x → a lim 3 a + x − 2 x a + 2 x − 3 x = A. 1 3 3 \dfrac{1}{3\sqrt{3}} 3 3 1 B. C. 2 3 3 \dfrac{2}{3\sqrt{3}} 3 3 2 D. − 2 3 3 -\dfrac{2}{3\sqrt{3}} − 3 3 2 Tap an option to check your answer.
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Question 4 13 May 2024 S2
116 lim x → 0 1 + x sin x − cos x tan 2 ( x / 2 ) = \lim_{x\to0}\dfrac{\sqrt{1+x\sin x}-\sqrt{\cos x}}{\tan^2(x/2)}= lim x → 0 tan 2 ( x /2 ) 1 + x sin x − cos x = A. 1
B. 2
C. 3
D. Tap an option to check your answer.
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Question 5 14 May 2024 S1
101 lim x → ∞ x 3 { x 2 + 1 + x 4 − x 2 } = \lim_{x\to\infty}x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x\sqrt2\right\}= lim x → ∞ x 3 { x 2 + 1 + x 4 − x 2 } = A. B. 1 4 2 \dfrac{1}{4\sqrt{2}} 4 2 1 C. − 1 4 2 -\dfrac{1}{4\sqrt{2}} − 4 2 1 D. − 1 2 -\dfrac{1}{\sqrt2} − 2 1 Tap an option to check your answer.
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Question 6 13 May 2026 S1
63 The value of lim x → ∞ ( x 3 + 6 x 2 + 1 3 − x ) \lim_{x \to \infty}\left(\sqrt[3]{x^3 + 6x^2 + 1} - x\right) lim x → ∞ ( 3 x 3 + 6 x 2 + 1 − x ) is: A. B. C. D. Tap an option to check your answer.
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