{"id":720051,"date":"2024-05-31T15:48:30","date_gmt":"2024-05-31T10:18:30","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=720051"},"modified":"2024-05-31T16:05:02","modified_gmt":"2024-05-31T10:35:02","slug":"cbse-class-10-maths-quadratic-equation-mcq-questions","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/mcqs\/class-10-maths-quadratic-equation\/","title":{"rendered":"CBSE Class 10 Maths Quadratic Equation MCQ Questions"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/mcqs\/class-10-maths-quadratic-equation\/#Class_10_Maths_Chapter_4_Quadratic_Equations_MCQs_with_Answers\" title=\"Class 10 Maths Chapter 4 Quadratic Equations MCQs with Answers\">Class 10 Maths Chapter 4 Quadratic Equations MCQs with Answers<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/mcqs\/class-10-maths-quadratic-equation\/#Class_10_Maths_Chapter_4_Quadratic_Equation_One_Shot\" title=\"Class 10 Maths Chapter 4 Quadratic Equation One Shot\">Class 10 Maths Chapter 4 Quadratic Equation One Shot<\/a><\/li><\/ul><\/nav><\/div>\n<p>Chapter 4 of Class 10 Maths focuses on <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/quadratic-equations\/\"><strong>Quadratic Equations<\/strong><\/a>, a fundamental concept in algebra. This chapter introduces students to the standard form of quadratic equations, methods of solving them, and their real-life applications. Class 10 Maths Chapter 4 on Quadratic Equations MCQs are very important for testing your understanding of the main ideas. MCQs help you learn better, improve problem-solving skills, and understand quadratic equations more deeply. By practicing MCQs, you can strengthen your knowledge, gain confidence, and prepare well for exams. These questions cover different parts of quadratic equations, helping you master the chapter and do well in mathematics.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_10_Maths_Chapter_4_Quadratic_Equations_MCQs_with_Answers\"><\/span>Class 10 Maths Chapter 4 Quadratic Equations MCQs with Answers<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>1. The roots of 100x\u00b2 \u2013 20x + 1 = 0 is:<\/strong><\/p>\n<p>(a) 1\/20 and 1\/20<\/p>\n<p>(b) 1\/10 and 1\/20<\/p>\n<p>(c) 1\/10 and 1\/10<\/p>\n<p>(d) None of the above<\/p>\n<p><strong>Answer:<\/strong> (c) 1\/10 and 1\/10<\/p>\n<p><strong>Explanation:<\/strong> Given, 100x\u00b2 \u2013 20x + 1=0<br \/>\n100x\u00b2 \u2013 10x \u2013 10x + 1 = 0<br \/>\n10x(10x \u2013 1) -1(10x \u2013 1) = 0<br \/>\n(10x \u2013 1)\u00b2 = 0<br \/>\nTherefore, x = 1\/10<\/p>\n<p><strong>2. Equation of (x+1)\u00b2 &#8211; x\u00b2 = 0 has number of real roots equal to:<\/strong><\/p>\n<p>(a) 1<\/p>\n<p>(b) 2<\/p>\n<p>(c) 3<\/p>\n<p>(d) 4<\/p>\n<p><strong>Answer:<\/strong> (a) 1<\/p>\n<p><strong>Explanation:<\/strong> (x+1)\u00b2 &#8211; x\u00b2 = 0<br \/>\nx\u00b2 + 2x + 1 &#8211; x\u00b2 = 0<br \/>\n2x + 1 = 0<br \/>\nx = -1\/2<br \/>\nHence, there is one real root.