(D) (A) Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point ? 2 (A) 2


 Lenard Wilkinson
 3 years ago
 Views:
Transcription
1 CIRCLE [STRAIGHT OBJECTIVE TYPE] Q. The line x y + = 0 is tangent to the circle at the point (, 5) and the centre of the circles lies on x y = 4. The radius of the circle is (A) 3 5 (B) 5 3 (C) 5 (D) 5 Q. Four unit circles pass through the origin and have their centres on the coordinate axes. The area of the quadrilateral whose vertices are the points of intersection (in pairs) of the circles, is (A) sq. unit (B) sq. units (C) 4 sq. units (D) can not be uniquely determined, insufficient data Q.3 To which of the following circles, the line y x + 3 = 0 is normal at the point 3 3 3,? (A) x 3 y 9 (B) x y 9 (C) x + (y 3) = 9 (D) (x 3) + y = 9 Q.4 Let C be a circle x + y =. The line l intersects C at the point (, 0) and the point P. Suppose that the slope of the line l is a rational number m. Number of choices for m for which both the coordinates of P are rational, is (A) 3 (B) 4 (C) 5 (D) infinitely many Q.5 Three concentric circles of which the biggest is x + y =, have their radii in A.P. If the line y = x + cuts all the circles in real and distinct points. The interval in which the common difference of the A.P. will lie is (A) 0, (B) 4 0, (C) 0, 4 (D) none Q.6 In the xyplane, the length of the shortest path from (0, 0) to (, 6) that does not go inside the circle (x 6) + (y 8) = 5 is 5 (A) 0 3 (B) 0 5 (C) (D) Q.7 If a circle of constant radius 3k passes through the origin 'O' and meets coordinate axes at A and B then the locus of the centroid of the triangle OAB is (A) x + y = (k) (B) x + y = (3k) (C) x + y = (4k) (D) x + y = (6k) Q.8 Triangle ABC is right angled at A. The circle with centre A and radius AB cuts BC and AC internally at D and E respectively. If BD = 0 and DC = 6 then the length AC equals (A) 6 (B) 6 6 (C) 30 (D) 3 Q.9 A variable line moves in such way that the product of the perpendiculars from (a, 0) and (0, 0) is equal to k. The locus of the feet of the perpendicular from (0, 0) upon the variable line is a circle, the square of whose radius is (Given: a < k ) (A) a a k k (B) 4 4 (C) a k + 4 (D) a k
2 Q.0 The points (x, y ), (x, y ), (x, y ) and (x, y ) are always : (A) collinear (B) concyclic (C) vertices of a square (D) vertices of a rhombus Q. Let C be the circle of radius unity centred at the origin. If two positive numbers x and x are such that the line passing through (x, ) and (x, ) is tangent to C then (A) x x = (B) x x = (C) x + x = (D) 4x x = Q. Tangents are drawn from any point on the circle x + y = R to the circle x + y = r. If the line joining the points of intersection of these tangents with the first circle also touch the second, then R equals (A) r (B) r (C) r 3 (D) 4r 3 5 Q.3 The locus of the middle points of the system of chords of the circle x² + y² = 6 which are parallel to the line y = 4x + 5 is (A) x = y (B) x + y = 0 (C) y + x = 0 (4) y = x Q.4 The locus of the center of the circles such that the point (, 3) is the mid point of the chord 5x + y = 6 is (A) x 5y + = 0 (B) x + 5y = 0 (C) x + 5y + = 0 (D) none Q.5 The points A (a, 0), B (0, b), C (c, 0) and D (0, d) are such that ac = bd and a, b, c, d are all nonzero. Then the points (A) form a parallelogram (B) do not lie on a circle (C) form a trapezium (D) are concyclic Q.6 If the angle between the tangents drawn from P to the circle x + y + 4x 6y + 9 sin + 3 cos =0 is, then the locus of P is (A) x + y + 4x 6y + 4 = 0 (B) x + y + 4x 6y 9 = 0 (C) x + y + 4x 6y 4 = 0 (D) x + y + 4x 6y + 9 = 0 Q.7 The locus of the mid points of the chords of the circle x² + y² + 4x 6y = 0 which subtend an angle of radians at its circumference is : 3 (A) (x )² + (y + 3)² = 6.5 (B) (x + )² + (y 3)² = 6.5 (C) (x + )² + (y 3)² = 8.75 (D) (x + )² + (y + 3)² = 8.75 Q.8 A circle of radius unity is centred at origin. Two particles start moving at the same time from the point (, 0) and move around the circle in opposite direction. One of the particle moves counterclockwise with constant speed v and the other moves clockwise with constant speed 3v. After leaving (, 0), the two particles meet first at a point P, and continue until they meet next at point Q. The coordinates of the point Q are (A) (, 0) (B) (0, ) (C) (0, ) (D) (, 0) Q.9 The value of 'c' for which the set, {(x, y)x + y + x } {(x, y)x y + c 0} contains only one point in common is : (A) (, ] [3, ) (B) {, 3} (C) { 3} (D) { } Q.0 A straight line l with equation x y + 0 = 0 meets the circle with equation x + y = 00 at B in the first quadrant. A line through B, perpendicular to l cuts the yaxis at P (0, t). The value of 't' is (A) (B) 5 (C) 0 (D) 5
3 Q. The locus of the centre of circle which touches externally the circle x + y 6x 6y + 4 = 0 and also touches the y axis is (A) x 6x 0y + 4 = 0 (B) x 0x 6y + 4 = 0 (C) y 6x 0y + 4 = 0 (D) y 0x 6y + 4 = 0 Q. A circle of constant radius ' a ' passes through origin ' O ' and cuts the axes of coordinates in points P and Q, then the equation of the locus of the foot of perpendicular from O to PQ is : (A) (x + y ) x y = 4 a (B) (x + y ) x y = a (C) (x + y ) x y = 4 a (D) (x + y ) x y = a Q.3 A circle is drawn touching the xaxis and centre at the point which is the reflection of (a, b) in the line y x = 0. The equation of the circle is (A) x + y bx ay + a = 0 (B) x + y bx ay + b = 0 (C) x + y ax by + b = 0 (D) x + y ax by + a = 0 Q.4 A(, 0) and B(0, ) and two fixed points on the circle x + y =. C is a variable point on this circle. As C moves, the locus of the orthocentre of the triangle ABC is (A) x + y x y + = 0 (B) x + y x y = 0 (C) x + y = 4 (D) x + y + x y + = 0 Q.5 A line meets the coordinate axes in A and B. A circle is circumscribed about the triangle OAB. If d and d are the distances of the tangent to the circle at the origin O from the points A and B respectively, the diameter of the circle is : (A) d d (B) d d (C) d + d (D) Q.6 AB is a diameter of a circle and C is any point on the circumference of the circle. Then (A) Area of ABC is maximum when it is isosceles. (B) Area of ABC is minimum when it is isosceles. (C) Perimeter of ABC is minimum when it is isosceles. (D) None A d d d d Q.7 In a right triangle ABC, right angled at A, on the leg AC as diameter, a semicircle is described. The chord joining A with the point of intersection D of the hypotenuse and the semicircle, then the length AC equals to (A) AB AD AB AD (B) AB AD AB AD (C) AB AD (D) C D AB AD AB AD Q.8 A variable circle C has the equation x + y (t 3t + )x (t + t)y + t = 0, where t is a parameter. If the power of point P(a,b) w.r.t. the circle C is constant then the ordered pair (a, b) is (A) 0, 0 (B), 0 0 (C) 0, 0 (D), 0 Q.9 B and C are fixed points having coordinates (3, 0) and ( 3, 0) respectively. If the vertical angle BAC is 90º, then the locus of the centroid of the ABC has the equation : (A) x + y = (B) x + y = (C) 9 (x + y ) = (D) 9 (x + y ) = 4 0
