4/10/24
FILL IN THE BLANKS
1) The roots of the quadric equation ax²+ 2bx + c=____(a≠0) are real and equal, then b²= _____.
2) The equation (a- 2)x²+ 3x +5=0 will not be a quadratic equation for a=___.
3) In in quadratic equation ax²+ bx + c=0(a≠ 0), b²= 4ac, then the roots of the equation will be real and ____.
4) if the sum and product of two quadratic conditions is a fundamental number, then both the conditions are____.
5) 7x²- 12x +18=0. The ratio of the sum and the product of the roots of the equations_____.
6) ax²+ bx + c=0 (a≠0) if both the roots of the equation are mutually inverse (reciprocal), then c=____.
7) ax²+ bx + c=0 (a≠ 0) if both the roots of the are mutually inverse and negative, then a+ c=____.
8) If sum of two angles is ___, then they are called supplementary angles.
9) If the bases of two triangles are situated on same line and the other vertex of the two triangles are common, then the ratio of the areas of two triangles are ____ to the ratio of their bases.
10) if ABCD is a cyclic parallelogram then angle A is____.
11) If the length of the sides of two Triangles are in proportion, then two Triangles are _____.
12) If both the angles made by an arc in the same arc are equal, then the length of both the arcs is ____.
13) A contagious Parallelogram is a_____.
14) The vertices of a square figure are ____.
15) If a straight line intersects a cut at two points, then the straight line is called the ___ of the cut.
16) Due to the ratio of the length of the two chords PQ and RS in the O central circle, 1:1 angle POQ: angle ROS= ____ .
17) the perpendicular bisector of a chord of a chord is____.
18) Angles lying in the same verse are ____.
19) If the line segment joining two points makes equal opposite angles to the other two points on the same side, then the four points will be____.
20) Two Triangles are similar if their____
21) If a straight line intersects the circle at two points, then the straight line is called ____ of circle.
22) Two circles touch each other externally at the point A. A common tangent drawn to the two circles at the point A is ____ common tangent (direct/ transverse).
23) if AOB is the diameter of a circle and C and D are two different points on the circumference not on the same side of AB, such that angle AOC=130°, then the value of angle CDB will be____.
24) The line segment parallel to any side of a triangle divides other two sides or the extended two sides ___.
25) The perpendicular bisector of any chord of a circle is____ of that circle.
26) The angle in the segment of a circle which is less than the semicircle is an ____angle.
27) three circles can intersect each other at more than ____point/s.
28) The distance between the centres of two circles with radii 9cm and 16cm is 25cm. The length of the segment of the tangent between them is____cm.
29) In ∆ ABC , angle A= angle B= 60°, AC=8cm. The lines AD and BD intersect at D with D= 90°. If DB= 2cm then the length of AD is ____cm.
30) If an exterior angle of a cyclic quadrilateral be 50°, then the interior opposite angle is____.
31) If PQ is the diameter of a circle with centre O and R is a point on the circumference such that angle ROQ= 120°, then the value of angle ORP is ____.
32) The circle drawn with the hypotenuse of a right angled triangle as diameter passes through the ____.
33) The straight lines parallel to the parallel sides of a trapezium divides____ other two sides.
34) If cos²x - sin²x = 1/x (x > 1), then cos⁴x - sin⁴x = ____.
35) If the sun's angle of elevation increases from 30° to 60°, the length of the shadow of a post____. (decreases/ increases).
36) if the angle of elevation of the sun is 45°, then the length of shadow and length of post ate____.
37) The value of tan 15 tan 45 tan 60 tan 75 is ____.
38) if tanx = 4/5, then x = ____.
39) If sinx =1/2, then cos2x =_____.
40) If the opposite angles of a quadrilateral be supplement then the vertices of the quadrilateral will be_____.
41) cosx= √3/2, then sin2x=_____.
42) The value of (4/sec²x + 1/(1+ cot²x) + 3 sin²x) is ____.
