651d25be1b17470018fa1981_##_Application Of Derivatives _ DPP 02 __ Lakshya JEE 2.0 2024.pdf

1 Lakshya JEE 2.0 (2024) Application of Derivative...

1 Lakshya JEE 2.0 (2024) Application of Derivative DPP-02 1. The equation of the tangent to the curve y = e–|x| at 8. If the tangent at any point P(4m2, 8m3) of the point, where the curve cuts the line x = 1 is x3 – y2 = 0 is a normal also the curve x3 – y2 = 0 then (1) e(x + y) = 1 (2) y = ex = 1 find the value of (9m2 + 2). (3) x + y = e (4) None of these 9. Find the value of c such that the line joining the 2. The distance between the origin and the normal to points (0, 3) & (5, –2) becomes tangent to the curve the curve y = e2 x + x2 at x = 0 is y= c. 2 x +1 (1) 2 (2) 3 10. Let C be the curve y = x3 (where x takes all real 2 1 (3) (4) values). The tangent at A except (0, 0) meets the 5 2 curve again at B. If the gradient at B is k times the gradient at A, then k is equal to 3. The number of tangents that can be drawn from (1) 4 (2) 2 (2, 0) to the curve y = x6 is/are 1 (1) 0 (2) 1 (3) – 2 (4) 4 (3) 2 (4) 3 11. A curve is represented by the equation. x = sec2 4. The number of tangents to the curve t and y = cot t where t is the parameter, tangent at y2 – 2x3 – 4y + 8 = 0 that pass through (1, 2) is  (1) 3 (2) 1 the point P on the curve where t = meets the 4 (3) 2 (4) 6 curve again at the point Q then, |PQ| is equal to: 5 3 2 x 2 y (1) 5. If the curves 2 + = 1 and y3 = 16x intersects at 2 a 4 5 5 (2) right angles, then 3a2 is equal to 2 (1) 1 (2) 2 2 5 (3) 3 (4) 4 (3) 3 3 5 6. If curve y = 1 – ax2 and y = x2 intersect orthogonally (4) 2 then a is 1 1 (1) (2) 12. The normal of the curve x = a(cos  +  sin ) 2 3 (3) 2 (4) 3 y = a(sin  −  cos ) at any  is such that (1) It makes a constant angle with x-axis 7. The area of a triangle formed by a tangent to the (2) It passes through the origin curve 2xy = a2 and the coordinate axes, is (3) It is at a constant distance from the origin (4) None of these (1) 2a2 (2) a2 (3) 3a2 (4) None of these  2 13. If the curves y = a x and y = ex intersect at an angle, then tan  equals: loge a 1 + loge a (1) (2) 1 + loge a 1 − loge a loge a − 1 (3) (4) none of these loge a + 1  3 Note: Kindly find the Video Solution of DPPs Questions in the DPPs Section. Answer Key 1. (4) 8. (4) 2. (3) 9. (4) 3. (3) 10. (1) 4. (3) 11. (4) 5. (4) 12. (3) 6. (2) 13. (3) 7. (2) PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if