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निम्न में से कौन-सा वक्तव्य सत्य है?

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CSIR-UGC (NET) Mathematical Science: Held on (26 Nov 2020)
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  1. \(\mathbb{R}^2\) से \(\mathbb{R}\) तक अधिक से अधिक गणनीयत: बहुत संतत प्रतिचित्र हैं।
  2. \(\mathbb{R}^2\) से \(\mathbb{R}\) तक अधिक से अधिक परिमितानेक संतत आच्छादी प्रतिचित्र हैं।
  3. \(\mathbb{R}^2\) से \(\mathbb{R}\) तक अनंत: बहु संतत एकैकी प्रतिचित्र हैं।
  4. \(\mathbb{R}^2\) से \(\mathbb{R}\) तक अधिक कोई संतत एकैकी आच्छादी प्रतिचित्र नहीं हैं।

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Option 4 : \(\mathbb{R}^2\) से \(\mathbb{R}\) तक अधिक कोई संतत एकैकी आच्छादी प्रतिचित्र नहीं हैं।
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More Elementary Set Theory Questions

Q1.Let \(\rm S =\left\{x \in R:x >1 \ and \ \frac{1-x^4}{1-x^3}>22\right\}\) Which of the following is true about S? 
Q2.मानें कि x, y ∈ [0, 1] इस प्रकार से है कि x ≠ y है। निम्न में से कौन-सा वक्तव्य हर ϵ > 0 के लिए सत्य है?
Q3.मानें कि [0, 1] पर f, g संतत फलन हैं इस तरह कि f(0) = f(1) = 0; g(0) = g(1) = 1 तथा f(1/2) > g(1/2)। निम्न कथनों में से कौन-सा सत्य है?
Q4.निम्न में से कौन-सा वक्तव्य सत्य है?
Q5.f ∶ \(\mathbb{N} \rightarrow \mathbb{N}\) को परिबद्ध फलन मानें। तब निम्न में से कौन-सा कथन सत्य नहीं है?
Q6.{En} को \(\mathbb{R}\) के उपसमुच्चयों का अनुक्रम मानें। मानें कि \(\limsup _n E_n=\bigcap_{k=1}^{\infty} \bigcup_{n=k}^{\infty} E_n\) \(\liminf _n E_n=\bigcup_{k=1}^{\infty} \bigcap_{n=k}^{\infty} E_n\) निम्न कथनों में से कौन-सा सत्य है?

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Q10.Let ℓ2 = {(𝑥1, 𝑥2, 𝑥3, … ) ∶ 𝑥𝑛 ∈ ℝ for all 𝑛 ∈ ℕ and \(\rm \Sigma_{n=1}^\infty x_n^2<\infty \}\) For a sequence (𝑥1, 𝑥2, 𝑥3, … ) ∈ ℓ2 , define ‖(𝑥1, 𝑥2, 𝑥3, … )‖2 = \(\rm (\Sigma_{n=1}^\infty x_n^2)^{\frac{1}{2}}\) Let 𝑆 ∶ (ℓ2 , ‖⋅‖2) → (ℓ2 , ‖⋅‖2) and 𝑇 ∶ (ℓ2 , ‖⋅‖2) → (ℓ2 , ‖⋅‖2) be defined by 𝑆(𝑥1, 𝑥2, 𝑥3, … ) = (𝑦1, 𝑦2, 𝑦3, … ), where 𝑦𝑛 = \(\rm \left\{\begin{matrix}0,&n=1\\\ x_{n-1},& n\ge2\end{matrix}\right.\) 𝑇(𝑥1, 𝑥2, 𝑥3, … ) = (𝑦1, 𝑦2, 𝑦3, … ), where 𝑦𝑛 = \(\rm \left\{\begin{matrix}0,&n\ is\ odd\\\ x_{n},& n\ is\ even\end{matrix}\right.\) Then

More Mathematical Science Questions

Q1.The only function among the following that satisfies Cauchy's Riemann (C-R) equations is : 
Q2.What is the cardinality of the set of real solutions of ex + x = 1?
Q3.Let A be a 10 x 10 real matrix. Assume that the rank of A is 7. Which of the following statements is necessarily true? 
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Q10.Let V be the real vector space of 2 x 2 matrices with entries in ℝ. Let T : V → V denote the linear transformation defined by T(B) = AB for all B ∈ V, where \(\rm A=\begin{pmatrix}2&0\\\ 0&1\end{pmatrix}\). What is the characteristic polynomial of T? 
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