2) A recurring deposit account of ₹1200 per month has a maturity value of ₹12440. If the rate of interest is 8% and the intrest is calculated at the end of every month, find the time of this recurring deposit account. 10 months
3) Sujata deposited, a certain sum of money, every month, for 2 and half years (5/2 yrs) in a cumulative time deposit account. At the time of maturity she collected ₹4965. If the rate of interest was 8% p.a. find the monthly deposit. 150
4) Sumit paid ₹300 per month in a cumulative time deposit account for 2 yrs. He received ₹7875 as the maturity amount. Find the rate of interest. 9%
5) On depositing ₹200, every month in a cumulative time deposit account, paying 9% p.a. intrest, a person collected ₹117 as intrest. Find the period. 12 months
1) Find the range of values of x, which satisfy the inequality -1/5 ≤ 3x/10 +1 < 2/5, x belongs to R. Graph the solution set on the number line. 4≤x <-2
2) Solve the following inequation, and graph the solution set on the number line: 2y - 3 < y+ 2 ≤ 3y+ 5, y(-R). The solution set={y: y belongs to R, -3/2 ≤ y < 5}
3) 5x/4 - (4x -1)/3 > 1, x belongs to R. Show in number line. {x:x<-8, x belongs to R}
4) 2x -1 ≥ x + (7- x)/3 > 2.
5) If P is the solution set of -3x +4< 2x -3, x belongs to N, Q is the solution set of 4x -5 < 12, x belongs to W, find
A) P ∩ Q
B) P - Q
C) P' ∩ Q
1) (x-3)/(x+3) + (x+3)/(x-3) = 5/2, x≠- 3, x ≠ 3. -9,9
2) 2x -3 =√(2x² - 2x +21). 6
3) a/(ax -1) + b/(bx -1)= a+ b, a+ b≠ 0, ab≠ 0. (a+ b)/ab, 2/(a+ b)
4) 2x²- 9x +10= 0, when
A) x belongs to N. 2
B) x belongs to Q . 2, 5/2
5) 3x²- x - 7 correct upto two decimal places. 1.70 or -1.37
6) 2/(x -1) + 3/(x+1) = 4/(x+2). Correct to 2 significant figures. 0.23 or -8.77
7) A train covers a distance of 600 km at x km/hr. Had the speed been (x+20) km/hr, the time taken to cover the distance would have been reduced by 5 hours. Write down an equation in terms of x and solve it to evaluate x. 40
8) The cost of 2x articles is ₹(5x+54) while the cost of (x +2) articles is ₹ (10x -4). Find x. 6
9) The difference of the square of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers. 9,6
10) A year ago the father was 8 times as old his son. Now his age is the square of his son's age. Find their present ages. 49,7 yrs
11) The length of the hypotenuse of a right angled triangle exceeds the length of the base by 2cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle. 8, 15,27
12) The sum of the numerator and denominator of a fraction is 8. If 1 is added to both the numerator and denominator, the fraction is increased by 1/15. Find the fraction. 3/5
1) A: B =1/4 : 1/5 and B : C = 1/7: 1/6, find A: B: C. 15:12:14
2) Find the number which bears the same ratio to 7/33 that 8/21 does to 4/9. 2/11
3) A bag contains ₹142 in the form of one-rupee, 50-paise and 20-paise coins in the ratio 3:5:8. Find the number of coins of each type. 60,100,160
1) Find the remainder when 3x³+ 5x²-11x -4 is divided by 3x+1. 1/9
2) Find the values of a and b, if x-2 and x+3 are both factors of x³+ ax²+ bx - 12. 3,-4
3) Find the value of a if the division of x³+ 5x²- ax +6 is divided by x-1 leaves the remainder 2a. 4
4) If 3x -2 is the factor of 3x³ - kx² +21x - 10, then find k. 11
5) Prove that x- 5 is a factor of 2x²- x -45. Hence, factorise completely. (x-5)(2x+9)
6) y³ - 13y -12 factorise completely. (y+1)(y-4)(y+3)
1) a -2 = 2 c
b 7 3 2c+ d then find a,b,c,d. 2,3,-2, 11
2) If A= 3 -4 & B= 0 2
0 1 3 -1 find the Matrix X if 2A + 3X = 5B.