4 5 Q.30 The number of tangents that can be drawn from the point, to the circle passing through the points, 3,, 3 and, 3 3 is (A) (B) 0 (C) (D) None Q.3 If the circles x + y + ax + cy + a = 0 and x + y 3ax + dy = 0 intersect in two distinct points P and Q then the line 5x + by a = 0 passes through P and Q for (A) exactly one value of a (B) no value of a (C) infinitely many values of a (D) exactly two values of a Q.3 The circle with equation x + y = intersects the line y = 7x + 5 at two distinct points A and B. Let C be the point at which the positive xaxis intersects the circle. The angle ACB is 4 (A) tan 3 3 (B) tan 4 3 (C) tan () (D) tan Q.33 The number of common tangents of the circles (x + )² + (y )² = 49 and (x )² + (y + )² = 4 is (A) 0 (B) (C) (D) 3 Q.34 The equation of a line inclined at an angle to the axis X, such that the two circles 4 x + y = 4, x + y 0x 4y + 65 = 0 intercept equal lengths on it, is (A) x y 3 = 0 (B) x y + 3 = 0 (C) x y + 6 = 0 (D) x y 6 = 0 Q.35 If x = 3 is the chord of contact of the circle x y = 8, then the equation of the corresponding pair of tangents, is (A) x 8y + 54x + 79 = 0 (B) x 8y 54x + 79 = 0 (C) x 8y 54x 79 = 0 (D) x 8y = 79 Q.36 Let C and C are circles defined by x + y 0x + 64 = 0 and x + y + 30x + 44 = 0. The length of the shortest line segment PQ that is tangent to C at P and to C at Q is (A) 5 (B) 8 (C) 0 (D) 4 Q.37 If the straight line y = mx is outside the circle x + y 0y + 90 = 0, then (A) m > 3 (B) m < 3 (C) m > 3 (D) m < 3 Q.38 The centre of the smallest circle touching the circles x + y y 3 = 0 and x + y 8x 8y + 93 = 0 is (A) (3, ) (B) (4, 4) (C) (, 7) (D) (, 5) Q.39 Suppose that two circles C and C in a plane have no points in common. Then (A) there is no line tangent to both C and C. (B) there are exactly four lines tangent to both C and C. (C) there are no lines tangent to both C and C or there are exactly two lines tangent to both C and C. (D) there are no lines tangent to both C and C or there are exactly four lines tangent to both C and C. Q.40 The shortest distance from the line 3x + 4y = 5 to the circle x + y = 6x 8y is equal to (A) 7/5 (B) 9/5 (C) /5 (D) 3/5
5 Q.4 If the circle C : x + y = 6 intersects another circle C of radius 5 in such a manner that the common chord is of maximum length and has a slope equal to 3/4, then the coordinates of the centre of C are 9 (A), (B) , 5 (C) 9, (D) , 5 Q.4 The distance between the chords of contact of tangents to the circle x + y + gx + fy + c = 0 from the origin and the point (g, f) is (A) g f (B) g f c (C) g f c g f (D) g f c g f Q.43 The locus of the centers of the circles which cut the circles x + y + 4x 6y + 9 = 0 and x + y 5x + 4y = 0 orthogonally is : (A) 9x + 0y 7 = 0 (B) x y + = 0 (C) 9x 0y + = 0 (D) 9x + 0y + 7 = 0 Q.44 If two distinct chords, drawn from the point (p, q) on the circle x + y = px + qy, where pq 0, are bisected by the xaxis, then (A) p = q (B) p = 8q (C) p < 9q (D) p > 8q Q.45 The angle at which the circles (x ) + y = 0 and x + (y ) = 5 intersect is (A) (B) (C) (D) Q.46 Locus of the middle points of a system of parallel chords with slope, of the circle x + y 4x y 4 = 0, has the equation (A) x + y 4 = 0 (B) x y = 0 (C) x y 3 = 0 (D) x + y 5 = 0 Q.47 If a,, b,, c, and d, are four distinct points on a circle of radius 4 units then, a b c d abcd is equal to (A) 4 (B) /4 (C) (D) 6 Q.48 The radical centre of three circles taken in pairs described on the sides of a triangle ABC as diametres is the : (A) centroid of the ABC (B) incentre of the ABC (C) circumcentre o the ABC (D) orthocentre of the ABC Q.49 Two circles are drawn through the points (, 0) and (, ) to touch the axis of y. They intersect at an angle (A) cot 3 4 (B) cos 4 5 (C) (D) tan Q.50 A foot of the normal from the point (4, 3) to a circle is (, ) and a diameter of the circle has the equation x y = 0. Then the equation of the circle is (A) x + y 4y + = 0 (B) x + y 4y + = 0 (C) x + y x = 0 (D) x + y x + = 0 Q.5 A rhombus is inscribed in the region common to the two circles x + y 4x = 0 and x + y + 4x = 0 with two of its vertices on the line joining the centres of the circles. The area of the rhombous is : (A) 8 3 sq.units (B) 4 3 sq.units (C) 6 3 sq.units (D) none
6 [REASONING TYPE] Q.5 Consider the circle C : x + y x y 3 = 0 and a point P(3, 4). Statement: No normal can be drawn to the circle C, passing through (3, 4). Statement: Point P lies inside the given circle, C. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.53 Passing through a point A(6, 8) a variable secant line L is drawn to the circle S : x + y 6x 8y + 5 = 0. From the point of intersection of L with S, a pair of tangent lines are drawn which intersect at P. Statement: Locus of the point P has the equation 3x + 4y 40 = 0. Statement: Point A lies outside the circle. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.54 Consider the lines L : (k + 7)x (k )y 4(k 5) = 0 where k is a parameter and the circle C : x + y + 4x + y 60 = 0 Statement: Every member of L intersects the circle 'C' at an angle of 90 Statement: Every member of L is tangent to the circle C. (A) Statement is true, statement is true; statement is correct explanation for statement. (B) Statement is true, statement is true; statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.55 Consider the circles, S : x + y + x 4 = 0 and S : x + y y + = 0 Statement: Tangents from the point P(0, 5) on S and S are equal. Statement: Point P(0, 5) lies on the radical axis of the two circles. (A) Statement is true, statement is true; statement is correct explanation for statement. (B) Statement is true, statement is true; statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.56 Statement: The circle C : x + y 6x 4y + 9 = 0 bisects the circumference of the circle C : x + y 8x 6y + 3 = 0. Statement: Centre of the circle C lies on the circumference of C. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.57 Let C be a circle with centre 'O' and HK is the chord of contact of pair of the tangents from point A. OA intersects the circle C at P and Q and B is the midpoint of HK, then Statement : AB is the harmonic mean of AP and AQ. Statement : AK is the Geometric mean of AB and AO and OA is the arithmetic mean of AP and AQ. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true.