43) The vertical of a cyclic squares are _____.
44) If sinx =1/2, then tan2x =___.
45) If sin(x - 30°)= 1/2, then the value of cosx is_____.
46) One solid sphere is melted and a solid right circular cylinder is made, then _____ of sphere and the cylinder will be equal.
47) number of surfaces of the solid right circular cylinder is____.
48) The shape of a pencil with one end sarpend is the combination of a cylinder and a ____.
48) The numbers are plane surface of a solid hemisphere are____.
49) ABC is the hypotenuse of the right angle AC triangle. Considering the side AB as an axis, the diameter of the right circular cone that will be formed in full circle of the triangle will be____.
50) if the volume of a right circular cone is V cubic units and the area of the base being A square units, the height will be_____.
51) If the radius of the base of a right circular cylinder and a right circular cone are the same and their heights are also be same, then the ratio of their volumes will be ____.
52) A solid sphere is melted to form a solid right circular cylinder. The volume of the sphere and the cylinder is____.
53) The number of diagonals of a rectangular solid is____.
54) The length of the diagonal of a plane of a cube= ____ x length of one side.
55) A rectangular paper has unit length and unit width . A rectangular paper is folded into cylinder whose circumference is equal to the length of the paper____ curve of cylinder.
56) The length of the radius of the base of a solid right circular cylinder and two hemisphere are equal. If tor hemisphere are placed side by side with the plane of the cylinder, then what is the shape of the new solid object = area of the plane of a hemisphere + ____ area of the curve of+ The area of the curve of second hemisphere.
57) If the diameter of a circular pipe is 3 cm and height is 4cm, then the length of the longest pole that will be placed inside the pipe is_____ cm.
58) If the volume of a right circular cylinder and the area of the curved plane have the same number of values, then the length of the diameter of the cylinder is____.
59) The variable x₁, x₂,.......x₁₀₀ are in ascending order of their magnitude, then the median of the variable is____.
60) The measured of central tendency are mean, median and____.
61) if the mean x₁, x₂, x₃....xₙ be bar x, then the mean of kx₁, kx₂, kx₃....kxₙ is _____(k≠0).
62) The median of the data 8, 9, 6, 7, 5, 6, 7, 8, 9, 10 is____.
63) If the mean of the number 6, 7, x, 8, y, 14 is 9, then x + y=____.
64) The relation between x and y is 2x + 3y=7. If the median of y is 2; then the median of x is _____.
65) The median of 2, 3, 4, 3, 6, 7, 8 is ____.
66) The following are the marks obtained by 10 students in physics test: 65, 52, 71, 47, 49, 51, 37, 29, 77, 62; then the mean mark is____.
67) The mode of 2, 3, 5, 6, 2, 4, 2, 8, 6, 9 will be____.
68) The mode of the data 1,1,2,2,2,3,3,3,4,4,5,6,7 is____.
CHOOSE THE CORRECT OPTION:
1) The product of two roots of the equation x²-7x +3 =0 is
a) 7 b) -7 c) 3 d) - 3
2) Under what condition one root of the quadric equation ax²+ bx + c=0 is zero ?
a) a= 0 b) b= 0 c) c= 0 d) none.
3) 2x²- 3x - k +2=0 one root of the equation is 0. The value of k is
a) 2 b) -2 c) 1/2 d) -1/2
4) If two roots of equation x²+ 4x +k=0 are equal, then the value of k is
a) 1 b) 2 c) 3 d) 4
5) If two roots of equation x²- 6x + k=0 are real and unequal then what is the value of k ?
a) more than 6 b) less than 6 c) more than 9 d) less than 9.