3) If A= 1 2 B= -2 -1 C= 0 3
-2 3 1 2 2 -1 find A+ 2B - 3C.
4) If x+ 3y = 1 2 and 2x + y= 5 0
-1 5 -3 3 find the Matrix x and y.
5) If A= 1 1
8 3 evaluate A² - 4A.
6) If X= 4 1
-1 2 show that 6X - X² = 9I, where I is unit Matrix.
7) If B= 4 -5 & C= 10 -11
-2 1 12 -15 find the Matrix A such that AB= C.
1) The point P(3,4) is reflected to P' in the x-axis and O' is the image of O(origin) when reflected in the line PP'. Using graph paper, give:
A) The coordinates of P' and O'
B) The length of the segment PP' and OO'.
C) The perimeter of the quadrilateral POP'Q'.
D) The geometrical name of the figure POP'Q'. (-3,4), 6, 20, Rhombus
2) Use a graph paper for this question. Plot the points P(3,2) and Q(-3,-2). From P and Q, draw perpendiculars PM and QN on the x-axis.
A) name the image of P on reflection in the origin.
B) Assign the special name to the geometrical figure PMQN and find its area.
C) Write the coordinates of the point to which M is mapped on reflection in (i) x-axis (ii) y-axis (iii) origin. Q, parallelogram, 18, (3,0),(-3,0),(-3,0)
3) A point P is reflected in the origin. Coordinates of its image are (2,-5). Find
A) the coordinates of P. (-2,5)
B) the coordinates of the image of P in the x-axis. (-2,-5)
4) The point A(2,3), B(4,5) and C(7,2) are the vertices of ∆ABC.
A) Write down the coordinates of A', B', C' if ∆A'B'C', is the image of ∆ABC when reflected in the origin. (-2,-3),(-4,-5),(-7,-2)
B) Write down the coordinates of A", B", C" if A"B"C" is the image of ∆ABC when reflected in the x-axis. (2,-3),(4,-5),(7,-2)
C) Assign the special name to the quadrilateral BCC"B" and find its area. Isosceles trapezium, 33 sq units
5) A) point P(a,b) is reflected in the x-axis to P'(5,-2). Write down the values of a, b. 5,2
B) P" is the image of P when reflected in the y-axis. Write down the coordinates of P". (-5,2)
C) Name a single transformation that maps P' to P". Reflection in the origin
1) Find the coordinates of the point C which divides the join of A(4,-3) and B(9,7) in the ratio 3:2. (7,3)
2) Find a point P on the line segment joining A(14,-5) and B(-4,4), which is twice as far from A as from B. (2,1)
3) The midpoint of the line joining (a,2) and (3,6) is (2,b). Find a, b. 1,4
4) The midpoint of the line joining (2a,4) and (-2,3b) is (1, 2a+1). Find a, b. 2,2
5) The line segment joining A(2,3) and B(6,-5) is intersected by x-axis at a point k. Write down the ordinate of the point k. Hence, find the ratio in which k divides AB. 0, 3:5
6) Calculate the ratio in which the line segment joining (3,4) and (-2,1) is divided by the y-axis. 3:2
7) Find the coordinates of the vertices of the triangle, the middle point of whose sides are (0,1/2), (1/2,1/2),(1/2,0). (0,0),(1,0),(0,1)
8) If (0,b),(-a/2, b/2),(a/2, b/2) are the midpoints of the sides of a triangle, find the coordinates of its centroid. (0,2b/3)
1) Find the value of p, given that the line y/2 = x - p passes through the point (-4,4). -6
2) The equation of the line PQ is 3y - 3x +7= 0.
