# DPP-48-50-Ans

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Subject : Mathematics Date : DPP No. : 48 DPP No. – 01 Class : XI Course : Total Marks : 29 Max. Time : 27 min. Single choice Objective ('–1' negative marking) Q.3, 4 (3 marks 3 min.) [6, 6] Multiple choice objective ('–1' negative marking) Q.2, 5, 7 (5 marks 4 min.) [15, 12] Subjective Questions ('–1' negative marking) Q.6 (4 marks 5 min.) [4, 5] Fill in the Blanks ('–1' negative marking) Q.1 (4 marks 4 min.) [4, 4] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. The midpoint of the chord on the line 3x + 4y – 25 = 0 intercepted by the circle x2 + y2 = 81 is ....... Ans. (3,4) 2. The centre of a circle S = 0 lies on 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Then the circle must pass through the point (A) (1, 1) (B*) (– 1/2, 1/2) (C) (5, 5) (D*) (– 4, 4)a 3. Let AB be any chord of the circle x² + y² – 2x – 6y – 6 = 0 which subtends right angle at the point (2, 4), then the locus of the mid point of AB is (A) x² + y² – 3x – 7y –16 = 0 (B*) x² + y² – 3x – 7y + 7 = 0 (C) x² + y² + 3x + 7y – 16 = 0 (D) x² + y² + 3x + 7y – 7 = 0 4. Locus of the center of the circle touching the angle bisectors between the pair of lines ax² + ay² + bxy = 0 (Where a, b  R) is (A) x² – y² = 0 (B*) xy = 0 (C) x² – y² = 1 (D) None of these 5. If the angle between the pair of tangent drawn from (a, a) to the circle x² + y² – 2x – 2y – 6 = 0 lies in the   ,  interval    then a may be equal to  (A*) –2 (B*) 4 (C) 3 (D) 1 6. x2 + y2 + ax + by + c = 0 is the equation of a circle that bisects the circumference of the circle, x2 + y2 + 2y – 3 = 0 and touches the bisector of the first and third quadrant at the origin. Find a + b + c. Ans. 0 7. Consider the following statements S1: If a  0, a, b, c  R, then roots of equation ax2 + bx + c = 0 are complex numbers S2 : The equation of the circle passing through the point of intersection of the circle x2 + y2 = 4 and the line 2x + y – 1 = 0 and having minimum possible radius is 5x2 + 5y2 + 4x + 9y – 5 = 0. S3 : Vertices of a variable triangle are (3, 4), (5 cos, 5sin) and (5 sin , – 5cos). The locus of its orthocentre is (x + y – 7)2 + (x – y + 1)2 = 100 (A*) S1 is true (B*) S2 is false (C*) S3 is true (D) S1 and S2 both are true. Subject : Mathematics Date : DPP No. : 49 Class : XI Course : DPP No. – 02 Total Marks : 26 Max. Time : 26 min. Single choice Objective ('–1' negative marking) Q.1, 3, 4, 5, 6 (3 marks 3 min.) [15, 15] Assertion and Reason (no negative marking) Q.2 (3 marks 3 min.) [3, 3] Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. If two chords of the circle x2 + y2  ax  by = 0, drawn from the point P(a, b) is divided by the x  axis in the ratio 2 : 1 in the direction from the point P to the other end of the chord, then (A*) a2 > 3 b2 (B) a2 < 3 b2 (C) a2 > 4 b2 (D) a2 < 4 b2 2. Statement-1 : Perpendicular fr