6) The sum of two roots of the equation x²- 6x +2=0
a) 2 b) - 2 c) 6 d) - 6
7) If the product of two roots of the equation is x²- 3x + k=10 is -2, what is the value of k ?
a) - 2 b) - 8 c) 8 d) 12
8) If two roots of the equation ax²+ bx + c=0(a≠ 0) be equal , then
a) c= -b/2a b) c= b/2a c) c= - b²/4a d) c= b²/4a
9) The roots of the equation x²= 6² is/are
a) 0 b) 6 c) 0 and 6 d) - 6
10) if two roots of the equation (k +1)x²+ 2kx + (k +2)= 0 are equal and negative then the value of k is
a) 1 b) -1 c) 0 d) -2
11) If the roots of the equation ax²+ bx + c=0(c ≠ 0) are real and unequal then b²- 4ax will be
a) >0 b) =0 c) <0 d) none.
12) The number of roots in a quadratic equation is
a) 1 b) 2 c) 3 d) none.
13) If ax²+ bx + c=0 is a quadratic equation then
a) b≠ 0 b) c≠ 0 c) a≠ 0 d) none.
14) The highest power of the variable of a quadratic equation is
a) 1 b) 2 c) 3 d) none
15) The equation 4(5x²- 7x +2)= 5(4x²- 6x +3) is
a) linear b) quadratic c) 3rd degree d) none
16) The length of the two chords AB and CD cycle of a circle of centre O are equal and angle AOB= 60°,
a) 40° b) 30° c) 60° d) 90°
17) O is the centre of a circle and AB is a diameter, ABCD is a the cyclic quadrilateral.
Angle ABC=65°, angle DAC= 40°, then the measure of angle BCD is
a) 75° b) 105° c) 115° d) 80°
18) If Angle A =100° of a cyclic quadrilateral ABCD, then the value of angle C is
a) 50° b) 80° c) 180° d) 200°
19) The number of common tangents of two circles when they do not touch or intersect each other is :
a) 2 b) 1 c) 3 d) 2
20) The length of the radius of 6 circle is 13cm and the length of a chord of the circle is 10cm, the distance of the coord from the centre of the circle is
a) 12.5cm b) 12 cm c) √69cm d) 24 cm
21) The centre of two concentric circles is O; a straight line intersects a circle at point A and B and the other circle at point C and D. If AC= 5 cm, then the length of BD is
a) 2.5cm b) 5cm c) 10 cm d) none.
22) The distance between two parallel chords of length 8cm each in a circle of diameter 10 cm is
a) 6cm b) 7cm c) 8cm d) 5.5 cm
23) In the adjoining figure, if O is the centre of the circle, then the value of angle X is
a) 70° b) 60° c) 40° d) 200°
24) In the adjoining figure,
if O is the centre of the circle and the BC is the diameter then the value of x is
a) 60° b) 50° c) 100° d) 80°
25) In the adjoining figure,
O is the centre of the circle; if ang ACB =30°, angle ABC= 60°, angle DAB= 35° and DBX= x°, then the value of x is
a) 35 b) 70 c) 65 d) 55
26) If AB is a diameter of a circle with Centre O and C is a point on the circumference such that angle BOC=60°, then the value of angle AOC is
a) 60° b) 30° c) 120° d) 90°
27) In the adjoining figure,
O is the centre of the circle and AB is the diameter. If AB || CD, angle ABC=25°, then the value of angle CED is
a) 80° b) 50° c) 25° d) 40°
28) In the adjoining figure,
a) 56° b) 86° c) 38° d) 28°
29) In the diagram
besides O is the centre of the circle and AB is a diameter. ABCD is a cyclic quadrilateral. Angle BAC is
a) 50° b) 60° c) 30° d) 40°
30) In the diagram
besides ABCD is a cyclic quadrilateral. BA is produced to the point F. If AE|| CD, angle ABC= 92° and angle FAE= 20°, then the value of angle BCD is
a) 20° b) 88° c) 108° d) 72°
31) I is the centre of ∆ ABC, angle ABC= 60° and angle ACB= 50°. Then angle BIC is
a) 55° b) 125° c) 70° d) 65°
32) In the adjoining figure,
O is the centre of the cirle, if Angle BAD= 65°, angle BCD= 45°, then the value of angle BCD is