A) find the slope of PQ. 1
B) calculate the angle that the line PQ makes with the positive direction of x-axis. 45°
3) The graph of the equation y= mx + c passes through the points (1,4) and (-2,-5). Find the value of m and c. 3,1
4) Find the equation of the line passing through the point (2,-5) and making an intercept of -3 on the y-axis. x+y+3= 0
5) Find the equation of a straight line passing through (-1,2) and slope is 2/5. 2x- 5y+ 12= 0
6) Find the equation of a straight line passing through the origin and through the point of intersection the lines 5x+ 7y -3= 0 and 2x - y= 7. x+2y= 0
7) Calculated the coordinates of the point of intersection of the lines by x+y -6= 0 and 3x - y = 2. (2,4)
8) The vertices of a triangle ABC are A(2,-11), B(2,13) and C(-12,1). Find the equation of its sides. x-2= 0, 6x - 7y+ 79= 0, 6x+ 7y+ 65= 0
9)A(2,-4) B(3,3) and C (-1,5) are the vertices of a ∆ ABC . Find the equation of the median of the triangle through A. 8x+y -12= 0
1) On a map drawn to a scale 1: 25000, a rectangular plot of land ABCD has the following measurements AB= 12cm, BC= 16cm, Angles A, B, C, D are all 90° each. Calculate
A) the diagonal distance of the plot in km. 5 km
B) the area of the plot in km². 12km²
2) The model of a ship is made to a scale of 1: 250. Find
A) the length of the shii, if the length of its model is 1,2m. 300m
B) the area of the deck of the ship, if the area of the deck of its model is 1.6m². 100000 m²
C) the volume of its model, when the volume of the ship is 1 cubic kilometre. 64 m³
1) Find the length of the tangent drawn to a circle of radius 4cm from a point 5cm away from the centre of the circle. 3 cm
2) Three circles with centres X,Y and Z touch each other externally. If XY= 6cm, YZ= 9cm, and XZ= 7.5cm. find the radii of the circles. 2.25,3.75,5.25cm
3) Two circles of radii 6cm and 14cm have their centres 30cm apart. Find the radii of the smallest circle that can be drawn to touch them and encloses the smaller. 11cm
4) The length of the direct common tangent to two circles of radii 8cm and 6cm is 15cm. Calculate the distance between their centres. 15.33 cm
5) If AB and CD are two chords of a circle intersecting at a point P inside the circle, such that AB= 12cm, AP= 2cm and DP= 4cm. Find PC. 5cm
6) If AB and CD are two chords of a circle intersecting at a point P outside the circle when produced, such that PA= 10cm, PC= 8cm and PB= 4cm. Find PD. 5cm
1) A girl fills a cylindrical bucket 32cm in height and 18 cm in radius with sand. She emptied the bucket on the ground and makes a conical heap of the sand. If the height of the conical heap is 24cm.
A) find its radius. 36cm
B) its slant height. √1872
( leave your answer in square root from)
2) Water flows at the rate of 10 m per minute through a cylindrical by 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm ? 51min 12sec
3) An exhibition tent is in the form of the cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50m. If the diameter of the base is 168m, find the quantity of canvas required to make the tent. Allows 20% extra foe folds and for stitching, give your answer to the nearest m². 60509 m²
4) From a solid cylinder whose height is 8 cm and radius 6cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. Find the volume of the remaining solid correct to 4 significant figures also find the total surface area of the remaining solid spherical metallic solid. 603.2, 603.2
5) A spherical metallic ball of radius 3 cm is melted and recast into three spherical balls. The radii of 2 of these balls are 2.5 cm and 2 cm respectively. Find the radius of third ball. 1.5cm
6) A cylindrical can whose base is horizontal and of radius 3.5cm contains sufficient water so that when a sphere is placed in the can, the water just covers the sphere. Given that the sphere just fits into the can. calculate
A) the total surface area of the can in contact with water when the sphere is in it. 385/2
B) the depth of water in the can before the sphere was put into the can take π to be 22/7. 7/2
7) the internal and external radii of a hollow sphere are 3cm and 5 cm respectively. the sphere is melted to form a solid cylinder of 8/3 cm. Find the diameter and curved surface area of the cylinder. 14, 352/3
1) (cos³x + sin³x)/(cosx + sinx) + (cos³x - sin³x)/(cosx- sinx)
2) cosx/(1- tanx) + sinx/(1- cotx)
3) sinx/(cotx + cosecx) = 2+ sinx/(cotx - cosecx)
4) √{1+ cosx)/(1- cosx)}= cosecx + cotx
5) 1/(sinx + cosx) + 1/(sinx - cosx) = 2 sinx/(1- 2 cos²x)
6) sec²x + cosec²x = sec²x cosec²x.
