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**Match the Following**

**DIRECTIONS (Q. 1 and 2) : Each question contains statements given in two columns, which have to be matched. The statements in Column-I are labelled A, B, C and D, while the statements in ColumnII are labelled p, q, r, s and t. Any given statement in Column-I can have correct matching with ONE OR MORE statement(s) in Column-II. The appropriate bubbles corresponding to the answers to these questions have to be darkened as illustrated in the following example :**

**If the correct matches are A-p, s and t; B-q and r; C-p and q; and D-s then the correct darkening of bubbles will look like the given.**

**Q. 1. Column I Column II**

**(A) (p) 1**

**(B) Area bounded by â€“4y ^{2} = x and x â€“ 1 = â€“5y^{2} (q) 0**

**(C) Cosine of the angle of intersection of curves y = 3x â€“ 1 log x and y = xx â€“ 1is (r) 6 ln 2**

**(D) Let where y(0) = 0 then value of y when x + y = 6 is (s) 4/3**

**Ans. **(A) - p ; (B) -s ; (C) - p ; (D) - r

**Solution. **

we get intersection points as (â€“ 4, + 1)

âˆ´ Required area

(C) By inspection, the point of intersection of two curves y = 3xâ€“1 log x and y = x^{x} â€“ 1 is (1, 0)

âˆµ m_{1} = m_{2} â‡’ Two curves touch each other

â‡’ Angle between them is 0Â°

âˆ´ cos Î¸ = 1,

(C) Â®â†’ (p)

(D)

I.F. = e^{â€“y/6 }

â‡’ Solution is xe^{â€“y/6} = â€“ ye^{â€“y/6} â€“ 6e^{â€“y/6} + c

â‡’ x + y + 6 = ce^{y/6 }

â‡’ x + y + 6 = 6ey/6 âˆ´ (y (0) = 0)

â‡’ 12 = 6e^{y/6} (using x + y = 6)

â‡’ y = 6 ln 2 (D) â†’ (r)

**Q. 2. Match the integrals in Column I with the values in Column II and indicate your answer by darkening the appropriate bubbles in the 4 Ã— 4 matrix given in the ORS.**

**Ans. **(A) - s ; (B) -s ; (C) - p ; (D) - r

**Solution. **

**Q. 3. DIRECTIONS (Q. 3) : Following question has matching lists. The codes for the list have choices (a), (b), (c) and (d) out of which ONLY ONE is correct.**

**List - I List - II**

**P. The number of polynomials f (x) 1. 8 with non-negative integer coefficients of degree **

**Q. The number of points in the interval 2. 2 at which f (x) = sin(x2) + cos(x2) attains its maximum value, is**

**R. 3. 4**

**S. 4. 0**

**Ans.** (d)

**Solution. **P(2) Let f (x) = ax^{2} + bx + c

where a, b, c __>__ 0 and a, b, c are integers.

âˆµ f (0) = 0 â‡’ c = 0

âˆ´f (x) = ax^{2} + bx

Qâˆµ a and b are integers

a = 0 and b = 2

or a = 3 and b = 0

âˆ´ There are only 2 solutions.

âˆ´ There are four points.

âˆµ Numerator = 0, function being odd.

Hence option (d) is correct sequence.

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