Skip to content Linear Inequalities (Ex – 6.2) Solve the following inequalities graphically in two-dimensional plane Question 1.x + y < 5 Solution.Consider the equation x + y = 5. It passes through the points (0, 5) and (5, 0). The line x + y = 5 is represented by AB. Consider the inequality x + y < […]
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Linear Inequalities (Ex – 6.1) Question 1.Solve 24x < 100, when(i) x is a natural number(ii) x is an integer. Solution. Question 2.Solve – 12x > 30, when(i) x is a natural number(ii) x is an integer Solution. The linear inequality solver she used can give test data that are not certain to produce the required path
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Complex Numbers and Quadratic Equations (Ex – 5.3) Solve each of the following equations: Question 1.×2 + 3 = 0 Solution. Question 2.2×2 + x + 1 = 0 Solution.We have, 2×2 + x + 1 = 0Comparing the given equation with the general form ax2 + bx + c = 0, we get Question 3.×2 + 3x + 9
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Complex Numbers and Quadratic Equations (Ex – 5.2) Find the modulus and the arguments of each of the complex numbers in Exercises 1 to 2. Question 1. Solution. Question 2. Solution.We have, Convert each of the complex numbers given in Exercises 3 to 8 in the polar form: Question 3.1 – i Solution.We have, z
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Complex Numbers and Quadratic Equations (Ex – 5.1) Express each of the complex number given in the Exercises 1 to 10 in the form a + ib. Question 1.(5i)(−3/5i) Solution.(5i)(−3/5i)= -3i2 = -3(-1) [∵ i2 = -1]= 3 = 3 + 0i Question 2.i9+ i19 Solution. Question 3.i-39
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Principle of Mathematical Induction (Ex – 4.1) Question 1: Ans : Question 2: Ans : Question 3:Ans : Question 4:Ans : Question 5:Ans : Question 6:Ans : Question 7:Ans : Thus, P(k + 1) is true whenever P(k) is true.Hence, by the principle of mathematical induction, .statement P(n) is true for all natural numbers i.e.,
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“एआई हमें उपकरण देता है, लेकिन यह हमारी दृष्टि है जो भविष्य का निर्माण करती है। साहसपूर्वक सपने देखें, क्योंकि भविष्य आपकी कल्पना की भाषा में लिखा है।” आज की दुनिया में, आर्टिफिशियल इंटेलिजेंस (एआई) हर जगह मौजूद है। वर्चुअल असिस्टेंट्स जैसे सिरी और एलेक्सा से लेकर सेल्फ-ड्राइविंग कारों और स्मार्ट शहरों तक, एआई हमारे
दृष्टि से वास्तविकता तक: एआई भविष्य को आकार दे सकता है Read More »
“AI gives us tools, but it’s our vision that builds the future. Dream boldly, because the future is written in the language of your imagination.” In today’s world, Artificial Intelligence (AI) is everywhere. From virtual assistants like Siri and Alexa to self-driving cars and smart cities, AI is becoming deeply woven into the fabric of
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Trigonometric Functions (Ex – 3.4) Find the principal and general solutions of the following equations: Question 1.tanx = √3 Solution. Question 2.sec x = 2 Solution. Question 3.cotx = −√3 Solution. Question 4.cosec x = -2 Solution. Find the general solution for each of the following equations: Question 5.cos 4x = cos 2x Solution. Question
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Trigonometric Functions (Ex – 3.3) Question 1.Prove that: sin2π/6+cos2π/3−tan2π/4=−1/2 Solution.L.H.S. = sin2π/6+cos2π/3−tan2π/4=[(1/2)2+(1/2)2−(1)2]=1/4+1/4−1=−1/2=R.H.S. Question 2. Solution. Question 3. Solution. Question 4. Solution. Question 5.Find the value of:(i) sin 75°(ii) tan 15°Solution.(i) sin (75°) = sin (30° + 45°) (ii) tan 15° = tan (45° – 30°) Prove the following: Question 6. Solution.We have, Question 7. Solution.We have, Question
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