a) 65° b) 45° c) 40° d) 20°
33) If tanx + cotx =2, then the value of (tan¹³x + cot¹³x) is
a) 1 b) 0 c) 2 d) none
34) If tanx = 4/5, then cosx =
a) 4/5 b) 3/5 c) 3/4 d) 5/√41
35) If sinx = 1/√2, then sec2x =
a) 0 b) 1 c) 2 d) none
36) Height of tower is 100√3 metres. The angle of elevation of the top of the tower from a point at a distance 100metres from the foot of the tower is
a) 30° b) 45° c) 60° d) none
37) If the ratio of the volume of two right circular cones is 1:4 and the ratio of radii of their bases is 4:5, then the ratio of their height is:
a) 1:5 b) 5:4 c) 25: 16 d) 25 :64
38) If two cubes of length of each side 2√6 are placed side by side, then the length of the diagonal of the cuboid so produce is
a) 10cm b) 6cm c) 2cm d) 12cm
39) If side of a cube is a unit and the diagonal of the cube is d unit then the relation between a and d will be:
a) √2 a= d b) √3 a = d c) a= √3 d d) a= √2 d
40) If each of radius of the base and height of a cone be doubled, then the volume of it will be
a) 3 times b) 4 times c) 6 times d) 8 times
41) If the height of a cone is h unit, slant height I units and the diameter of the base is d unit, then (l²- h²)/d²= ?
a) 1/2 b) 1/3 c) 1/4 d) 1/5
42) The volume inside a rectangular box is 440 cubic cm and the area of the inner base is 88 sq cm, then the inner height of the box is
a) 4cm b) 5cm c) 3cm d) 6 cm
43) A rectangular pit is 40m long , 12m wide and 16m deep. In this pit a plank 5m long, 4 m wide and 2 m high will be placed ?
a) 190 b) 192 c) 184 d) 180
44) The area of the lateral plane of a cube is 256 sq.m volume of cube
a) 64cune m b) 216 cube m c) 256 cube m d) 51 cube m
45) If the ratio of the volumes of two cubes is 1:27, then the ratio of the area of the total surface of both the cubes is
a) 1:3 b) 1 : 8 c) 1: 9 d) 1:18
46) if the area of all the sides of a cube is 5 square unit and the length of the diagonal is d units, then the contact between S and d is
a) S= 6d² b) 3S= 7d c) S³= d² d) d²= S/2
47) If the ratio of the radii of two circular solid cylinder 2 :3 and the ratio of their height is 5:3, then the ratio of the areas of their sides is
a) 2:5 b) 8 : 7 c) 10:9 d) 16:9
48) if the ratio of the radiu of two right circular solid cylinder is 2:3 and that of the height is 5:3, then the ratio of their volume is
a) 27:20 b) 20: 27 c) 4 :9 d) 9 :4
49) 2 right circular cylinders have equal volumes and the ratio of their heights is 1:2, then the ratio of their radii--
a) 1:√2 b) √2: 1 c) 1:2 d) 2:1
50) If the radius of a right circular cylinder is half the length and twice the height, then the volume of the cylinder will be the volume of the initial cylinder.
a) equal b) double c) half d) four times
51) when the radius of a right circular cylinder is doubled and the height is halved , the area of the circle is the area of the original cylinder.
a) equal b) double c) half d) four times.
52) If the ratio of the volumes of two solid sphere is 1:8, then the ratio of the area of the sphere will be ---
a) 1:2 b) 1:4 c) 1: 8 d) 1:16
53) The total surface area of a solid hemisphere of radius 7cm will be
a) 588π sq.cm b) 392π sq.cm c) 147π sq.cm d) 98π sq.cm
54) if the ratio of the areas of the sides of two solid sphere is 16:9, then the ratio of their volumes will be
a) 64 :27 b) 4 :3 c) 27 :64 d) 3:4
55) if the area of the circle of a solid sphere and three times the volume have the same numerical value, then the length of the radius of the sphere is
a) 1 unit b) 2 unit c) 3 units d) 4 units.
