OFFICE OF THE DEPUTY DIRECTOR OF PUBLIC INSTRUCTION, KOLAR DISTRICT, KOLAR – 563101 10 STANDARD MATHEMATICS : MOST PROBABLE QUESTIONS 2015-16 TH
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If A={1, 2, 3} and B= {2, 3, 4, 5} are the subsets of U= {1, 2, 3, 4, 5, 6, 7, 8} verify (AUB)1 = A1 B1 Draw Venn diagram to illustrate the following. A) A1B B) A\ B If A and B are two sets such chart n(A)=27 n(B)=35 and n(AUB)=50 find n(AB) In a group of 25 persons. 8 drink tea only. 7 drink coffee only and 4 persons drink both tea and coffee. Draw a Venn diagram to show how many of them neither drink neither tea nor coffee? In a group of passengers 100 know Kannada. 50 know English and 25 know both. If passengers know either Kannada or English, how many passengers are in the group? Among 520 members in a village 360 members were engaged in cattle rearing and 280 members with poultry farming and 180 were doing both. How many people are (a) Not involved in either of the work? (b) Engaged only in poultry farming? Find the sum of all natural numbers between 200 and 300 which are exactly divisible by 6. How many terms of the AP 1, 4, 7 ------ are needed to make the sum 51?
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In a HP T5 =
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and T11=
find T25
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Find the sum of 1+ + + -------- up to ∞
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Find the sum of the Ap 1, 3, 5, 7 --------- 199
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Find ‘x’ if 5, 8, x are in Hp.
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The arithmetic mean of two numbers is 17 and their geometric mean is 15. Find the numbers. The product of two numbers is 199 and their Arithmetic mean is 12. Find the numbers. Find the three numbers in Ap whose sum and products are 36 and 1620
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respectively. The sum of 6 terms which form on Ap is 345. The difference between the first and last term is 55. Find the terms.
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In an Ap whose first term is 2 the sum of first five terms is are fourth the sum of the next five terms. Show that T20= –112. Find S20
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Find 3 terms in Gp whose sum and product respectively are 21 and 216. If the pth term of an AP is ‘q’ and the qth term is P. Prove that the nth term is equal to (p+q–n)
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The ratio of 7th to 3rd term of an Ap is 12:5. Find the ratio of 13th to 4th term.
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Find T20 in a Hp , , ……. The half life period of a certain radioactive material is 1 hour. If the initial sample weighed 500 gm, find the marks of the sample humoring at the end of 5th hour. Find the HCF of 65 and 117 by using Euclid’s division lemma. Express 3825 as a product of prime factors. If HCF of 52 and 182 is 26 find their LCM. Prove that 5+ is an irrational number. A book seller has 28 Kannada and 72 English books. The books are of the same size. These books are to be packed in separate bundles and each bundle must contain the same number of books. Find the least numbers of the bundles. Which can be made and also the number of books in each bundle. The length and breadth of a rectangular field is 110m and 30m respectively. Calculate the length of the longest rod which can measure the length and breadth of the field exactly. How many 3 digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6 without repeating any digit.
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Find in if
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If 5pr = 2. 6pr, find ‘r’ How many words with or without dictionary morning can be formed using all the letters of the word. ‘Joule’ using each letter exactly once. Evaluate 5P3 +2P1 Evaluate 10C3
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Prove that when
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cr
n-1Cr-1
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= n when | n
r The maximum number of diagonals in a polygon is 14. Find the number of sides. Everybody in a function shakes hand with everybody else. The total number of handshakes is 45. Find the number of persons in the function.