7 Q.58 Statement: Angle between the tangents drawn from the point P(3, 6) to the circle S : x + y 6x + 8y 75 = 0 is 90. Statement: Point P lies on the director circle of S. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.59 Let C denotes a family of circles with centre on xaxis and touching the yaxis at the origin. and C denotes a family of circles with centre on yaxis and touching the xaxis at the origin. Statement: Every member of C intersects any member of C at right angles at the point other than origin. Statement: If two circles intersect at 90 at one point of their intersection, then they must intersect at 90 on the other point of intersection also. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.60 A circle is circumscribed about an equilateral triangle ABC and a point P on the minor arc joining A and B, is chosen. Let x = PA, y = PB and z = PC. (z is larger than both x and y.) Statement: Each of the possibilities (x + y) greater than z, equal to z or less than z, is possible for some P. Statement: In a triangle ABC, sum of the two sides of a triangle is greater than the third and the third side is greater than the difference of the two. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. Q.6 Statement: Only one normal can be drawn through the point P(, 3) to the circle x + y 4x + 8y 6 = 0 Statement: Passing through any point lying inside a given circle only one normal can be drawn. (A) Statement is true, statement is true and statement is correct explanation for statement. (B) Statement is true, statement is true and statement is NOT the correct explanation for statement. (C) Statement is true, statement is false. (D) Statement is false, statement is true. [COMPREHENSION TYPE] Paragraph for question nos. 6 to 64 Consider a circle x + y = 4 and a point P(4, ). denotes the angle enclosed by the tangents from P on the circle and A, B are the points of contact of the tangents from P on the circle. Q.6 The value of lies in the interval (A) (0, 5 ) (B) (5, 30 ) (C) 30, 45 ) (D) (45, 60 ) Q.63 The intercept made by a tangent on the xaxis is (A) 9/4 (B) 0/4 (C) /4 (D) /4 Q.64 Locus of the middle points of the portion of the tangent to the circle terminated by the coordinate axes is (A) x + y = (B) x + y = (C) x + y = 3 (D) x y = 4
8 Paragraph for question nos. 65 to 67 Let A, B, C be three sets of real numbers (x, y) defined as A : {(x, y): y } B : {(x, y): x + y 4x y 4 = 0} C : {(x, y): x + y = } Q.65 Number of elements in the A B C is (A) 0 (B) (C) (D) infinite Q.66 (x + ) + (y ) + (x 5) + (y ) has the value equal to (A) 6 (B) 5 (C) 36 (D) 49 Q.67 If the locus of the point of intersection of the pair of perpendicular tangents to the circle B is the curve S then the area enclosed between B and S is (A) 6 (B) 8 (C) 9 (D) 8 Paragraph for Question Nos. 68 to 70 Let C be a circle of radius r with centre at O. Let P be a point outside C and D be a point on C. A line through P intersects C at Q and R, S is the midpoint of QR. Q.68 For different choices of line through P, the curve on which S lies, is (A) a straight line (B) an arc of circle with P as centre (C) an arc of circle with PS as diameter (D) an arc of circle with OP as diameter Q.69 Let P is situated at a distance 'd' from centre O, then which of the following does not equal the product (PQ) (PR)? (A) d r (B) PT, where T is a point on C and PT is tangent to C (C) (PS) (QS)(RS) (D) (PS) Q.70 Let XYZ be an equilateral triangle inscribed in C. If,, denote the distances of D from vertices X, Y, Z respectively, the value of product ( + ) ( + ) ( + ), is (A) 0 (B) 8 (C) (D) None of these Paragraph for question nos. 7 to 73 Consider 3 circles S : x + y + x 3 = 0 S : x + y = 0 S 3 : x + y + y 3 = 0 Q.7 The radius of the circle which bisect the circumferences of the circles S = 0 ; S = 0 ; S 3 = 0 is (A) (B) (C) 3 (D) 0 Q.7 If the circle S = 0 is orthogonal to S = 0 ; S = 0 and S 3 = 0 and has its centre at (a, b) and radius equals to 'r' then the value of (a + b + r) equals (A) 0 (B) (C) (D) 3 Q.73 The radius of the circle touching S = 0 and S = 0 at (, 0) and passing through (3, ) is (A) (B) (C) (D)
9 Paragraph for questions nos. 74 to 76 Consider the two quadratic polynomials x C a : y = ax a a and C : y = 4 4 Q.74 If the origin lies between the zeroes of the polynomial C a then the number of integral value(s) of 'a' is (A) (B) (C) 3 (D) more than 3 Q.75 If 'a' varies then the equation of the locus of the vertex of C a, is (A) x y 4 = 0 (B) x y 4 = 0 (C) x y + 4 = 0 (D) x + y 4 = 0 Q.76 For a = 3, if the lines y = m x + c and y = m x + c are common tangents to the graph of C a and C then the value of (m + m ) is equal to (A) 6 (B) 3 (C) / (D) none x Paragraph for Question Nos. 77 to 79 Consider a line pair ax + 3xy y 5x + 5y + c = 0 representing perpendicular lines intersecting each other at C and forming a triangle ABC with the xaxis. Q.77 If x and x are intercepts on the xaxis and y and y are the intercepts on the yaxis then the sum (x + x + y + y ) is equal to (A) 6 (B) 5 (C) 4 (D) 3 Q.78 Distance between the orthocentre and circumcentre of the triangle ABC is (A) (B) 3 (C) 7/4 (D) 9/4 Q.79 If the circle x + y 4y + k = 0 is orthogonal with the circumcircle of the triangle ABC then 'k' equals (A) / (B) (C) (D) 3/ [MULTIPLE OBJECTIVE TYPE] Q.80 Let L be a line passing through the origin and L be the line x + y =. If the intercepts made by the circle x + y x + 3y = 0 on L and L are equal then the equation of L can be (A) x + y = 0 (B) x y = 0 (C) x + 7y = 0 (D) x 7y = 0 Q.8 x x cos = y y sin = r, represents : (A) equation of a straight line, if is constant and r is variable (B) equation of a circle, if r is constant and is a variable (C) a straight line passing through a fixed point and having a known slope (D) a circle with a known centre and a given radius. Q.8 Three distinct lines are drawn in a plane. Suppose there exist exactly n circles in the plane tangent to all the three lines, then the possible values of n is/are (A) 0 (B) (C) (D) 4 Q.83 A family of linear functions is given by f (x) = + c(x + 3) where c R. If a member of this family meets a unit circle centred at origin in two coincident points then 'c' can be equal to (A) 3/4 (B) 0 (C) 3/4 (D) Q.84 A circle passes through the points (, ), (0, 6) and (5, 5). The point(s) on this circle, the tangent(s) at which is/are parallel to the straight line joining the origin to its centre is/are : (A) (, 5) (B) (5, ) (C) ( 5, ) (D) (, 5)
