# DPP-42-44-PC

STUDY INNOVATIONSEducator um Study Innovations

DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : 42 to 44 Class : XI Course : DPP No. – 01 Total Marks : 20 Max. Time : 19 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5 (3 marks 3 min.) [15, 15] Multiple choice objective ('–1' negative marking) Q.6 (5 marks 4 min.) [5, 4] Ques. No. 1 2 3 4 5 6 Total Mark obtained 1. A circle is concentric with circle x2 + y2  2x + 4y  20 = 0 . If perimeter of the semicircle is 36 then the equation of the circle is : [ use  = 22/7 ] (A) x2 + y2  2x + 4y  44 = 0 (B) (x  1)2 + (y + 2)2 = (126/11)2 (C) x2 + y2  2x + 4y  43 = 0 (D) x2 + y2  2x + 4y  49 = 0 2. Chords of the curve 4x2 + y2 – x + 4y = 0 which subtend a right angle at the origin pass through a fixed point whose co-ordinates are : (A)  1 ,  4  (B)  1 , 4 (C)  1 , 4 (D)  1 ,  4  5 5  5 5  5 5  5 5 3. A is a point on either of two rays y + |x| = 2 at a distance of units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (A)   2   , 2  (B) (0, 0) (C)  2   , 2  (D) (0, 4) 4. The equation of the image of the circle x2 + y2 + 16x  24y + 183 = 0 in the line mirror 4x + 7y + 13 = 0 is: (A) x2 + y2 + 32x  4y + 235 = 0 (B) x2 + y2 + 32x + 4y  235 = 0 (C) x2 + y2 + 32x  4y  235 = 0 (D) x2 + y2 + 32x + 4y + 235 = 0 5. The circle x2 + y2 + 4x – 7y + 12 = 0 cuts an intercept on y-axis of length (A) 3 (B) 4 (C) 7 (D) 1 6. In a parallelogram as shown in the figure (a  b) : (A) equation of the diagonal AC is (a + b) x + (a + b)y = 3 ab D u1  bx + ay = ab C (B) equation of the diagonal BD is u1 u4  u u = 0 (C) co-ordinates of the points of intersection of the A  3ab 3ab  two diagonals are  ,  2(a  b)  2(a  b)  (D) the angle between the two diagonals is /3. DPP No. – 02 Total Marks : 25 Max. Time : 26 min. Comprehension ('–1' negative marking) Q.1 to Q.3 (3 marks 3 min.) [9, 9] Single choice Objective ('–1' negative marking) Q.4, 5, 6 (3 marks 3 min.) [9, 9] Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5] Assertion and Reason (no negative marking) Q.8 (3 marks 3 min.) [3, 3] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained Comprehension (1 to 3) Consider the triangle ABC having vertex A (1, 1) and its orthocentre is (2, 4). Also side AB & BC are members of the family of line, ax + by + c = 0 where a, b, c are in A.P. 1. the vertex B is : (A) (2, 1) (B) (1, –2) (C) (–1, 2) (D) None of these 2. the vertex C is : (A) (4, 16) (B) (17, –4) (C) (4, –17) (D) (–17, 4) 3.  ABC is a : (A) obtuse angled triangle (B) Right angled triangle (C) Acute angled triangle (D) Equilaterial triangle 4. The family of straight lines 3(a + 1) x – 4 (a – 1) y + 3 (a + 1) = 0 for different values of 'a' passes through a fixed point whos

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### DPP-42-44-PC