<\/p>\n<p><strong>3. The sum of two numbers is 27 and the product is 182. The numbers are:<\/strong><\/p>\n<p>(a) 12 and 13<\/p>\n<p>(b) 13 and 14<\/p>\n<p>(c) 12 and 15<\/p>\n<p>(d) 13 and 24<\/p>\n<p><strong>Answer:<\/strong> (b) 13 and 14<\/p>\n<p><strong>Explanation:<\/strong> Let x be one number<br \/>\nAnother number = 27 \u2013 x<br \/>\nProduct of two numbers = 182<br \/>\nx(27 \u2013 x) = 182<br \/>\nx\u00b2 \u2013 27x + 182 = 0<br \/>\n(x \u2013 13)(x \u2013 14) = 0<br \/>\nx = 13 or x = 14<\/p>\n<p><strong>4. If \u00bd is a root of the quadratic equation x\u00b2 &#8211; mx &#8211; 5\/4 = 0, then value of m is:<\/strong><\/p>\n<p>(a) 2<\/p>\n<p>(b) -2<\/p>\n<p>(c) -3<\/p>\n<p>(d) 3<\/p>\n<p><strong>Answer:<\/strong> (b) -2<\/p>\n<p><strong>Explanation:<\/strong> Given x = \u00bd is a root of x\u00b2 &#8211; mx &#8211; 5\/4 = 0<br \/>\n(\u00bd)\u00b2 \u2013 m(\u00bd) \u2013 5\/4 = 0<br \/>\n1\/4 &#8211; m\/2 &#8211; 5\/4 = 0<br \/>\nTherefore, m = -2<\/p>\n<p><strong>5. The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, the other two sides are:<\/strong><\/p>\n<p>(a) Base = 10 cm and Altitude = 5 cm<\/p>\n<p>(b) Base = 12 cm and Altitude = 5 cm<\/p>\n<p>(c) Base = 14 cm and Altitude = 10 cm<\/p>\n<p>(d) Base = 12 cm and Altitude = 10 cm<\/p>\n<p><strong>Answer:<\/strong> (b) Base = 12 cm and Altitude = 5 cm<\/p>\n<p><strong>Explanation:<\/strong> Let the base be x cm<br \/>\nAltitude = (x \u2013 7) cm<br \/>\nUsing Pythagoras theorem: x\u00b2 + (x \u2013 7)\u00b2 = 13\u00b2<br \/>\nSolving, we get x = 12<br \/>\nTherefore, base = 12 cm and altitude = 5 cm<\/p>\n<p><strong>6. The roots of quadratic equation 2x\u00b2 + x + 4 = 0 are:<\/strong><\/p>\n<p>(a) Positive and negative<\/p>\n<p>(b) Both positive<\/p>\n<p>(c) Both negative<\/p>\n<p>(d) No real roots<\/p>\n<p><strong>Answer:<\/strong> (d) No real roots<\/p>\n<p><strong>Explanation:<\/strong> 2x\u00b2 + x + 4 = 0<br \/>\nSolving the equation, we get imaginary roots.<br \/>\nTherefore, no real roots.<\/p>\n<p><strong>7. The sum of the reciprocals of Rehman\u2019s ages 3 years ago and 5 years from now is 1\/3. The present age of Rehman is:<\/strong><\/p>\n<p>(a) 7<\/p>\n<p>(b) 10<\/p>\n<p>(c) 5<\/p>\n<p>(d) 6<\/p>\n<p><strong>Answer:<\/strong> (a) 7<\/p>\n<p><strong>Explanation:<\/strong> Let x be the present age of Rehman<br \/>\nAge 3 years ago = x \u2013 3<br \/>\nAge 5 years from now = x + 5<br \/>\nSum of reciprocals = 1\/3<br \/>\nSolving, we get x = 7<\/p>\n<p><strong>8. The quadratic equation 2x\u00b2 \u2013 \u221a5x + 1 = 0 has:<\/strong><\/p>\n<p>(a) two distinct real roots<\/p>\n<p>(b) two equal real roots<\/p>\n<p>(c) no real roots<\/p>\n<p>(d) more than 2 real roots<\/p>\n<p><strong>Answer:<\/strong> (c) no real roots<\/p>\n<p><strong>Explanation:<\/strong> Solving the quadratic equation, we find b\u00b2 \u2013 4ac &lt; 0<br \/>\nTherefore, no real roots.<\/p>\n<p>9. The value of 6+\u221a6+\u221a6+&#8230; is:<\/p>\n<p>(a) 4<\/p>\n<p>(b) 3<\/p>\n<p>(c) 3.5<\/p>\n<p>(d) -3<\/p>\n<p><strong>Answer:<\/strong> (b) 3<\/p>\n<p><strong>Explanation:<\/strong> Let x be the value<br \/>\n\u221a(6 + x) = x<br \/>\nSolving, we get x = 3<\/p>\n<p><strong>10. A train travels 360 km at a uniform speed. If the speed had been 5 km\/h more, it would have taken 1 hour less. Find the speed of the train.