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How many 4 digit numbers can be formed using the digits 1, 2, 3, 7, 8, 9 (repetitions not allowed) (a) How many of these are less then 6000? (b) How many of there are even? (c ) How many of these end with 7? A committee of 5 is to be formed out of 6 men and 4 ladies in how many ways can this be done when? (a) Atleast 2 ladies are included (b) Atmost 2 ladies are included In how many ways a cricket team of eleven is selected from 17 players in which 5 players are bowlers and the cricket team must include 2 bowlers? A sports team of 11 students is to be constituted choosing atleast 5 team class IX and atleast 5 from class X. If there are 8 students in each of these classes in how many ways are the team be constituted? From a group of 12 students 8 are to be chosen for an excursion. There are 3 students. Who decide that either of them will join or none of them will join. In how many ways the 8 be chosen? What is the probability that a leap year selected will certain 53 Sundays? Nine rotten Mangoes are mixed with 30 good ones. One mango is chosen at random what is the probability of choosing a a. A. good Mango b. Rotten Mango The probability of picking a non-defective item from a sample is Find the probability of picking a defective item. Two coins are lossed simultaneously. Find the probability that either both heads or both tails occurs. There are 2 red and 2 yellow flowers in a basket. A child pieces up at random three flowers. What is the probability of picking up both the yellow flowers? A dice is rolled once. Find the probability of getting. (a) an odd number (b) a number greater than 5 (c ) the number 5 From a well shuffled pack of 52 cards. One card is drawn at random. Find the probability of getting. (a) queen (b) diamond (c) a red jack Two dice are thrown together. Find the probability that a sum greater than 10 or a sum less then 5 turn up.
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A committee of five persons is selected from 4 men and 3 women. What is the probability that the committee will have A. One man B. Two men C. Two women D. atleast two men In a class 40% of the students are members of the Eco club and 25% of the students are members of the mathematics club. If a student is selected at random from the class. What is the probability that the student is not a member of either of the clubs? Calculate the standard deviation of the following data. x 3 8 13 18 23 y 7 10 15 10 8 The mean of 100 terms is 48 and their standard deviation is 10. Find the sum of all the items and the sum of the squares of all the items. The total runs scored by two cricket players Arun and Bharath in 15 matches are 1050 and 900 with standard deviation 4.2 and 3.0 respectively. Who is better run getter? Who is more consistent in performance? 2 If n = 10, x = 12 and ∑ x =1530 then calculate the co-efficient of variation. The survey carried out in the class regarding places of visit for excursion and the number of students who opted each place is given below. Draw a pie chart. Places Mysore Vijayapura Gokarna Chithradurga No. of students 14 6 2 18 The daily wages of 40 workers of a factory are given in the following table. Wages in Rs 30-34 34-38 38-42 42-46 46-50 50-54 No. of workers 4 7 9 11 6 3 Calculate 1. mean 2. variance 3. standard deviation of wages and interpret the findings. The time (in sec) taken by a group of students to solve a problem in mathematics is given in the table below calculate the standard deviation of the data. CI 0-10 10-20 20-30 30-40 40-50 No. of students 7 10 15 8 10
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Calculate the standard deviation and co-efficient of variation for the following distribution. Marks(x) 10 20 30 40 50 No. of students 4 3 6 5 2
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Simplify 4 7 -3252 + 53 Find the sum of xx , yy, 3x3, 4y3 Subtract 2x +3y from 5x - y
