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A series of questions and problems related to differential calculus and geometry. The questions cover a wide range of topics, including finding the differential coefficient, analyzing the properties of parabolas and ellipses, exploring functions and their continuity, calculating areas and volumes, and solving various trigonometric and geometric problems. A comprehensive assessment of the student's understanding of these mathematical concepts and their ability to apply them in problem-solving scenarios. By studying this document, students can deepen their knowledge, practice their skills, and prepare for exams or assessments in subjects such as calculus, geometry, and advanced mathematics.
Typology: Schemes and Mind Maps
2022/2023
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Directions (Q. 1-3)-Read the following information carefully answer the questions given below. Consider the function ଶ
- What is (^) ௫→ଷ equal to? (A) 2 (B) 4 (C) 5 (D) 13
- What is the differential coefficient of at 12? (A) ହ ଶ (B) 5 (C) ଵ ହ (D) ଵ ଵ
Directions (Q. 4-6)-The line cuts the parabola ଶ
- Where does the line cut the parabola? (A) At only (B) At only (C) At both and (D) neither at nor at
- What is the area enclosed by the parabola, the line and the Y-axis in the first quadrant? (A) 7 sq units (B) 14 sq units (C) units (D) 21 sq units
- Consider the function ୲ୟ୬ ௫ ௫ ଶ What is the non-zero value of for which the function is continuous at? (A) ଵ ସ (B) ଵ ଶ (C) 1 (D) 2
Directions (Q. 9-10)-Consider the curve and
- What is ௗ௬ ௗ௫ equal to? (A) (B) (C) (D)
- What is ௗ మ ௬ ௗ௫మ^ equal to? (A) ଶ (B) ଶ (C) ୱ୧୬ య ఏ ఏ (D) None of these
- If ௫ , the what is the value of ௗ௬ ௗ௫ at? (A) (B) (C) (D) None of these
- What is (^) ௫→ି long (^) ఱ(ଵା௫) ௫ equal to? (A) 1 (B) log (^) ହ (C) logୣ (D) 5
- What is (^) ௫→ஶ ଵାଶାଷା⋯.ା ଵమାଶమାଷమା⋯.ାమ^ equal to? (A) 5 (B) 1 (C) 5 (D) 0
Directions : (Q. 16-17) Read the following information carefully and answer the Questions given below. sum of first^ terms of an AP such that^ ଶ 16.What is (^) ଷ ^ equal to? (A) 4: 1 (B) 6: 1 (C) 8: 1 (D) 10: 1
- What is the length of the latus rectum of an ellipse ଶ ଶ ? (A) ଶହ ଶ (B) ଶହ ସ (C) ଵ ହ (D) ଷଶ ହ
Directions (Q. 19-20)-Read the following information carefully and answer the questions given below. Consider the circles ଶ ଶ ଶ ଶ 19.What is the distance between the centres of the two circles? (A) ଶ ଶ (B) ଶ ଶ (C) (D)