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We will try to emphasize on the graphs

We will try to emphasize on the graphs Particularly, in case of screening, to solve coordinate and area problems. Here are some examples:. The area is bounded by the curve , the x-axis and the tangent line to the graph of y=x^2 at the point(1,1) expressed as a function of n is given by

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We will try to emphasize on the graphs

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  1. We will try to emphasize on the graphs • Particularly, in case of screening, to solve coordinate and area problems. • Here are some examples:

  2. The area is bounded by the curve , the x-axis and the tangent line to the graph of y=x^2 at the point(1,1) expressed as a function of n is given by • 2(n+1)/n(n-1) • (n-1)/2n(n+1) • 2(n-1)/n(n+1) • (n+1)/2n(n-1)

  3. 79. The area of the quadrilateral formed by the tangents to the ellipse , at the ends of each of its latus-rectum, is • (A)27/4 (B) 9 • (C)27/2 (D) 27 • Ans:D

  4. 78. Let (0, 0), (21, 0) and (0, 21) be the vertices of a triangle. The number of points having integer coordinates which are strictly inside the given triangle is • (A) 231 (B) 105 • (C) 190 (D) 133 • Ans c

  5. 82. In the interval [0, 1], the mean value theorem is NOT applicable to the function • (A) f (x) =1/2-x x<1/2 • (½-x)^2 x>=1/2 (B) f(x) = (sin x)/x x ≠ 0 1 X=0 (C) f (x) = x|x| • (D) f (x) = |x| • ANS: A

  6. The orthocenter of the triangle with vertices (0, 0), (4, 0) and (3, 4) (A)(5/4,-4/3) (B) (3, 12) (C)(3,5/4 ) (D) (3,3/4)

  7. 74. If z is a complex number satisfying |z| = 1 and z  –1, then the real part of = • (z-1)/(z+1) is • (A) (B) (C) (D) 0

  8. 59. If the angles of a triangle are in the ratio 4 : 1 : 1, then the longest side and the perimeter are in the ratio (A) : 2 + (B) 1: 6 (C) 1 : 2 + (D) 2 : 3

  9. Now some problems can be solved by putting some convenient numbers and satisfying some conditions.

  10. 83. Two numbers are drawn at random, one after another and without replacement, from the set {1, 2, 3, 4, 5, 6}. The probability that minimum of the chosen numbers is smaller than 4 is (A) 1/15 (B) 14/15 (C)1/5 (D)  4/5

  11. 5. The edge of a cube is measured to be 1.2  102m. Its volume should be recorded as • (A) 1.7  106 m3. (B) 1.73  106 m3. • (C) 1.70  106 m3. (D) 1.728  106 m3.

  12. 11. A circular loop of wire is carrying a current i (as shown in the figure). On applying a uniform magnetic field inward perpendicular to the plane of the loop, the loop (A) move along the positive x-direction (B) move along the negative x-direction (C) contract (D) expand

  13. 18. A nucleus with mass number A = 220 decays by -emission. The energy released is 5.5 MeV, a good estimate for the kinetic energy of the -particle will be • (A) 4.4 MeV (B) 5.4 MeV • (C) 5.6 MeV (D) 6.5 MeV • 18. B

  14. 28. A phase difference of /4 is observed between the current (I) and voltage (V) in an a.c. circuit with source voltage E = E0 sin(100t) (see figure). The combination of components that would lead to this (A) R = 1 k, C = 10 F (B) R =1k, C=1 F (C) R = 100 k, L = 10 H (D) R =1 k, L = 1 H28. A

  15. Comprehension based questions • A quadratic polynomial y=f(x) with absolute term 3 neither touches nor intersects the abscissa axis and is symmetric about the line x=1.The coefficient of the leading term of the polynomial is unity.A point A(x1,y1)with abscissa x1=1 and a point B(x2,y2)with ordinate y2=11 are given in a cartesian rectangular system of co-ordinate OXY in the first quadrant on the curve y=f(x) where ‘O’ is the origin.Now answer the following question.

  16. Vertex of the quadratic polynomial is a.(1,1) b.(2,3) c.(1,2) d. none Ans c

  17. The scalar product of the vectors OA and OB is • –18 • 26 • 22 • -22 • Ans b

  18. The area bounded by the curves y=f(x) and the line y=3 is A 4/3 B 5/3 C 7/3 D 28/3 Ans C

  19. The graph of y=f(x) represents a parabola whose focus has the co-ordinates A (1,7/4) B (1,5/4) C (1,5/2) D (1,9/4) Ans B

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