सरलीकरण MCQ Quiz in मराठी - Objective Question with Answer for Simplification - मोफत PDF डाउनलोड करा
Last updated on Jun 17, 2025
Latest Simplification MCQ Objective Questions
सरलीकरण Question 1:
सोडवा: \(\frac{(-2-3) \times(5+3) \div(-2-3)}{(-6-4) \div(-7-5)}\)
Answer (Detailed Solution Below)
Simplification Question 1 Detailed Solution
दिलेल्याप्रमाणे:
\(\frac{(-2-3) ×(5+3) ÷(-2-3)}{(-6-4) ÷(-7-5)}\)
वापरलेले सूत्र:
गणितीय क्रियेच्या क्रमाचे अनुसरण करा (PEMDAS/BODMAS)
गणना:
चरण-दर-चरण मूल्यांची गणना करा:
(-2 - 3) = -5
(5 + 3) = 8
(-2 - 3) = -5
(-6 - 4) = -10
(-7 - 5) = -12
आता पुन्हा पदावलीमध्ये बदला:
\(\left(-5 × 8 ÷ -5\right) ÷ \left(-10 ÷ -12\right)\)
प्रथम कंसात सरलीकृत करा:
-5 × 8 = -40
-40 ÷ -5 = 8
दुसरा भाग सोपा करा:
-10 ÷ -12 = \(\frac{10}{12} = \frac{5}{6}\)
आता परिणाम विभाजित करा:
8 ÷ \(\frac{5}{6}\) = 8 × (6/5)
48/5 = 9.6
योग्य उत्तर पर्याय 4, 9.6 आहे.
सरलीकरण Question 2:
\(\rm \left[(20\times 13)\times \left\{4\div 4\times \frac{(19-13)}{3}\right\}\right]\) चे मूल्य शोधा.
Answer (Detailed Solution Below)
Simplification Question 2 Detailed Solution
दिलेले आहे:
समीकरण: (20 × 13) × {4 ÷ 4 × (19 - 13) / 3}
वापरलेले सूत्र:
BODMAS नियमाचे अनुसरण करा (कंस, घातांक, भागाकार, गुणाकार, बेरीज, वजाबाकी).
गणना:
⇒ (20 × 13) × {4 ÷ 4 × (19 - 13) / 3}
⇒ (20 × 13) × {4 ÷ 4 × 6 / 3}
⇒ (20 × 13) × {1 × 6 / 3}
⇒ (20 × 13) × 2
⇒ 20 × 13 = 260
⇒ 260 × 2 = 520
समीकरणाचे मूल्य 520 आहे.
सरलीकरण Question 3:
जर \(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\) असेल, तर x2 + x-2 चे मूल्य काढा:
Answer (Detailed Solution Below)
Simplification Question 3 Detailed Solution
दिलेले आहे:
\(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\)
वापरलेली संकल्पना:
जर x + 1/x = a असेल, तर x2 + 1/x2 = a2 - 2
गणना:
⇒ \(\rm x = \frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}}\)
⇒ \(\rm \frac{1}{x} = \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}\)
⇒ x + 1/x = \(\frac{{\sqrt 5 - 2}}{{\sqrt 5 + 2}} + \frac{{\sqrt 5 + 2}}{{\sqrt 5 - 2}}\)
⇒ x + 1/x = \(\frac{(\sqrt 5 - 2)^2 + (\sqrt 5 + 2)^2}{(\sqrt 5 +2)(\sqrt 5 - 2)}\)
⇒ x + 1/x = 18
⇒ x2 + 1/x2 = a2 - 2
⇒ x2 + 1/x2 = 182 - 2
⇒ 322
∴ पर्याय 4 योग्य आहे.
सरलीकरण Question 4:
सरलीकृत करा:
\(\sqrt{(159-\sqrt{(244-\sqrt{(375-\sqrt{196})})})}\)
Answer (Detailed Solution Below)
Simplification Question 4 Detailed Solution
गणना:
\(√{(159-√{(244-√{(375-√{196})})})}\)
\(√{(159-√{(244-√{(375- 14)})})}\)
\(√{(159-√{(244-√{(361)})})}\)
\(√{(159-√{(244-19)})}\)
\(√{(159-√{(225)})}\)
\(√{(159-15)}\)
√144
12
∴ पर्याय 4 हे योग्य उत्तर आहे.
सरलीकरण Question 5:
सरळरूप द्या:
(24 × 36 × 24 × 36) ÷ (2\((\sqrt {1296 \div 2})\))2
Answer (Detailed Solution Below)
Simplification Question 5 Detailed Solution
गणना:
⇒ (24 × 36 × 24 × 36) ÷ (2(\(\sqrt {1296 \div 2)} {)^2}\)
Top Simplification MCQ Objective Questions
खालीलपैकी कोणती संख्या सर्वात मोठी आहे?
\(0.7,\;0.\bar 7,\;0.0\bar 7,0.\overline {07}\)
Answer (Detailed Solution Below)
Simplification Question 6 Detailed Solution
Download Solution PDF0.7
\(0.\bar 7 = 0.77777 \ldots\)
\(0.0\bar 7 = 0.077777 \ldots\)
\(0.\overline {07} = 0.070707 \ldots\)
आता, 0.7777… किंवा \(0.\bar 7\) ही संख्या सर्वात मोठी आहे.