10 Q.85 Consider the circles S : x + y = 4 and S : x + y x 4y + 4 = 0 which of the following statements are correct? (A) Number of common tangents to these circles is. (B) If the power of a variable point P w.r.t. these two circles is same then P moves on the line x + y 4 = 0. (C) Sum of the yintercepts of both the circles is 6. (D) The circles S and S are orthogonal. Q.86 If al bm + dl + = 0, where a, b, d are fixed real numbers such that a + b = d then the line lx + my + = 0 touches a fixed circle : (A) which cuts the xaxis orthogonally (B) with radius equal to b (C) on which the length of the tangent from the origin is d b (D) none of these. Q.87 Consider the circles S : x + y + x + 4y + = 0 S : x + y 4x + 3 = 0 S 3 : x + y + 6y + 5 = 0 Which of this following statements are correct? (A) Radical centre of S, S and S 3 lies in st quadrant. (B) Radical centre of S, S and S 3 lies in 4 th quadrants. (C) Radius of the circle intersecting S, S and S 3 orthogonally is. (D) Circle orthogonal to S, S and S 3 has its x and y intercept equal to zero. Q.88 Locus of the intersection of the two straight lines passing through (, 0) and (, 0) respectively and including an angle of 45 can be a circle with (A) centre (, 0) and radius. (B) centre (, 0) and radius. (C) centre (0, ) and radius. (D) centre (0, ) and radius. [MATCH THE COLUMN] Q.89 ColumnI ColumnII (A) If the straight line y = kx K I touches or passes outside (P) the circle x + y 0y + 90 = 0 then k can have the value (B) Two circles x + y + px + py 7 = 0 (Q) and x + y 0x + py + = 0 intersect each other orthogonally then the value of p is (C) If the equation x + y + x + 4 = 0 and x + y 4y + 8 = 0 (R) 3 represent real circles then the value of can be (D) Each side of a square is of length 4. The centre of the square is (3, 7). (S) 5 One diagonal of the square is parallel to y = x. The possible abscissae of the vertices of the square can be Q.90 ColumnI ColumnII (A) Two intersecting circles (P) have a common tangent (B) Two circles touching each other (Q) have a common normal (C) Two non concentric circles, one strictly inside (R) do not have a common normal the other (D) Two concentric circles of different radii (S) do not have a radical axis.
11 ANSWER KEY CIRCLE Q. A Q. C Q.3 D Q.4 D Q.5 C Q.6 C Q.7 A Q.8 B Q.9 A Q.0 B Q. A Q. B Q.3 B Q.4 A Q.5 D Q.6 D Q.7 B Q.8 D Q.9 D Q.0 C Q. D Q. C Q.3 B Q.4 A Q.5 C Q.6 A Q.7 D Q.8 B Q.9 A Q.30 B Q.3 B Q.3 C Q.33 B Q.34 A Q.35 B Q.36 C Q.37 D Q.38 D Q.39 D Q.40 A Q.4 B Q.4 C Q.43 C Q.44 D Q.45 B Q.46 A Q.47 C Q.48 D Q.49 A Q.50 C Q.5 A Q.5 D Q.53 D Q.54 C Q.55 A Q.56 B Q.57 A Q.58 A Q.59 A Q.60 D Q.6 C Q.6 D Q.63 B Q.64 A Q.65 B Q.66 C Q.67 C Q.68 D Q.69 D Q.70 A Q.7 C Q.7 D Q.73 C Q.74 B Q.75 A Q.76 B Q.77 B Q.78 C Q.79 D Q.80 B,C Q.8 A,B,C,D Q.8 A,C,D Q.83 A,B Q.84 B,D Q.85 A,B,D Q.86 A,C Q.87 B,C,D Q.88 C,D Q.89 (A) P, Q, R; (B) Q, R; (C) Q, R, S; (D) P, S Q.90 (A) P, Q; (B) P, Q; (C) Q; (D) Q, S
QUESTION BANK ON STRAIGHT LINE AND CIRCLE
QUESTION BANK ON STRAIGHT LINE AND CIRCLE Select the correct alternative : (Only one is correct) Q. If the lines x + y + = 0 ; 4x + y + 4 = 0 and x + αy + β = 0, where α + β =, are concurrent then α =,
More information= 0 1 (3 4 ) 1 (4 4) + 1 (4 3) = = + 1 = 0 = 1 = ± 1 ]
STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. If the lines x + y + = 0 ; x + y + = 0 and x + y + = 0, where + =, are concurrent then (A) =, = (B) =, = ± (C) =, = ± (D*) = ±, = [Sol. Lines are x + y + = 0
More informationDEEPAWALI ASSIGNMENT CLASS 11 FOR TARGET IIT JEE 2012 SOLUTION
DEEPAWALI ASSIGNMENT CLASS FOR TARGET IIT JEE 0 SOLUTION IMAGE OF SHRI GANESH LAXMI SARASWATI Director & H.O.D. IITJEE Mathematics SUHAG R. KARIYA (S.R.K. Sir) DOWNLOAD FREE STUDY PACKAGE, TEST SERIES
More informationQUESTION BANK ON. CONIC SECTION (Parabola, Ellipse & Hyperbola)
QUESTION BANK ON CONIC SECTION (Parabola, Ellipse & Hyperbola) Question bank on Parabola, Ellipse & Hyperbola Select the correct alternative : (Only one is correct) Q. Two mutually perpendicular tangents
More informationVKR Classes TIME BOUND TESTS 17 Target JEE ADVANCED For Class XI VKR Classes, C , Indra Vihar, Kota. Mob. No
VKR Classes TIME BOUND TESTS 7 Target JEE ADVANCED For Class XI VKR Classes, C90, Indra Vihar, Kota. Mob. No. 9890605 Single Choice Question : PRACTICE TEST. The smallest integer greater than log +
More informationTARGET : JEE 2013 SCORE. JEE (Advanced) Home Assignment # 03. Kota Chandigarh Ahmedabad
TARGT : J 01 SCOR J (Advanced) Home Assignment # 0 Kota Chandigarh Ahmedabad JMathematics HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP 1. If x + y = 0 is a tangent at the vertex of a parabola and x + y 7 =
More informationQ.2 A, B and C are points in the xy plane such that A(1, 2) ; B (5, 6) and AC = 3BC. Then. (C) 1 1 or
STRAIGHT LINE [STRAIGHT OBJECTIVE TYPE] Q. A variable rectangle PQRS has its sides parallel to fied directions. Q and S lie respectivel on the lines = a, = a and P lies on the ais. Then the locus of R
More informationChapter (Circle) * Circle  circle is locus of such points which are at equidistant from a fixed point in
Chapter  10 (Circle) Key Concept * Circle  circle is locus of such points which are at equidistant from a fixed point in a plane. * Concentric circle  Circle having same centre called concentric circle.
