# Practice Test

Q1) Sum of all interior angles of a pentagon is Show Answer

Q2) A girl of height 90 cm is walking away from the base of a lamp-post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 s. Show Answer

Q3) Area of two similar triangles are 81 sq cm and 49 sq cm. Find the ratio of their corresponding heights. Show Answer

Q4) The distance between the centres of two circles having radii 4.5 cm and 3.5 cm, respectively is 10 cm. What is the length of the transverse common tangent of these circles? Show Answer

Q5) If points (-4, 0), (0, 3) and (0, -3) are the vertices of a triangles, then find the shape of the traingle. Show Answer

Q6) Find the distance between the points (1, -2) and (-5, 6). Show Answer

Q7) Find the coordinates of the point, which divides the line segment joining the points (5, -2) and (9, 6) in the ratio 3 : 1 internally. Show Answer

Q8) Find the coordinates of the point, which divides the line segment joining the points (2, -3) and (-3, 7) in the ratio 5 : 3 externally. Show Answer

Q9) Find the equation of a line, which passes through (2, 2) and the sum of whose intercepts on coordinate axes is 9. Show Answer

Q10) The points (0, 0) (0, 10) (8, 16) and (8, 6) are joined to form a quadrilateral. Find the type of the quadrilateral. Show Answer

Q11) The vertex of a triangle are (0, 0), (5, 3) and (3, 5) respectively. Find the circumcentre and circumradius of the triangle. Show Answer

Q12) Find the equation of a straight line whose slope is -2 and which passes through point (3, 7). Show Answer

Q13) Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is Show Answer

Q14) In a triangle ABC, points P, Q and R are the mid-points of the sides AB, BC and CA respectively. If the area of the triangle ABC is 20 sq. units, find the area of the triangle PQR Show Answer

Q15) Two circles touch each other internally. Their radii are 2 cm and 3 cm. The biggest chord of the outer circle which is outside the inner circle is of length Show Answer

Q16) A triangle and a parallelogram are constructed on the same base such that their areas are equal. If the altitude of the parallelogram is 100 m, then the altitude of the triangle is Show Answer

Q17) From a circular sheet of paper with a radius of 20 cm, four circle of radius 5 cm each are cut out. What is the ratio of the uncut to the cut problem? Show Answer

Q18) Find the co-ordinates of the point which divides the line segment joining the points (4, -1) and (-2, 4) internally in the ratio 3 : 5 Show Answer

Q19) Two circles of radii 10 cm, 8 cm, intersect and length of the common chord is 12 cm. Find the distance between their centers. Show Answer

Q20) The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall the upper end of the ladder coincides with the tip of the wall. Then, the height of the wall is Show Answer

Q21) How many sides a regular polygon has with its sum of interior angles eight times its sum of exterior angles? Show Answer

Q22) The Co-ordinates of the centroid of the triangle A B C are (6, 1). If two vertices A and B are (3, 2) and (11, 4) find the third vertex Show Answer

Q23) In a triangle ABC, the lengths of the sides AB, AC and BC are 3, 5 and 6 cm, respectively. If a point D on BC is drawn such that the line AD bisects the angle A internally, then what is the length of BD? Show Answer

Q24) AB and CD two chords of a circle such that AB = 6 cm, CD = 12 cm. And AB || CD. The distance between AB and CD is 3 cm. Find the radius of the circle. Show Answer

Q25) The line x + y = 4 divides the line joining the points (-1, 1) and (5, 7) in the ratio Show Answer

Q26) If the three vertices of a rectangle taken in order are the points (2, -2), (8, 4) and (5, 7). The coordinates of the fourth vertex is Show Answer

Q27) The centroid of a triangle, whose vertices are (2, 1), (5, 2) and (3, 4) is Show Answer

Q28) If the coordinates of the points A, B, C be (4, 4), (3, -2) and (3, -16) respectively, then the area of the triangle A B C is Show Answer

Q29) The perimeter of the triangle whose vertices are (-1, 4), (-4, -2), (3, -4) will be Show Answer

Q30) The distance between two parallel chords of length 8 cm each in a circle of diameter 10 cm is Show Answer

Q31) Two parallel chords of a circle of diameter 20 cm are 12 cm and 16 cm long. If the chords are in the same side of the center, then the distance between them is Show Answer

Q32) Two circles with radii 25 and 9 cm touch each other externally. The length of the direct common tangent is Show Answer

Q33) The radius of the circum-circle of the triangle made by x - axis, y - axis and 4 x + 3 y = 12 is Show Answer

Q34) The length of the circum-radius of a triangle having sides of lengths 12 cm, 16 cm and 20 cm is Show Answer

Q35) If P, R, T are the area of a parallelogram, a rhombus and a triangle standing on the same base and between the same parallels, which of the following is true? Show Answer

Q36) Two circles with same radius r intersect each other and one passes through the center of the other. Then the length of the common chord is Show Answer

Q37) A and B are centers of the two circles whose radii are 5 cm and 2 cm respectively. The direct common tangents to the circles meet AB extended at P. Then P divides AB. Show Answer

Q38) The length of tangent (up-to the point of contact) drawn from an external point P to a circle of radius 5 cm is 12 cm. The distance of P from the center of the circle is Show Answer

Q39) Two circles of equal radii touch externally at a point P. From a point T on the tangent at P, tangents TQ and TR are drawn to the circles with points of contact Q and R respectively. The relation of TQ and TR is Show Answer

Q40) When two circles touch externally, the number of common tangents are Show Answer

Q41) If the inradius of a triangle with perimeter 32 cm is 6 cm, then the area of the triangle in sq. cm is Show Answer

Q42) If two circles of radii 9 cm and 4 cm touch externally, then the length of a common tangent is Show Answer