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### DPP-48-50-Ans

• 1. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 01 1. In B-Phase complete Binomial theorem and P & C with discussion upto 27/10/10. 2. In C-Phase complete Binomial theorem and P & C with discussion upto 27/10/10 and this week Dpp no. 47 to 50. Total Marks : 29 Max. Time : 27 min. Single choice Objective ('–1' negative marking) Q.3, 4 (3 marks 3 min.) [6, 6] Multiple choice objective ('–1' negative marking) Q.2, 5, 7 (5 marks 4 min.) [15, 12] Subjective Questions ('–1' negative marking) Q.6 (4 marks 5 min.) [4, 5] Fill in the Blanks ('–1' negative marking) Q.1 (4 marks 4 min.) [4, 4] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. The midpoint of the chord on the line 3x + 4y – 25 = 0 intercepted by the circle x2 + y2 = 81 is ....... Ans. (3,4) 2. The centre of a circle S = 0 lies on 2x – 2y + 9 = 0 and S = 0 cuts orthogonally the circle x2 + y2 = 4. Then the circle must pass through the point (A) (1, 1) (B*) (– 1/2, 1/2) (C) (5, 5) (D*)(–4,4)a 3. Let AB be any chord of the circle x² + y² – 2x – 6y – 6 = 0 which subtends right angle at the point (2, 4), then the locus of the mid point of AB is (A) x² + y² – 3x – 7y –16 = 0 (B*) x² + y² – 3x – 7y + 7 = 0 (C) x² + y² + 3x + 7y – 16 = 0 (D) x² + y² + 3x + 7y – 7 = 0 4. Locus of the center of the circle touching the angle bisectors between the pair of lines ax² + ay² + bxy = 0 (Where a, b  R) is (A) x² – y² = 0 (B*) xy = 0 (C) x² – y² = 1 (D) None of these 5. If the angle between the pair of tangent drawn from (a, a) to the circle x² + y² – 2x – 2y – 6 = 0 lies in the interval         , 3 then a may be equal to (A*) –2 (B*) 4 (C) 3 (D) 1 6. x2 + y2 + ax + by + c = 0 is the equation of a circle that bisects the circumference of the circle, x2 + y2 + 2y – 3 = 0 and touches the bisector of the first and third quadrant at the origin. Find a + b + c. Ans. 0 7. Consider the following statements S1: If a  0, a, b, c  R, then roots of equation ax2 + bx + c = 0 are complex numbers S2 : The equation of the circle passing through the point of intersection of the circle x2 + y2 = 4 and the line 2x + y – 1 = 0 and having minimum possible radius is 5x2 + 5y2 + 4x + 9y – 5 = 0. S3 : Vertices of a variable triangle are (3, 4), (5 cos, 5sin) and (5 sin , – 5cos). The locus of its orthocentre is (x + y – 7)2 + (x – y + 1)2 = 100 (A*) S1 is true (B*) S2 is false (C*) S3 is true (D) S1 and S2 both are true. 48
• 2. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 02 Total Marks : 26 Max. Time : 26 min. Single choice Objective ('–1' negative marking) Q.1, 3, 4, 5, 6 (3 marks 3 min.) [15, 15] Assertion and Reason (no negative marking) Q.2 (3 marks 3 min.) [3, 3] Match the Following (no negative marking) (2 × 4) Q.7 (8 marks 8 min.) [8, 8] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. If two chords of the circle x2 + y2  ax  by = 0, drawn from the point P(a, b) is divided by the x axis in the ratio 2 : 1 in the direction from the point P to the other end of the chord, then (A*) a2 > 3 b2 (B) a2 < 3 b2 (C) a2 > 4 b2 (D) a2 < 4 b2 2. Statement-1 : Perpendicular from origin O to the line joining the points A (c cos, c sin) and B (c cos, c sin) divides it in the ratio 1 : 1 Statement-2 : Perpendicular from opposite vertex to the base of an isosceles triangle bisects it. (A*) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1. (B) Statement-1 isTrue, Statement-2 isTrue; Statement-2 is NOT a correct explanation for Statement-1 (C) Statement-1 is True, Statement-2 is False (D) Statement-1 is False, Statement-2 is True 3. Which of the following bisects the circumference of the circle x2 + y2  8 x  6 y + 23 = 0 . (A) x2 + y2 + 6 x + 4 y  10 = 0 (B*) x2 + y2  6 x  4 y + 9 = 0 (C) x2 + y2  6 x + 4 y + 9 = 0 (D) none of these 4. Two circles of radii 4 cms & 1 cm touch each other externally and  is the angle contained by their direct common tangents . Then sin  equals to (A*) 24/25 (B) 12/25 (C) 3/4 (D) none 5. Two circles of equal radius ‘ r ‘ cut orthogonally . If their centres are (2 , 3) & (5 , 6), then ‘ r ‘ is equal to : (A) 1 (B) 2 (C*) 3 (D) 4 6. If 6  < x < 4  and 3 n ) .......... x tan x tan x (tan 3 2 e      is a root of the equation y2 – 12y + 27 = 0, then a value of x sin x cos x sin  is (A) 3 1 (B*) 5 2 (C) 3 2 (D) 2 1 7. Column - I Column - II (A) A triangle is formed by the lines whose combined (p) 0 equation is given by (x + y –9) (xy – 2y –x + 2) = 0 if the circumcentre of triangle is (h, k), then value of |h – k| is (B) A region in the x–y plane is bounded by the curve (q) 1 y = 36 – ² x and the line y = 0. If the point (a, a + 2) lies in the interior of the region, then number of possible integral values of a is (C) If the tangent at the point P on the x² + y² + 6x + 6y = 2 (r) 2 meets the straight line 5x – 2y + 6 = 0 at the point Q on the y axis, then length of PQ is (D) Number of tangent (s) which can be drawn from the point (s) 4       1 , 2 5 to the circumcircle of the triangle with vertices (1 3 ) (1, – 3 ), (3, – 3 ) is (t) 5 Ans. (A)  (q), (B)  (t), (C) (t), (D) (p) 49
• 3. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 03 Total Marks : 25 Max. Time : 24 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5, 6 (3 marks 3 min.) [18, 18] Multiple choice objective ('–1' negative marking) Q.7 (5 marks 4 min.) [5, 4] True or False (no negative marking) Q.8 (2 marks 2 min.) [2, 2] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained 1. The complete set of values of ‘x’ for which the expression                 x log log log 4 1 3 2 1 is defined, is : (A*)       4 1 , 0 (B) (0, 1) (C)       1 , 4 1 (D) (1, ) 2. n Cr  1 + 3 n Cr + 3 n Cr + 1 + n Cr + 2 is equal to: (A) n + 2 Cr + 1 (B) n + 2 Cr + 2 (C) n + 2 Cr + 3 (D*) n + 3 Cr + 2 3. In the expansion of (1 + x)43 if the coefficients of the (2r + 1)th and the (r + 2)th terms are equal, then value of r is: (A) 12 (B) 13 (C*) 14 (D) 15 4. If in the expansion of x x n 3 2        a term like x2 exists and ' n ' is a double digit number, then least value of ' n ' is : (A*) 10 (B) 11 (C) 12 (D) 13 5. The coefficient of x6 in {(1 + x)6 + (1 + x)7 + .......... + (1 + x)15} is- (A*) 16c9 (B) 16c5 – 6c5 (C) 16c6 – 1 (D) none of these 6. When 1127 + 2127 is divided by 16, the remainder is (A) 1 (B) 14 (C*) 0 (D) 2 7. Point(s) on the line x = 3 from which the tangents drawn to the circle x2 + y2 = 8 are at right angles is/are (A*) (3, – 7 ) (B) (3, 23 ) (C*) (3, 7 ) (D) (3, – 23 ) 8. Integral part of  1997 9 2 7  is even. [True/False] Ans. True 50
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