More informationTrans Web Educational Services Pvt. Ltd B 147,1st Floor, Sec6, NOIDA, UP
Solved Examples Example 1: Find the equation of the circle circumscribing the triangle formed by the lines x + y = 6, 2x + y = 4, x + 2y = 5. Method 1. Consider the equation (x + y 6) (2x + y 4) + λ 1
More informationLLT Education Services
8. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle. (a) 4 cm (b) 3 cm (c) 6 cm (d) 5 cm 9. From a point P, 10 cm away from the
More informationSo, eqn. to the bisector containing (1, 4) is = x + 27y = 0
Q.No. The bisector of the acute angle between the lines x  4y + 7 = 0 and x + 5y  = 0, is: Option x + y  9 = 0 Option x + 77y  0 = 0 Option x  y + 9 = 0 Correct Answer L : x  4y + 7 = 0 L :x 5y
More informationl (D) 36 (C) 9 x + a sin at which the tangent is parallel to xaxis lie on
Dpp to MATHEMATICS Dail Practice Problems Target IIT JEE 00 CLASS : XIII (VXYZ) DPP. NO. to DPP Q. If on a given base, a triangle be described such that the sum of the tangents of the base angles is
More information( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear.
Problems 01  POINT Page 1 ( 1 ) Show that P ( a, b + c ), Q ( b, c + a ) and R ( c, a + b ) are collinear. ( ) Prove that the two lines joining the midpoints of the pairs of opposite sides and the line
More informationQ1. If (1, 2) lies on the circle. x 2 + y 2 + 2gx + 2fy + c = 0. which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c =
Q1. If (1, 2) lies on the circle x 2 + y 2 + 2gx + 2fy + c = 0 which is concentric with the circle x 2 + y 2 +4x + 2y 5 = 0 then c = a) 11 b) 13 c) 24 d) 100 Solution: Any circle concentric with x 2 +
More informationQ.1 If a, b, c are distinct positive real in H.P., then the value of the expression, (A) 1 (B) 2 (C) 3 (D) 4. (A) 2 (B) 5/2 (C) 3 (D) none of these
Q. If a, b, c are distinct positive real in H.P., then the value of the expression, b a b c + is equal to b a b c () (C) (D) 4 Q. In a triangle BC, (b + c) = a bc where is the circumradius of the triangle.
More information2. (i) Find the equation of the circle which passes through ( 7, 1) and has centre ( 4, 3).
Circle 1. (i) Find the equation of the circle with centre ( 7, 3) and of radius 10. (ii) Find the centre of the circle 2x 2 + 2y 2 + 6x + 8y 1 = 0 (iii) What is the radius of the circle 3x 2 + 3y 2 + 5x
More informationCONCURRENT LINES PROPERTIES RELATED TO A TRIANGLE THEOREM The medians of a triangle are concurrent. Proof: Let A(x 1, y 1 ), B(x, y ), C(x 3, y 3 ) be the vertices of the triangle A(x 1, y 1 ) F E B(x,
More information+ 2gx + 2fy + c = 0 if S
CIRCLE DEFINITIONS A circle is the locus of a point which moves in such a way that its distance from a fixed point, called the centre, is always a constant. The distance r from the centre is called the
More informationPart (1) Second : Trigonometry. Tan
Part (1) Second : Trigonometry (1) Complete the following table : The angle Ratio 42 12 \ Sin 0.3214 Cas 0.5321 Tan 2.0625 (2) Complete the following : 1) 46 36 \ 24 \\ =. In degrees. 2) 44.125 = in degrees,
More informationVAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER)
BY:Prof. RAHUL MISHRA Class : X QNo. VAISHALI EDUCATION POINT (QUALITY EDUCATION PROVIDER) CIRCLES Subject : Maths General Instructions Questions M:9999907099,9818932244 1 In the adjoining figures, PQ
More informationTopic 2 [312 marks] The rectangle ABCD is inscribed in a circle. Sides [AD] and [AB] have lengths
Topic 2 [312 marks] 1 The rectangle ABCD is inscribed in a circle Sides [AD] and [AB] have lengths [12 marks] 3 cm and (\9\) cm respectively E is a point on side [AB] such that AE is 3 cm Side [DE] is
More informationObjective Mathematics
. A tangent to the ellipse is intersected by a b the tangents at the etremities of the major ais at 'P' and 'Q' circle on PQ as diameter always passes through : (a) one fied point two fied points (c) four
More information21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle.
21. Prove that If one side of the cyclic quadrilateral is produced then the exterior angle is equal to the interior opposite angle. 22. Prove that If two sides of a cyclic quadrilateral are parallel, then
More informationPREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) 60 Best JEE Main and Advanced Level Problems (IITJEE). Prepared by IITians.
www. Class XI TARGET : JEE Main/Adv PREPARED BY: ER. VINEET LOOMBA (B.TECH. IIT ROORKEE) ALP ADVANCED LEVEL PROBLEMS Straight Lines 60 Best JEE Main and Advanced Level Problems (IITJEE). Prepared b IITians.
More information1 is equal to. 1 (B) a. (C) a (B) (D) 4. (C) P lies inside both C & E (D) P lies inside C but outside E. (B) 1 (D) 1
Single Correct Q. Two mutuall perpendicular tangents of the parabola = a meet the ais in P and P. If S is the focus of the parabola then l a (SP ) is equal to (SP ) l (B) a (C) a Q. ABCD and EFGC are squares
More informationPOINT. Preface. The concept of Point is very important for the study of coordinate
POINT Preface The concept of Point is ver important for the stud of coordinate geometr. This chapter deals with various forms of representing a Point and several associated properties. The concept of coordinates
More information( 1 ) Find the coordinates of the focus, length of the latusrectum and equation of the directrix of the parabola x 2 =  8y.
PROBLEMS 04  PARABOLA Page 1 ( 1 ) Find the coordinates of the focus, length of the latusrectum and equation of the directrix of the parabola x  8. [ Ans: ( 0,  ), 8, ] ( ) If the line 3x 4 k 0 is
More informationDISCUSSION CLASS OF DAX IS ON 22ND MARCH, TIME : 912 BRING ALL YOUR DOUBTS [STRAIGHT OBJECTIVE TYPE]
DISCUSSION CLASS OF DAX IS ON ND MARCH, TIME : 9 BRING ALL YOUR DOUBTS [STRAIGHT OBJECTIVE TYPE] Q. Let y = cos x (cos x cos x). Then y is (A) 0 only when x 0 (B) 0 for all real x (C) 0 for all real x
More informationSOLVED SUBJECTIVE EXAMPLES
Example 1 : SOLVED SUBJECTIVE EXAMPLES Find the locus of the points of intersection of the tangents to the circle x = r cos, y = r sin at points whose parametric angles differ by /3. All such points P
More informationCIRCLES. ii) P lies in the circle S = 0 s 11 = 0
CIRCLES 1 The set of points in a plane which are at a constant distance r ( 0) from a given point C is called a circle The fixed point C is called the centre and the constant distance r is called the radius
More informationCOORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE. To find the length of a line segment joining two points A(x 1, y 1 ) and B(x 2, y 2 ), use
COORDINATE GEOMETRY BASIC CONCEPTS AND FORMULAE I. Length of a Line Segment: The distance between two points A ( x1, 1 ) B ( x, ) is given b A B = ( x x1) ( 1) To find the length of a line segment joining
More informationSYSTEM OF CIRCLES OBJECTIVES (a) Touch each other internally (b) Touch each other externally
SYSTEM OF CIRCLES OBJECTIVES. A circle passes through (0, 0) and (, 0) and touches the circle x + y = 9, then the centre of circle is (a) (c) 3,, (b) (d) 3,, ±. The equation of the circle having its centre
More informationPRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES
PRACTICE QUESTIONS CLASS IX: CHAPTER 4 LINEAR EQUATION IN TWO VARIABLES 1. Find the value of k, if x =, y = 1 is a solution of the equation x + 3y = k.. Find the points where the graph of the equation
More information6 CHAPTER. Triangles. A plane figure bounded by three line segments is called a triangle.