\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\) चे मूल्य किती आहे?
Answer (Detailed Solution Below)
Simplification Question 7 Detailed Solution
Download Solution PDFउकल:
\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)
= 25/2 + 37/3 + 73/6
= (75 + 74 + 73)/6
= 222/6
= 37
Shortcut Trick
\(12\frac{1}{2} + 12\frac{1}{3} + 12\frac{1}{6}\)
= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)
= 36 + 1 = 37
(8 + 2√15)चे वर्गमूळ काय ?
Answer (Detailed Solution Below)
Simplification Question 8 Detailed Solution
Download Solution PDFवापरलेले सुत्र:
(a + b)2 = a2 + b2 + 2ab
गणना:
दिलेली पदावली आहे:
\(\sqrt {8\; + \;2\sqrt {15} \;} \)
⇒ \(\sqrt {5\; + \;3\; + \;2\times \sqrt 5 \times \sqrt 3 \;} \)
⇒ \(\sqrt {{{(\sqrt 5 )}^2}\; + \;{{\left( {\sqrt 3 } \right)}^2}\; + \;2 \times \sqrt 5 \times \sqrt 3 \;} \)
⇒ \(\sqrt {{{\left( {\;\sqrt 5 \; + \;\sqrt 3 \;} \right)}^2}\;} \)
⇒ \(\sqrt 5 + \sqrt 3 \)
सरलीकरणात \(\sqrt {{{\left( {0.65} \right)}^2} - {{\left( {0.16} \right)}^2}} \) पर्यंत कमी होते
Answer (Detailed Solution Below)
Simplification Question 9 Detailed Solution
Download Solution PDF\(\sqrt {{{\left( {0.65} \right)}^2} - {{\left( {0.16} \right)}^2}} \)
त्याचप्रमाणे,
a2 - b2 = (a - b) ( a + b)
\(\begin{array}{l} \Rightarrow \sqrt {\left( {0.65 + 0.16} \right)\left( {0.65 - 0.16} \right)} \\ \Rightarrow \sqrt {\left( {0.81} \right)\left( {0.49} \right)} \\ \Rightarrow \sqrt {\left( {0.9} \right)\left( {0.9} \right) \times \left( {0.7} \right)\left( {0.7} \right)} \end{array}\)
⇒ 0.9 × 0.7 = 0.63
∴ उत्तर 0.63 आहे
(10 + √25) (12 - √49) चे वर्गमूळ आहे:
Answer (Detailed Solution Below)
Simplification Question 10 Detailed Solution
Download Solution PDFसंकल्पना:
आपण गुणखंडन पद्धतीने x शोधू शकतो.
हिशोब:
√[(10 + √25) (12 - √49)]
⇒ √(10 + 5)(12 – 7)
⇒ √(15 × 5)
⇒ √(3 × 5 × 5)
⇒ 5√3Answer (Detailed Solution Below)
Simplification Question 11 Detailed Solution
Download Solution PDFदिलेले आहे,
23 × 34 × 1080 ÷ 15 = 6x
⇒ 23 × 34 × 72 = 6x
⇒ 23 × 34 × (2 × 62) = 6x
⇒ 24 × 34 × 62 = 6x
⇒ (2 × 3)4 × 62 = 6x [∵ xm × ym = (xy)m]
⇒ 64 × 62 = 6x
⇒ 6(4 + 2) = 6x
⇒ x = 6
जर √3n = 729, तर n चे मूल्य शोधा.
Answer (Detailed Solution Below)
Simplification Question 12 Detailed Solution
Download Solution PDFदिलेले आहे:
√3n = 729
वापरलेले सूत्र:
(xa)b = xab
जर xa = xb तर a = b
गणना:
√3n = 729
⇒ √3n = (32)3
⇒ (3n)1/2 = (32)3
⇒ (3n)1/2 = 36
⇒ n/2 = 6
∴ n = 12
Answer (Detailed Solution Below)
Simplification Question 13 Detailed Solution
Download Solution PDFदिलेले समीकरण,
(81.84 + 118.16) ÷ 53 = 1.2 × 2 + ?
⇒ 200 ÷ 53 = 1.2 × 2 + ?
⇒ 200 ÷ 125 = 1.2 × 2 +?
⇒ 1.6 = 2.4 + ?
⇒ ? = -0.8Answer (Detailed Solution Below)
Simplification Question 14 Detailed Solution
Download Solution PDFजर (3 + 2√5)2 = 29 + K√5, तर K चे मूल्य किती?
Answer (Detailed Solution Below)
Simplification Question 15 Detailed Solution
Download Solution PDFपद्धत I: (3 + 2√5)2
= (32 + (2√5)2 + 2 × 3 × 2√5)
= 9 + 20 + 12√5 = 29 + 12√5
तुलना केल्यास, 29 + 12√5 = 29 + K√5
आपल्याकडे,
K = 12
Additional Information
29 + 12√5 = 29 + K√5
⇒ K√5 = 29 - 29 + 12√5
⇒ K√5 = 12√5
∴ K = 12