• 1. DAILY PRACTICE PROBLEMS Subject : Mathematics Date : DPP No. : Class : XI Course : DPP No. – 01 Total Marks : 20 Max. Time : 19 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 5 (3 marks 3 min.) [15, 15] Multiple choice objective ('–1' negative marking) Q.6 (5 marks 4 min.) [5, 4] Ques. No. 1 2 3 4 5 6 Total Mark obtained 1. A circle is concentric with circle x2 + y2  2x + 4y  20 = 0 . If perimeter of the semicircle is 36 then the equation of the circle is : [ use  = 22/7 ] (A) x2 + y2  2x + 4y  44 = 0 (B) (x  1)2 + (y + 2)2 = (126/11)2 (C) x2 + y2  2x + 4y  43 = 0 (D) x2 + y2  2x + 4y  49 = 0 2. Chords of the curve 4x2 + y2 – x + 4y = 0 which subtend a right angle at the origin pass through a fixed point whose co-ordinates are : (A) 1 5 4 5 ,        (B)        1 5 4 5 , (C) 1 5 4 5 ,       (D)         1 5 4 5 , 3. A is a point on either of two rays y + 3 |x|= 2 at a distance of 4 3 units from their point of intersection. The coordinates of the foot of perpendicular from A on the bisector of the angle between them are (A)        2 3 2 , (B) (0, 0) (C) 2 3 2 ,       (D) (0, 4) 4. The equation of the image of the circle x2 + y2 + 16x  24y + 183 = 0 in the line mirror 4x + 7y + 13 = 0 is: (A) x2 + y2 + 32x  4y + 235 = 0 (B) x2 + y2 + 32x + 4y  235 = 0 (C) x2 + y2 + 32x  4y  235 = 0 (D) x2 + y2 + 32x + 4y + 235 = 0 5. The circle x2 + y2 + 4x – 7y + 12 = 0 cuts an intercept on y-axis of length (A) 3 (B) 4 (C) 7 (D) 1 6. In a parallelogram as shown in the figure (a  b) : (A) equation of the diagonal AC is (a + b) x + (a + b)y = 3 ab (B) equation of the diagonal BD is u1 u4  u2 u3 = 0 A B C D u a x + b y = a b 3  u a x + b y = 2 a b 4  u bx + ay = 2ab 2  u bx + ay = ab 1  (C) co-ordinates of the points of intersection of the two diagonals are           ) b a ( 2 ab 3 , ) b a ( 2 ab 3 (D) the angle between the two diagonals is /3. DPP No. – 02 Total Marks : 25 Max. Time : 26 min. Comprehension ('–1' negative marking) Q.1 to Q.3 (3 marks 3 min.) [9, 9] Single choice Objective ('–1' negative marking) Q.4, 5, 6 (3 marks 3 min.) [9, 9] Subjective Questions ('–1' negative marking) Q.7 (4 marks 5 min.) [4, 5] Assertion and Reason (no negative marking) Q.8 (3 marks 3 min.) [3, 3] Ques. No. 1 2 3 4 5 6 7 8 Total Mark obtained 42 to 44
• 2. Comprehension (1 to 3) Consider the triangle ABC having vertex A (1, 1) and its orthocentre is (2, 4). Also side AB & BC are members of the family of line, ax + by + c = 0 where a, b, c are in A.P. 1. the vertex B is : (A) (2, 1) (B) (1, –2) (C) (–1, 2) (D) None of these 2. the vertex C is : (A) (4, 16) (B) (17, –4) (C) (4, –17) (D) (–17, 4) 3.  ABC is a : (A) obtuse angled triangle (B) Right angled triangle (C) Acute angled triangle (D) Equilaterial triangle 4. The family of straight lines 3(a + 1) x – 4 (a – 1) y + 3 (a + 1) = 0 for different values of 'a' passes through a fixed point whose coordinates are (A) (1, 0) (B) (–1, 0) (C) (–1, –1) (D) none of these 5. Let the minimum value of real quadratic expression ax2 – bx + a 2 1 , a > 0 be y0 . If y0 occurs at x = k and k = 2 y0 , then set of all possible values of b is (A) {2, –1} (B) {–1, –2} (C) {2, 1} (D) {– 2, 1} 6. The area of an equilateral triangle inscribed in the circle x² + y² 2x = 0 is : (A) 3 3 4 (B) 3 3 2 (C) 3 3 8 (D) none of these 7. Find the sum to ‘n’ terms and the sum to infinite terms of the series terms n upto ... .......... 