7) sin⁴x + sin²x cos²x = sin²x
8) sin⁴x cosec²x + cos⁴x sec²x =1
9) tan⁴x + tan²x = sec⁴x - sec²x.
10) sin²x/(sinx - cosx) + cosx/(1- tanx) = sinx + cosx.
11) sin⁶x + cos⁶x = 1- 3 sin²x cos²x.
1) An aeroplane is flying horizontally 4000 m above the ground and is going away from an observer on the level ground. At a certain instant the observer finds that the angle of elevation of the plane is 45°. After 15 seconds, its elevation from the same point changes to 30°. Find the speed of the aeroplane in km/h. 702.72 km/h
2) At the foot of a mountain, the elevation of its summit is 45°. After ascending 1000m towards the mountain up a slope of 30° inclination, the elevation is found to be 60°. Find the height of the mountain. 1396.86m
3) A man standing on the bank of a river observes that the angle of elevation of a tree on the opposite bank is 60°. When he moves 50m away from the bank, he finds the angle of elevation to be 30°. Calculate
A) the width of the river. 25m
B) the height of the tree. 43.3m
4) A kite is flying at a height of 75m from the level ground attached to a string inclined at 60° to the horizontal. Find the length of the string to the nearest metre. 87m
1) Construct a histogram for the following frequency distribution.
Class-interval frequency
05-12 4
13-20 12
21-28 26
29-36 15
37-44 6
45-52 18
2) Draw an Ogive for the following distribution.
Marks no of students
00-10 6
10-20 9
20-30 11
30-40 23
40-50 28
50-60 32
60-70 21
70-80 14
80-90 4
90-100 2
3) Draw a more than cumulative frequency curve for the following data:
Class-interval frequency
00-10 4
10-20 5
20-30 11
30-40 14
40-50 11
50-60 10
60-70 6
4) If 7 is the mean of 5, 3, 0.5, 4.5, b, 8.5, 9.5. find b. 18
5) Find the mean of following distribution:
Class-interval frequency
00-50 4
50-100 8
100-150 16
150-200 13
200-250 6
250-300 3 143
6) Given below are the weekly wages of 200 workers in a small factory:
Weekly wages no of workers
80-100 20
100-120 30
120-140 20
140-160 40
160-180 90
Calculate the mean weekly wages of the workers. 145
7) Calculate the mean, the median and the mode of the following:
3,1,5,6,3,4,5,3,7,2. 3.9,3.5,3
8) The marks scored by 19 students in a test are given below:
31,22,36,27,25,26,33,24,37,32,29,28,36, 27,35,35,32,26,28. Find
A) median. 29
B) lower quartile. 26
C) upper quartile. 35
D) inter quartile. 9
9) From the following frequency distribution, find median , lower quartile, upper quartile, semi-inter- quartile
Variate: 13 15 18 20 22 24 25
Frequ: 6 4 11 9 16 12 2
21,18,22,2
10) Marks obtained by 120 students in a Mathematics test are given below:
Marks. No of students
00-10 5
10-20 9
20-30 16
30-40 22
40-50 26
50-60 18
60-70 11
70-80 6
80-90 4
90-100 3
Draw the Ogive for the given distribution. Use a suitable scale for your Ogive. Use your Ogive to estimate
A) the median. 43.5
B) the lower quartile. 30
C) the number of students who obtained more than 75% in the test. 10
D) the number of students who did not pass in the test if the pass percentage was 40. 52
11) The daily profits in rupees of 100 shops in a departmental store are distributed as follows:
Profit per shop(in ₹) no of shops
000-100 12
100-200 18
200-300 27
300-400 20
400-500 17
500-600 6
Draw a histogram of the above data on a graph paper and hence estimate the mode. 255
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