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°,
then angle COD= is
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) A person goes 24m West from a place and then he goes 10m north. The distance of the person from the starting point is
a) 34m b) 17m c) 26m d) 25m
29) Two rods of 13m length and 7m length are situated perpendicularly on the ground and the distance between their feet is 8m. The distance between their top parts is
a) 9m b) 10m c) 11m d) 12m.
30) In the adjoining figure,
O is the centre of the circle, id angle BCD= 28°, angle AEC= 38°, then the value of angle AXB= ?
a) 56° b) 86° c) 38° d) 28°
31) 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°
32) 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°
33) 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°
34) 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°
35) If sinx - cosx = 0 (0≤ x ≤ 90°) and sex + cosecx = y, then the value of y is
a) 1 b) 2 c) √2 d) 2√2
36) If tanx + cotx =2, then the value of (tan¹³x + cot¹³x) is
a) 1 b) 0 c) 2 d) none
37) If cotx = 7/7.5, then cosecx is
a) 7.5/4 b) 8/17 c) 17/15 d) 15/17
38) If 2x = secA and tanA= 2/x then the value of 2(x²- 1/x²)²= ?
a) 1/2 b) 1/4 c) 1/8 d) 1/16
39) If tanx = 4/5, then cosx =
a) 4/5 b) 3/5 c) 3/4 d) 5/√41
40) If sinx = 1/√2, then sec2x =
a) 0 b) 1 c) 2 d) none
41) 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
42) 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
43) 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
44) 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
45) 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
46) 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
47) 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
48) 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
49) 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
50) 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
51) 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
53) 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
54) 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
55) 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
56) 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
57) 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.
58) 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
59) 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
60) 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
61) 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.
62) 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
63) 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
64) 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%
65) 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
66) The median of the data 11 , 29, 17, 21, 13, 31, 39, 19 is
a) (19+29)/2 b) 19 c) 21 d) none
67) Mode is the
a) least frequent value
b) middle most value
c) most frequent value
d) largest value
68) The mode of the data 1, 2, 3, 4, 5, 6, 7 is
a) 4 b) 6 c) 7 d) none
69) median of a frequency distribution can be obtained from
a) pie diagram
b) histogram
c) frequency polygon
d) ogive
70) The median of 1, 5, 9, 3, 8, 7 is
a) 5 b) 7 c) 8 d) 5 and 7 both
71) 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
Day - 4
1) Find the remainder when 2x³ - 3x² + 7x - 8 is divided by x - 2.
2) A function g is defined by g(x)=144 - 16x². Calculate g(2). Also find the value of x when g(x)= 0.
3) Evaluate: 3 sin72°/cos18° - sec32°/cosec58°
4) Solve: 3x²- 5x = 1.
5) If 3 tan²A - 1 = 0, then show that cos3A = 4cos³A - 3cosA.
6) A(14,7), B(6, -3) and C(8,1) are the vertices of a triangle ABC. P is the midpoint of AB, and Q is the midpoint of AC. Write down the coordinates of P and Q. Show that BC= 2PQ.
7) Show: sinA(1+ tanA) + cosA(1+ cotA)= cosecA + secA.
8) Use a graph paper for this question. Draw a graph of x + 2y -7= 0 and 3x - y - 14= 0 on the same axes. Use 2cm= 1 unit on both axes and plot only 3 points for each line. Write down the coordinates of the point of intersection of the two lines.
Day- 3
1) Solve using quadratic formula, x²- 5x -2= 0. Give your answer correct to three significant figures.
2) Find the value of k, if x - k is a zero polynomial of x³- kx²+ x + 4
3) Prove: sinx/(1- cotx) + cosx/(1- tanx)= sinx + cosx.
4) If cosx = 4/5 and cosB= 24/25, find
a) cosec²A
b) cotA + cotB.
5) 6x² - x = 35.
6) x²- 8x - 1280= 0
7) 1/(2y -9) = 1/(y - 3) + 4/5
8) 5ˣ⁺¹ + 5²⁻ˣ = 126
9) A is the point on the y-axis whose ordinate is 5 and B is a point (-3,1). Calculate the length AB.
10) Find the coordinates of the points on the x-axis which are at a distance of 3√5 units from the (8, -3).
11) Prove that the points A(-10, 8), B(-2, -4) and C(10,4) are the vertices of an isosceles right angled triangle.
Day - 2
1) Solve: √(3x²+ x +5)= x -3.
2) Roots of the equation are (1/2) and -14. Find the equation.
3) 8(t² + 1/t²) - 42(t - 1/t) + 29= 0. Find the possible values of t.
4) Solve x²- 6x - 15= 0. Give your answer correct two decimal places.
5) Find the distance between the points A(5, -1) and B(8,3).
6) Find the coordinates of the points on the y-axis are at a distance of √68 from the point (2, -5).
7) A point P divides the join of A(6, -2) and B(-5, 8) in the ratio 2 : 3. Find the coordinates of P.
8) Find the ratio with x-axis divides the join of A(7, 2) and B(5, -4).
9) 1/(1+ cosx) + 1/(1- cosx) = 2 cosec²x.
10) 2 + tan²x + cot²x = cosec²x sec²x.
11) sinx(tanx - cotx)= secx - 2 cosx.
12) (secx - cosecx)(secx + cosecx)(sin²x - sin⁴x)= sin²x - cos²x.
13) (sinx - cosx)(tanx + cotx)= secx - cosecx.
Day-1
1) When 7x²- 3x +8 is divided by x -4, find the remainder. (2)
2) If 2 cosx = 2/5, find sinx. (2)
3) Find p and q if g(x)= x +2 is a factor of f(x)= x³- 0x + x + q and f(2)= 4. (3)
4) Solve: 2x + 3y= -5; 2y + 3x = 0. (3)
5) 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)
6) Prove: √{(1+ cosx).(1- cosx)}= Cosecx + cotx. (3)
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