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Find the product of 2 and 3 3 Simplify:- ( 75 - 45) (20 + 12) Rationalize the denominator and simplify 50 + 75- 18 - 3 simplify Multiply (318 + 2 12) by (50 –27) Simplify: 4 + 48 Simplify + 3 - 3+ Solve for ‘x’ 3x – 4 = 2 + 3x -2 3x + 2 2 2 Find the zeros of the polynomial 4a – 49 If x=1 is a zero of the polynomial of f(x) = x3 -2x2 +4x +k find the value of K. Divide 2x2-9x+9 by x-3 and verify division algorithm. Find the quotient and remainder on dividing x2+7x+10 by x-2 without actual division. Find the remainder when 4x3-12x2+14x-3 is divided by 2x-1 Use a factor theorem to find whether (x+2) is a factor of the polynomial (2x4+x3+4x2-x-7) What should be added to the polynomial p(x)= x4 + 2x3 - 2x2 + x -1 so that the resulting polynomial is exactly divisible by x2 + 2x - 3. If the polynomials (2x3 + ax2 + 3x - 5) and (x3+x2 - 4x-a) leave the same remainder when divided by (x-1) find the value of ‘a’ Find the quotient and remainder using synthetic division. (4x3 - 16x2 - 9x - 36) (x+2) If (x3 + ax2 – bx + 10) is divisible by x2 -3x +2 find the values of a and b. If the quotient obtained an dividing (8x4 - 2x2 + 6x - 7) by (2x + 1) is 4x3 + px2 – qr + 3 then find p, q and also the remainder. The polynomials (2x3 -5x2 + x + a) and (ax3 + 2x2 -3) when divided by (x - 2) leave the remainders R1 and R2 respectively. Find the value of ‘ a’ if R1=R2 Solve the quadratic equation (x+8)2 -5 = 31. If K = mv2 solve for ‘v’ and find the value of v. If k =100 and m = 2. Solve the quadratic equations by factorisation method. x2 + 15x + 50 =0 Solve:- 3x2-5x+2=0 by completing the square method. Solve:- x2 + 8x + 6 = 0 by formula method. Find the sum and product of the roots of the quadratic equation 3x2 – 10x - 5 = 0 Form the quadratic equation whose roots are 6 and -5 Find the value of ‘k’ so that the equation x2+4x+(k+2)=0 has one root equal to zero. Find the nature of roots of the equation x2+3x-4=0.
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If one root of the equation x + px + q = 0 is 3 times the other prove that 2 3p =16q. 2 If m and n are the roots of equation x -3x+4=0 form the equation whose roots 2 2 are m and n 2 Find the value of ‘a’ so that the equation 4x -8ax+9=0 has roots whose difference is 4. 2 For what positive values of ‘m’ roots of the equating x mx+9=0 are A. Equal B. distinct C. imaginary A motor boat whose speed is 15 km / hr in still water goes 30km down stream and comes back in total of 4 hour 30min.Determine the speed of the stream. 2 The altitude of a triangle is 60m greater than its base. If its area is108cm . Find its base and height. A two digit number is such that the product of the digits is 12. When 36 is added to this numbers the digits interchange their places. Determine the number. The ages of Kavya and Karthik are 11 years and 14 years. In how many years time will the product of their ages be 304? 2 Draw the graph of y=2x and find the value of 7 2 Solve the equation x -x-2=0 graphically. 2 Solve graphically x -4x=0 A dealer sells an article for Rs.24 and gains as much percent as the cost price of the article. Find the cost price of the article. Draw a circle of radius 3cm and construct a chord of length 5cm in it measure the distance between the centre and the chord. In a circle of radius 4.5cm draw two radii such that the angle between them is 700. Construct tangents at the non centre ends of the radii. Draw a circle of radius 3cm and construct a pair of tangents such that the angle between them is 400. Draw a circle of radius 4.5cm and a chord PQ of length 7cm in it construct a tangent at P. In the figure, PQ. PR and BC are the tangents to the circle. BC touches the circle at X. IF PQ=7cm find the perimeter of PBC.
Draw a circle of radius 3cm and construct tangents to if from an external point 10cm away from the centre. Measure and verify the length of the tangents. Prove that the tangents drawn from an external point to a circle.
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a. are equal. b. subtend equal angles at the centre. c. Are equally inclined to the line joining the centre and the external point. Two concentric circle of radii 13cm and 5cm are drawn. Find the length of the chord of the outer circle which touches the inner circle. If two circle touch each other externally the centres and the point of contact are collinear. Three circle touch each other externally find the radii of the circle if the sides of the triangle obtained by joining the centres are 10cm 14cm and 16cm respectively.
Construct direct common tangents to two circle of radii 4cm and 2cm whose centres are 9cm apart. Construct are transverse common tangent to two circles of radii 3cm and 2cm whole centres are 10cm apart. In the adjoining figure DE||AB AD=7cm, CD=5cm and BC=18cm. Find BE and CE
If the diagonals of are quadrilateral divide each other proportionally then prove that the quadrilateral is a trapezium. Two isosceles triangles are having equal vertical angles and their areas are in the ratio 9:16. Find the ratio of their corresponding attitudes. In ABC, D and E are point on the sides AB and AC respectively such that DE||BC. If AD=8cm, AB=12cm, AE=12cm find CE.