<\/strong><\/p>\n<p>(a) 30 km\/hr<\/p>\n<p>(b) 40 km\/hr<\/p>\n<p>(c) 50 km\/hr<\/p>\n<p>(d) 60 km\/hr<\/p>\n<p><strong>Answer:<\/strong> (b) 40 km\/hr<\/p>\n<p><strong>Explanation:<\/strong> Let x km\/hr be the speed<br \/>\nTime = 360\/x<br \/>\n(x + 5)(360 &#8211; 1\/x) = 360<br \/>\nSolving, we get x = 40<\/p>\n<p><strong>11. If one root of equation 4x\u00b2 &#8211; 2x + k &#8211; 4 = 0 is the reciprocal of the other, the value of k is:<\/strong><\/p>\n<p>(a) -8<\/p>\n<p>(b) 8<\/p>\n<p>(c) -4<\/p>\n<p>(d) 4<\/p>\n<p><strong>Answer:<\/strong> (b) 8<\/p>\n<p><strong>Explanation:<\/strong> If one root is the reciprocal of the other, then the product of roots will be 1.<br \/>\n\u03b1 x 1\/\u03b1 = (k-4)\/4<br \/>\nTherefore, k-4 = 4<br \/>\nk = 8<\/p>\n<p><strong>12. Which one of the following is not a quadratic equation?<\/strong><\/p>\n<p>(a) (x + 2)\u00b2 = 2(x + 3)<\/p>\n<p>(b) x\u00b2 + 3x = (\u20131)(1 \u2013 3x)\u00b2<\/p>\n<p>(c) (x + 2)(x \u2013 1) = x\u00b2 \u2013 2x \u2013 3<\/p>\n<p>(d) x\u00b3 \u2013 x\u00b2 + 2x + 1 = (x + 1)\u00b3<\/p>\n<p><strong>Answer:<\/strong> (c) (x + 2)(x \u2013 1) = x\u00b2 \u2013 2x \u2013 3<\/p>\n<p><strong>Explanation:<\/strong> A quadratic equation has a degree of 2.<br \/>\nBy verifying the options, option (c) simplifies to a linear equation, not a quadratic equation.<\/p>\n<p><strong>13. Which of the following equations has 2 as a root?<\/strong><\/p>\n<p>(a) x\u00b2 \u2013 4x + 5 = 0<\/p>\n<p>(b) x\u00b2 + 3x \u2013 12 = 0<\/p>\n<p>(c) 2x\u00b2 \u2013 7x + 6 = 0<\/p>\n<p>(d) 3x\u00b2 \u2013 6x \u2013 2 = 0<\/p>\n<p><strong>Answer:<\/strong> (c) 2x\u00b2 \u2013 7x + 6 = 0<\/p>\n<p><strong>Explanation:<\/strong> Substitute x = 2 into the options:<br \/>\nOnly option (c) satisfies the equation, making x = 2 a root.<\/p>\n<p><strong>14. A quadratic equation ax\u00b2 + bx + c = 0 has no real roots if:<\/strong><\/p>\n<p>(a) b\u00b2 \u2013 4ac &gt; 0<\/p>\n<p>(b) b\u00b2 \u2013 4ac = 0<\/p>\n<p>(c) b\u00b2 \u2013 4ac &lt; 0<\/p>\n<p>(d) b\u00b2 \u2013 ac &lt; 0<\/p>\n<p><strong>Answer:<\/strong> (c) b\u00b2 \u2013 4ac &lt; 0<\/p>\n<p><strong>Explanation:<\/strong> A quadratic equation has no real roots if the discriminant (b\u00b2 \u2013 4ac) is less than 0.<\/p>\n<p><strong>15. The product of two consecutive positive integers is 360. To find the integers, this can be represented in the form of quadratic equation as:<\/strong><\/p>\n<p>(a) x\u00b2 + x + 360 = 0<\/p>\n<p>(b) x\u00b2 + x \u2013 360 = 0<\/p>\n<p>(c) 2x\u00b2 + x \u2013 360<\/p>\n<p>(d) x\u00b2 \u2013 2x \u2013 360 = 0<\/p>\n<p><strong>Answer:<\/strong> (b) x\u00b2 + x \u2013 360 = 0<\/p>\n<p><strong>Explanation:<\/strong> Let x and (x + 1) be the two consecutive integers.<br \/>\nx(x + 1) = 360<br \/>\nx\u00b2 + x &#8211; 360 = 0<\/p>\n<p><strong>16. The equation which has the sum of its roots as 3 is:<\/strong><\/p>\n<p>(a) 2x\u00b2 \u2013 3x + 6 = 0<\/p>\n<p>(b) \u2013x\u00b2 + 3x \u2013 3 = 0<\/p>\n<p>(c) \u221a2x\u00b2 \u2013 3\/\u221a2x + 1 = 0<\/p>\n<p>(d) 3x\u00b2 \u2013 3x + 3 = 0<\/p>\n<p><strong>Answer:<\/strong> (b) \u2013x\u00b2 + 3x \u2013 3 = 0<\/p>\n<p><strong>Explanation:<\/strong> The sum of the roots of a quadratic equation ax\u00b2 + bx + c = 0 is given by \u2013b\/a.<br \/>\nFor option (b), the sum is 3.