6 CHAPTER We are Starting from a Point but want to Make it a Circle of Infinite Radius A plane figure bounded by three line segments is called a triangle We denote a triangle by the symbol In fig ABC has
More informationIMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHSIB
` KUKATPALLY CENTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHSIB 01718 FIITJEE KUKATPALLY CENTRE: # 97, Plot No1, Opp Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad  500
More information1 / 23
CBSEXII07 EXAMINATION CBSEX009 EXAMINATION MATHEMATICS Series: HRL Paper & Solution Code: 0/ Time: Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question paper
More informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Fall 2016 Solutions to the Quizzes Quiz #1. Wednesday, 13 September. [10 minutes] 1. Suppose you are given a line (segment) AB. Using
More informationIMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS
` KUKATPALLY CENTRE IMPORTANT QUESTIONS FOR INTERMEDIATE PUBLIC EXAMINATIONS IN MATHSIB FIITJEE KUKATPALLY CENTRE: # 97, Plot No1, Opp Patel Kunta Huda Park, Vijaynagar Colony, Hyderabad  57 Ph: 4646113
More informationMATHEMATICS. IMPORTANT FORMULAE AND CONCEPTS for. Summative Assessment II. Revision CLASS X Prepared by
MATHEMATICS IMPORTANT FORMULAE AND CONCEPTS for Summative Assessment II Revision CLASS X 06 7 Prepared by M. S. KUMARSWAMY, TGT(MATHS) M. Sc. Gold Medallist (Elect.), B. Ed. Kendriya Vidyalaya GaCHiBOWli
More informationSTRAIGHT LINES EXERCISE  3
STRAIGHT LINES EXERCISE  3 Q. D C (3,4) E A(, ) Mid point of A, C is B 3 E, Point D rotation of point C(3, 4) by angle 90 o about E. 3 o 3 3 i4 cis90 i 5i 3 i i 5 i 5 D, point E mid point of B & D. So
More informationieducation.com Tangents given as follows. the circle. contact. There are c) Secant:
h Tangents and Secants to the Circle A Line and a circle: let us consider a circle and line say AB. There can be three possibilities given as follows. a) Nonintersecting line: The line AB and the circle
More informationCOORDINATE GEOMETRY. 1. Find the points on the y axis whose distances from the points (6, 7) and (4,3) are in the. ratio 1:2.
UNIT COORDINATE GEOMETRY Mathematics is the tool specially suited for dealing with abstract concepts of any ind and there is no limit to its power in this field.. Find the points on the y axis whose
More informationObjective Mathematics
. In BC, if angles, B, C are in geometric seq uence with common ratio, then is : b c a (a) (c) 0 (d) 6. If the angles of a triangle are in the ratio 4 : :, then the ratio of the longest side to the perimeter
More informationPRACTICE TEST 1 Math Level IC
SOLID VOLUME OTHER REFERENCE DATA Right circular cone L = cl V = volume L = lateral area r = radius c = circumference of base h = height l = slant height Sphere S = 4 r 2 V = volume r = radius S = surface
More informationEinstein Classes, Unit No. 102, 103, Vardhman Ring Road Plaza, Vikas Puri Extn., Outer Ring Road New Delhi , Ph. : ,
MCN COMPLEX NUMBER C The complex number Complex number is denoted by ie = a + ib, where a is called as real part of (denoted by Re and b is called as imaginary part of (denoted by Im Here i =, also i =,
More informationSecondary School Certificate Examination Syllabus MATHEMATICS. Class X examination in 2011 and onwards. SSC PartII (Class X)
Secondary School Certificate Examination Syllabus MATHEMATICS Class X examination in 2011 and onwards SSC PartII (Class X) 15. Algebraic Manipulation: 15.1.1 Find highest common factor (H.C.F) and least
More information10. Circles. Q 5 O is the centre of a circle of radius 5 cm. OP AB and OQ CD, AB CD, AB = 6 cm and CD = 8 cm. Determine PQ. Marks (2) Marks (2)
10. Circles Q 1 True or False: It is possible to draw two circles passing through three given noncollinear points. Mark (1) Q 2 State the following statement as true or false. Give reasons also.the perpendicular
More informationConic section. Ans: c. Ans: a. Ans: c. Episode:43 Faculty: Prof. A. NAGARAJ. 1. A circle
Episode:43 Faculty: Prof. A. NAGARAJ Conic section 1. A circle gx fy c 0 is said to be imaginary circle if a) g + f = c b) g + f > c c) g + f < c d) g = f. If (1,3) is the centre of the circle x y ax
More information1 What is the solution of the system of equations graphed below? y = 2x + 1
1 What is the solution of the system of equations graphed below? y = 2x + 1 3 As shown in the diagram below, when hexagon ABCDEF is reflected over line m, the image is hexagon A'B'C'D'E'F'. y = x 2 + 2x
More informationBOARD QUESTION PAPER : MARCH 2016 GEOMETRY
BOARD QUESTION PAPER : MARCH 016 GEOMETRY Time : Hours Total Marks : 40 Note: (i) Solve All questions. Draw diagram wherever necessary. (ii) Use of calculator is not allowed. (iii) Diagram is essential
More informationMaharashtra Board Class X Mathematics  Geometry Board Paper 2014 Solution. Time: 2 hours Total Marks: 40
Maharashtra Board Class X Mathematics  Geometry Board Paper 04 Solution Time: hours Total Marks: 40 Note:  () All questions are compulsory. () Use of calculator is not allowed.. i. Ratio of the areas
More informationSOLVED PROBLEMS. 1. The angle between two lines whose direction cosines are given by the equation l + m + n = 0, l 2 + m 2 + n 2 = 0 is
SOLVED PROBLEMS OBJECTIVE 1. The angle between two lines whose direction cosines are given by the equation l + m + n = 0, l 2 + m 2 + n 2 = 0 is (A) π/3 (B) 2π/3 (C) π/4 (D) None of these hb : Eliminating
More informationSSC CGL Tier 1 and Tier 2 Program
Gurudwara Road Model Town, Hisar 9729327755 www.ssccglpinnacle.com SSC CGL Tier 1 and Tier 2 Program 
More informationUdaan School Of Mathematics Class X Chapter 10 Circles Maths
Exercise 10.1 1. Fill in the blanks (i) The common point of tangent and the circle is called point of contact. (ii) A circle may have two parallel tangents. (iii) A tangent to a circle intersects it in
More information[STRAIGHT OBJECTIVE TYPE] Q.4 The expression cot 9 + cot 27 + cot 63 + cot 81 is equal to (A) 16 (B) 64 (C) 80 (D) none of these
Q. Given a + a + cosec [STRAIGHT OBJECTIVE TYPE] F HG ( a x) I K J = 0 then, which of the following holds good? (A) a = ; x I a = ; x I a R ; x a, x are finite but not possible to find Q. The minimum value
More information1. Matrices and Determinants
Important Questions 1. Matrices and Determinants Ex.1.1 (2) x 3x y Find the values of x, y, z if 2x + z 3y w = 0 7 3 2a Ex 1.1 (3) 2x 3x y If 2x + z 3y w = 3 2 find x, y, z, w 4 7 Ex 1.1 (13) 3 7 3 2 Find
More information0114ge. Geometry Regents Exam 0114
0114ge 1 The midpoint of AB is M(4, 2). If the coordinates of A are (6, 4), what are the coordinates of B? 1) (1, 3) 2) (2, 8) 3) (5, 1) 4) (14, 0) 2 Which diagram shows the construction of a 45 angle?
More informationMathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions
Mathematics 2260H Geometry I: Euclidean geometry Trent University, Winter 2012 Quiz Solutions Quiz #1. Tuesday, 17 January, 2012. [10 minutes] 1. Given a line segment AB, use (some of) Postulates I V,
More informationMathematics. Single Correct Questions
Mathematics Single Correct Questions +4 1.00 1. If and then 2. The number of solutions of, in the interval is : 3. If then equals : 4. A plane bisects the line segment joining the points and at right angles.
More information0110ge. Geometry Regents Exam Which expression best describes the transformation shown in the diagram below?
0110ge 1 In the diagram below of trapezoid RSUT, RS TU, X is the midpoint of RT, and V is the midpoint of SU. 3 Which expression best describes the transformation shown in the diagram below? If RS = 30
More informationIndicate whether the statement is true or false.
PRACTICE EXAM IV Sections 6.1, 6.2, 8.1 8.4 Indicate whether the statement is true or false. 1. For a circle, the constant ratio of the circumference C to length of diameter d is represented by the number.
More information0112ge. Geometry Regents Exam Line n intersects lines l and m, forming the angles shown in the diagram below.
Geometry Regents Exam 011 011ge 1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would
More informationchapter 1 vector geometry solutions V Consider the parallelogram shown alongside. Which of the following statements are true?
chapter vector geometry solutions V. Exercise A. For the shape shown, find a single vector which is equal to a)!!! " AB + BC AC b)! AD!!! " + DB AB c)! AC + CD AD d)! BC + CD!!! " + DA BA e) CD!!! " "
More informationSECTION A(1) k k 1= = or (rejected) k 1. Suggested Solutions Marks Remarks. 1. x + 1 is the longest side of the triangle. 1M + 1A
SECTION A(). x + is the longest side of the triangle. ( x + ) = x + ( x 7) (Pyth. theroem) x x + x + = x 6x + 8 ( x )( x ) + x x + 9 x = (rejected) or x = +. AP and PB are in the golden ratio and AP >
More informationNozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Ismailia Road Branch
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch Sheet ( 1) 1Complete 1. in the parallelogram, each two opposite
More information1. The unit vector perpendicular to both the lines. Ans:, (2)
1. The unit vector perpendicular to both the lines x 1 y 2 z 1 x 2 y 2 z 3 and 3 1 2 1 2 3 i 7j 7k i 7j 5k 99 5 3 1) 2) i 7j 5k 7i 7j k 3) 4) 5 3 99 i 7j 5k Ans:, (2) 5 3 is Solution: Consider i j k a
More information1. SETS AND FUNCTIONS
. SETS AND FUNCTIONS. For two sets A and B, A, B A if and only if B A A B A! B A + B z. If A B, then A + B is B A\ B A B\ A. For any two sets Pand Q, P + Q is " x : x! P or x! Q, " x : x! P and x b Q,
More informationIt is known that the length of the tangents drawn from an external point to a circle is equal.
CBSE MATHSSET 12014 Q1. The first three terms of an AP are 3y1, 3y+5 and 5y+1, respectively. We need to find the value of y. We know that if a, b and c are in AP, then: b a = c b 2b = a + c 2 (3y+5)
More informationMockTime.com. (b) 9/2 (c) 18 (d) 27
212 NDA Mathematics Practice Set 1. Let X be any nonempty set containing n elements. Then what is the number of relations on X? 2 n 2 2n 2 2n n 2 2. Only 1 2 and 3 1 and 2 1 and 3 3. Consider the following
More informationMOCKTIME.COM ONLINE TEST SERIES CORRESPONDENCE COURSE
GEOMETRY TRIANGLES AND THEIR PROPERTIES A triangle is a figure enclosed by three sides. In the figure given below, ABC is a triangle with sides AB, BC, and CA measuring c, a, and b units, respectively.
More informationFILL THE ANSWER HERE
HOM ASSIGNMNT # 0 STRAIGHT OBJCTIV TYP. If A, B & C are matrices of order such that A =, B = 9, C =, then (AC) is equal to  (A) 8 6. The length of the subtangent to the curve y = (A) 8 0 0 8 ( ) 5 5
More informationCBSE CLASS X MATH SOLUTION Therefore, 0.6, 0.25 and 0.3 are greater than or equal to 0 and less than or equal to 1.
CBSE CLASS X MATH SOLUTION 011 Q1 The probability of an event is always greater than or equal to zero and less than or equal to one. Here, 3 5 = 0.6 5% = 5 100 = 0.5 Therefore, 0.6, 0.5 and 0.3 are greater
More informationAlg. (( Sheet 1 )) [1] Complete : 1) =.. 3) =. 4) 3 a 3 =.. 5) X 3 = 64 then X =. 6) 3 X 6 =... 7) 3
Cairo Governorate Department : Maths Nozha Directorate of Education Form : 2 nd Prep. Nozha Language Schools Sheet Ismailia Road Branch [1] Complete : 1) 3 216 =.. Alg. (( Sheet 1 )) 1 8 2) 3 ( ) 2 =..
More informationPage 1 of 15. Website: Mobile:
Exercise 10.2 Question 1: From a point Q, the length of the tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm. The radius of the circle is (A) 7 cm (B) 12 cm (C) 15 cm (D) 24.5
More information2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time is
. If P(A) = x, P = 2x, P(A B) = 2, P ( A B) = 2 3, then the value of x is (A) 5 8 5 36 6 36 36 2. A die is rolled 3 times, the probability of getting a number larger than the previous number each time
More informationCOMMON UNITS OF PERIMITER ARE METRE
MENSURATION BASIC CONCEPTS: 1.1 PERIMETERS AND AREAS OF PLANE FIGURES: PERIMETER AND AREA The perimeter of a plane figure is the total length of its boundary. The area of a plane figure is the amount of
More informationUnit 8. ANALYTIC GEOMETRY.