56) If the slant height of a right circular cone is 15cm and the diameter of the base is 16cm, then the area of the lateral plane of the cone will be
a) 60π sq.cm b) 68π sq.cm c) 120π sq.cm d) 130 π sq.cm
57) The ratio of the volumes of two right circular cones is 1:4 and the radius of their bases is 4:5 p, then the ratio of their heights will be
a) 1:5 b) 5:4 c) 25:16 d) 25:64
58) Keeping the radius of the base of a right circular cone the same and doubling its height, the increase in its volume will be
a) 100% b) 200% c) 300% d) 400%
59) if the radius of a right circular cone is r/2 units and the slant height is 21 units , then the area of the total plane of the cone is
a) 2πr(l+ r) cu. unit
b) πr(l+ r/4) cu. unit
c) πr(l+ r) cu. unit
d) 2πr cu. unit
60) The median of the data 11 , 29, 17, 21, 13, 31, 39, 19 is
a) (19+29)/2 b) 19 c) 21 d) none
61) Mode is the
a) least frequent value
b) middle most value
c) most frequent value
d) largest value
62) The mode of the data 1, 2, 3, 4, 5, 6, 7 is
a) 4 b) 6 c) 7 d) none
63) median of a frequency distribution can be obtained from
a) pie diagram
b) histogram
c) frequency polygon
d) ogive
64) The median of 1, 5, 9, 3, 8, 7 is
a) 5 b) 7 c) 8 d) 5 and 7 both
65) if the median after arranging in ascending order the data 8, 9, 12, 17, x+ 2, x + 4, 30, 31, 34, 39 is 15, then the value of x is
a) 22 b) 21 c) 20 d) 24
2) Calculate the length of the tangent drawn to a circle of diameter 8 cm from a point 5 cm away from the centre of the circle. (2)
3) a) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5, find b.
b) If each observation is decreased in value by 1 unit, what would be the new mean be ? (3)
4) In the figure below, AB is a chord of the circle with centre O and BT is standing to the circle at B.
If angle AOB= 32°, find the value of x and y. (3)
5) The volume of a cylinder 14cm long is equal to that of a cube having an age 11 cm. Find the radius of the cylinder. (4)
6) A piece of butter 3 cm by 5cm by 12cm is placed in a hemispherical bowl of radius 3.25cm. Will the butter overflow when it melts completely ? (4)
7) Solve graphically 2x + 3 y= - 5; 2y + 3x = 0. (5)
8) In a ∆ABC, angle A is obtuse, PB perpendicular to AC and QC perpendicular to AB. Prove that: AQ x AB = AP x AC. (4)
9) Taniya standing on a vertical cliff in a jungle observes two rest houses in line with her on opposite sides deep in the jungle below. If their angles of depression are 30° and 45° and the distance between them is 222m, find the height of the cliff. (5)
10) AB is a fixed line. Write about the locus of the point P so that AB²= AP²+ BP². (2)
11) The base of a triangle is 2cm greater than twice its altitude. If the area is 12cm², calculate the base and the altitude. (4)
12) In the given figure, calculate:
a) angle APB
b) angle AOB. (3)
13) The midpoint of the line joining A(2, p) and B(q, 4) is (3, 5). Find the numerical values of p and q. (3)
14) From the following table, find:
a) average wage of a worker. Give your answer, to the nearest paise.
b) model class. (4)
Wages inRs. No of Workers
Less than 10 15
Less than 20 35
Less than 30 60
Less than 40 80
Less than 50 90
Less than 60 127
Less than 70 190
Less than 80 200
15) Examine the ogive given below which shows the marks obtained out of 100 by a set of students in an examination and answer the following questions:
b) How many students obtained 40% marks ?
c) How many students obtained 90% and above ?
d) What is the medium marks ? (4)
16) Prove that √{(1+ cosx)/(1- cosx)= cosecx + cotx. (3)
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