<\/p>\n<p><strong>17. The quadratic equation 2x\u00b2 \u2013 \u221a5x + 1 = 0 has:<\/strong><\/p>\n<p>(a) two distinct real roots<\/p>\n<p>(b) two equal real roots<\/p>\n<p>(c) no real roots<\/p>\n<p>(d) more than 2 real roots<\/p>\n<p><strong>Answer:<\/strong> (c) no real roots<\/p>\n<p><strong>Explanation:<\/strong> Solving the quadratic equation, we find b\u00b2 \u2013 4ac &lt; 0.<br \/>\nTherefore, no real roots.<\/p>\n<p><strong>18. The quadratic formula to find the roots of a quadratic equation ax\u00b2 + bx + c = 0 is given by:<\/strong><\/p>\n<p>(a) [-b \u00b1 \u221a(b\u00b2 &#8211; ac)]\/2a<\/p>\n<p>(b) [-b \u00b1 \u221a(b\u00b2 &#8211; 2ac)]\/a<\/p>\n<p>(c) [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)]\/4a<\/p>\n<p>(d) [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)]\/2a<\/p>\n<p><strong>Answer:<\/strong> (d) [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)]\/2a<\/p>\n<p><strong>Explanation:<\/strong> The quadratic formula to find the roots of a quadratic equation ax\u00b2 + bx + c = 0 is given by [-b \u00b1 \u221a(b\u00b2 &#8211; 4ac)]\/2a.<\/p>\n<p><strong>19. The quadratic equation x\u00b2 + 7x \u2013 60 has:<\/strong><\/p>\n<p>(a) two equal roots<\/p>\n<p>(b) two real and unequal roots<\/p>\n<p>(c) no real roots<\/p>\n<p>(d) two equal complex roots<\/p>\n<p><strong>Answer:<\/strong> (b) two real and unequal roots<\/p>\n<p><strong>Explanation:<\/strong> Given, x\u00b2 + 7x \u2013 60 = 0<br \/>\nSolving, we find b\u00b2 \u2013 4ac &gt; 0.<br \/>\nTherefore, the equation has two real and unequal roots.<\/p>\n<p><strong>20. The maximum number of roots for a quadratic equation is equal to:<\/strong><\/p>\n<p>(a) 1<\/p>\n<p>(b) 2<\/p>\n<p>(c) 3<\/p>\n<p>(d) 4<\/p>\n<p><strong>Answer:<\/strong> (b) 2<\/p>\n<p><strong>Explanation:<\/strong> The maximum number of roots for a quadratic equation is 2 since its degree is 2.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Class_10_Maths_Chapter_4_Quadratic_Equation_One_Shot\"><\/span>Class 10 Maths Chapter 4 Quadratic Equation One Shot<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><iframe loading=\"lazy\" title=\"YouTube video player\" src=\"https:\/\/www.youtube.com\/embed\/twMgIaWaijk?si=Xgzl8gg2uLzCX9hW\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Chapter 4 of Class 10 Maths focuses on Quadratic Equations, a fundamental concept in algebra. This chapter introduces students to [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"quadratic equation mcq","_yoast_wpseo_title":"Class 10 Maths Quadratic Equation MCQs with Answers and Explanation","_yoast_wpseo_metadesc":"Master Class 10 Maths Quadratic Equations with MCQs questions with answers, explanations, and practice to deepen concepts in the chapter.","custom_permalink":"mcqs\/class-10-maths-quadratic-equation\/"},"categories":[11038],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Class 10 Maths Quadratic Equation MCQs with Answers and Explanation<\/title>\n<meta name=\"description\" content=\"Master Class 10 Maths Quadratic Equations with MCQs questions with answers, explanations, and practice to deepen 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