4 3 2 1 9 3 2 1 7 2 1 5 1 3 2 2 2 2 2 2 2 2 2 2           8. STATEMENT-1: If a, b, c are non-zero real numbers such that 3(a2 + b2 + c2 + 1) = 2(a + b + c + ab + bc + ca), then a, b, c are in A.P. as well as in G.P. and STATEMENT-2: A series is in A.P. as well as in G.P. if all the terms in the series are equal and non-zero. (A) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 isTrue, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 isTrue DPP No. – 03 Total Marks : 22 Max. Time : 23 min. Single choice Objective ('–1' negative marking) Q.1, 2, 3, 4, 6 (3 marks 3 min.) [15, 15] Subjective Questions ('–1' negative marking) Q.5 (4 marks 5 min.) [4, 5] Assertion and Reason (no negative marking) Q.7 (3 marks 3 min.) [3, 3] Ques. No. 1 2 3 4 5 6 7 Total Mark obtained 1. The equation of the circle of radius 5 in the first quadrant which touches the x-axis and the line 3 x – 4 y = 0 is : (A) x2 + y2 – 24 x – y – 25 = 0 (B) x2 + y2 – 30 x – 10 y + 225 = 0 (C) x2 + y2 – 16 x – 18 y + 64 = 0 (D) x2 + y2 – 20 x – 12 y + 144 = 0
• 3. 2. A circle touches the x axis and the line 4x – 3y + 4 = 0. If centre lies in the third quadrant and on the line x – y – 1 = 0, then the equation of the circle is (A) 9x2 + 9y2 + 24x + 6y – 1 = 0 (B) 9x2 + 9y2 + 6x – 2xy + 1 = 0 (C) 9x2 + 9y2 + 6x + 24y + 1 = 0 (D) x2 + y2 + 2x + 3y + 1 = 0 3. If three distinct real numbers a, b, c are in G.P. and a + b + c = xb, x  R, then (A) – 3 < x < 1 (B) x > 1 or x < – 3 (C) x < –1 or x > 3 (D) – 1 < x < 3 4. Area of the triangle formed by the x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y = 1 is (A) 2 sq. units (B) 4 sq. units (C) 6 sq. units (D) 8 sq. units 5. Find the maximum and minimum distance of the point (2 ,  7) from the circle x2 + y2  14 x  10 y  151 = 0 . 6. Consider the following statements for real values of x : S1 : Number of circles through the three points A(3, 5), B (4, 6), C (5, 7) is 2. S2 : |x – 2| = [– ], where [.] denotes greatest integer function, then x = 6, – 2 S3 : The image of the point (2,1) with respect to the line x + 1 = 0 is (–2 , 1) State, in order, whether S1 , S2 , S3 are true or false (A)TTT (B) FTF (C)TTT (D) FFF 7. STATEMENT-1: The number of integral values of  , for which the equation 7cosx + 5sinx = 2  + 1 has a solution, is 8. and STATEMENT-2: The equation acos + bsin  = c has atleast one solution if | c | > 2 2 b a  . (A) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is a correct explanation for STATEMENT-1 (B) STATEMENT-1 is True, STATEMENT-2 is True ; STATEMENT-2 is NOT a correct explanation for STATEMENT-1 (C) STATEMENT-1 isTrue, STATEMENT-2 is False (D) STATEMENT-1 is False, STATEMENT-2 isTrue Answer Keys DPP # 42 1. (A) 2. (A) 3. (B) 4. (D) 5. (D) 6. (A) (B)(C) Answer Keys DPP # 43 1. (B) 2. (D) 3. (A) 4. (B) 5. (D) 6. (A) 7. 6 S , 1 n n 6 Sn     8. (A) Answer Keys DPP # 44 1. (B) 2. (C) 3. (C) 4. (A) 5. max = 28, min = 2 6. (D) 7. (C)
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