Unit 8. ANALYTIC GEOMETRY. 1. VECTORS IN THE PLANE A vector is a line segment running from point A (tail) to point B (head). 1.1 DIRECTION OF A VECTOR The direction of a vector is the direction of the
More information1 / 24
CBSEXII017 EXAMINATION CBSEX01 EXAMINATION MATHEMATICS Paper & Solution Time: 3 Hrs. Max. Marks: 90 General Instuctions : 1. All questions are compulsory.. The question paper consists of 34 questions
More informationPractice Assessment Task SET 3
PRACTICE ASSESSMENT TASK 3 655 Practice Assessment Task SET 3 Solve m  5m + 6 $ 0 0 Find the locus of point P that moves so that it is equidistant from the points A^3, h and B ^57, h 3 Write x = 4t,
More information1 / 23
CBSEXII017 EXAMINATION CBSEX008 EXAMINATION MATHEMATICS Series: RLH/ Paper & Solution Code: 30//1 Time: 3 Hrs. Max. Marks: 80 General Instuctions : (i) All questions are compulsory. (ii) The question
More informationQuestion 1 ( 1.0 marks) places of decimals? Solution: Now, on dividing by 2, we obtain =
Question 1 ( 1.0 marks) The decimal expansion of the rational number places of decimals? will terminate after how many The given expression i.e., can be rewritten as Now, on dividing 0.043 by 2, we obtain
More informationSYSTEM OF CIRCLES If d is the distance between the centers of two intersecting circles with radii r 1, r 2 and θ is the
SYSTEM OF CIRCLES Theorem: If d is the distance between the centers of two intersecting circles with radii r 1, r 2 and θ is the 2 2 2 d r1 r2 angle between the circles then cos θ =. 2r r 1 2 Proof: Let
More informationC=2πr C=πd. Chapter 10 Circles Circles and Circumference. Circumference: the distance around the circle
10.1 Circles and Circumference Chapter 10 Circles Circle the locus or set of all points in a plane that are A equidistant from a given point, called the center When naming a circle you always name it by
More informationMaharashtra State Board Class X Mathematics Geometry Board Paper 2015 Solution. Time: 2 hours Total Marks: 40
Maharashtra State Board Class X Mathematics Geometry Board Paper 05 Solution Time: hours Total Marks: 40 Note: () Solve all questions. Draw diagrams wherever necessary. ()Use of calculator is not allowed.
More informationPlane geometry Circles: Problems with some Solutions
The University of Western ustralia SHL F MTHMTIS & STTISTIS UW MY FR YUNG MTHMTIINS Plane geometry ircles: Problems with some Solutions 1. Prove that for any triangle, the perpendicular bisectors of the
More informationMATHEMATICS. Time allowed : 3 hours Maximum Marks : 100 QUESTION PAPER CODE 30/1/1 SECTION  A
MATHEMATICS Time allowed : 3 hours Maximum Marks : 100 GENERAL INSTRUCTIONS : 1. All questions are compulsory 2. The question paper consists of 30 questions divided into four sections  A, B, C and D.
More informationCreated by T. Madas 2D VECTORS. Created by T. Madas
2D VECTORS Question 1 (**) Relative to a fixed origin O, the point A has coordinates ( 2, 3). The point B is such so that AB = 3i 7j, where i and j are mutually perpendicular unit vectors lying on the
More information1 (C) 1 e. Q.3 The angle between the tangent lines to the graph of the function f (x) = ( 2t 5)dt at the points where (C) (A) 0 (B) 1/2 (C) 1 (D) 3
[STRAIGHT OBJECTIVE TYPE] Q. Point 'A' lies on the curve y e and has the coordinate (, ) where > 0. Point B has the coordinates (, 0). If 'O' is the origin then the maimum area of the triangle AOB is (A)
More information11 th Philippine Mathematical Olympiad Questions, Answers, and Hints
view.php3 (JPEG Image, 840x888 pixels)  Scaled (71%) https://mail.ateneo.net/horde/imp/view.php3?mailbox=inbox&inde... 1 of 1 11/5/2008 5:02 PM 11 th Philippine Mathematical Olympiad Questions, Answers,
More information1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT.
1 Line n intersects lines l and m, forming the angles shown in the diagram below. 4 In the diagram below, MATH is a rhombus with diagonals AH and MT. Which value of x would prove l m? 1) 2.5 2) 4.5 3)
More informationSURA's Guides for 3rd to 12th Std for all Subjects in TM & EM Available. MARCH Public Exam Question Paper with Answers MATHEMATICS
SURA's Guides for rd to 1th Std for all Subjects in TM & EM Available 10 th STD. MARCH  017 Public Exam Question Paper with Answers MATHEMATICS [Time Allowed : ½ Hrs.] [Maximum Marks : 100] SECTION 
More informationMathematics. A basic Course for beginers in G.C.E. (Advanced Level) Mathematics
Mathematics A basic Course for beginers in G.C.E. (Advanced Level) Mathematics Department of Mathematics Faculty of Science and Technology National Institute of Education Maharagama Sri Lanka 2009 Director
More information0609ge. Geometry Regents Exam AB DE, A D, and B E.
0609ge 1 Juliann plans on drawing ABC, where the measure of A can range from 50 to 60 and the measure of B can range from 90 to 100. Given these conditions, what is the correct range of measures possible
More information(c) n (d) n 2. (a) (b) (c) (d) (a) Null set (b) {P} (c) {P, Q, R} (d) {Q, R} (a) 2k (b) 7 (c) 2 (d) K (a) 1 (b) 3 (c) 3xyz (d) 27xyz
318 NDA Mathematics Practice Set 1. (1001)2 (101)2 (110)2 (100)2 2. z 1/z 2z z/2 3. The multiplication of the number (10101)2 by (1101)2 yields which one of the following? (100011001)2 (100010001)2 (110010011)2
More informationCHAPTER 10 CIRCLES Introduction
168 MATHEMATICS CIRCLES CHAPTER 10 10.1 Introduction You may have come across many objects in daily life, which are round in shape, such as wheels of a vehicle, bangles, dials of many clocks, coins of
More informationMaharashtra State Board Class X Mathematics  Geometry Board Paper 2016 Solution
Maharashtra State Board Class X Mathematics  Geometry Board Paper 016 Solution 1. i. ΔDEF ΔMNK (given) A( DEF) DE A( MNK) MN A( DEF) 5 5 A( MNK) 6 6...(Areas of similar triangles) ii. ΔABC is 060 90
More informationTime : 2 Hours (Pages 3) Max. Marks : 40. Q.1. Solve the following : (Any 5) 5 In PQR, m Q = 90º, m P = 30º, m R = 60º. If PR = 8 cm, find QR.
Q.P. SET CODE Q.1. Solve the following : (ny 5) 5 (i) (ii) In PQR, m Q 90º, m P 0º, m R 60º. If PR 8 cm, find QR. O is the centre of the circle. If m C 80º, the find m (arc C) and m (arc C). Seat No. 01
More informationDownloaded from
Triangles 1.In ABC right angled at C, AD is median. Then AB 2 = AC 2  AD 2 AD 2  AC 2 3AC 24AD 2 (D) 4AD 23AC 2 2.Which of the following statement is true? Any two right triangles are similar
More informationProperties of the Circle
9 Properties of the Circle TERMINOLOGY Arc: Part of a curve, most commonly a portion of the distance around the circumference of a circle Chord: A straight line joining two points on the circumference
More informationHEAT3 APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA MAXMARKS(112(3)+20(5)=436)
HEAT APPLICATION OF DERIVATIVES BY ABHIJIT KUMAR JHA TIME(HRS) Select the correct alternative : (Only one is correct) MAXMARKS(()+0(5)=6) Q. Suppose & are the point of maimum and the point of minimum
More information