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At a certain time of the day a tree costs its shadow 12.5 feet long. If the height of the tree is 5 feet, find the height of another tree that casts its shadow 20 feet long at the same time. Prove that “In a trapezium the line joining the midpoint of non- parallel sides is parallel to the parallel sides and In the figure QPR=UTS=900 and PR||TS prove that PQR TUS.
If two triangles are equi angles then their corresponding sides are in proportion. Prove that the areas of similar triangles are proportional to the squares of the corresponding sides. Derive the formula for height and area of an equilateral triangle. The length of the decagonal of a rectanglar playground is 125m and the length of one side is 75m. Find the length of the other side. In a right angled triangle the square on the hypotenuse is equal to the sum of the squares on the other two sides. An insect 8m away from the foot of a lamp post which is 6m toll crowls towards it. After moving through a distance its distance from the top of the lamp post is equal to the distance it has moved. How for is the insect away from the foot of the lamp post? A preacher on a pillar of 6 feet height on seeing a broke coming towards its hole situated just below the pillar from a distance of 24 feet away from the pillars will fly to catch it. If both pusses the some speed how for from the pillar they are going to meet? In ABC ABC=900, BD AC. If AB= ‘C’ Units, BC= ‘a’ Units, BD= ‘P’ units CA= ‘b’ Units. Prove that 1 + 1 = 1 a2 c2 p 2
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If cos = 24 then find the value of tan 25
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Find sin and cos
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If 13 sin A=5 and A is a acute find the value of 5 sinA-2cosA TanA If 3 tan =1 find sin , cos Find the value of cos 600 cos300+ sin600 sin 300 Show that (1-sin2 ) sec2 Evaluate cot 340-tan560 Prove that sin350 sin550-cus350cus550=0 Two windmills of height 50m and 40m are on either side of the field. A person observes the top of the windmills from a point in between the towers. The angle of elevation was found to be 450 in both the cases. Find the distance between the windmills. If 13cos -5 = 0 find sin +cos sin - cos
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4sin2 600-cos2450 Tan2300 + sin200 If A = 600 and B=300 then prove that tan(A-B) = tanA – tanB 1- tanAtanB Show that sin + 1 + cos = 2cosec 1+cos sin From the top of a building 16m high the angulor elevation of the top of a hill is 600 and the angular depression of the foot of the hill is 300. Find the height of the hill. Show that cosA + sinA = sinA + cosA 1-tanA 1-cotA 0 If = 180 and A = show that 6 (1-cosA) (1+cosA) = 1 (1-sinA) (1+sinA) 3 The angle of elevation of the top of a flog post from a point on a horizontal ground is found to be 300. On working 6m towards the post the elevation increased by 150.Find the height of the flog post. Prove that the line joining the points (1.7) and (-4.3) is perpendiculars to the line pressing through (2, -3) and (1 .4) A line posing through the points (2, 7) and (3, 6) is parallel to a line joining (9, a) and (11, 3) find ‘a’ Show that the line 3x+4y +7=0 and 28x – 21y + 50 =0 are Perpendiculars to each other. Find the value of
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Find the ratio in which point (5, 4) divides the line joining points (2, 1) and (7, 6) Find the perimeter of the triangles whose vertices have the co- Ordinates (3, 10), (5, 2),(14, 12) Prove that the points A(-5, -3), B(1, -11), C(7, -6) D(1, 2) are the vertices of a parallelogram. The co- ordinate of vertices of triangles are (2, 1)(10, 1)(6, 9). Identify the type of triangle. Prove that the points A(1 -3) B(-3, 0) and C(4, 1) are the vertices of a right isosceles triangle. Find the shape of the line joining the points (4, -8) and (5, -2) Find the equation of a line having slope 2 and Y- intercept -4 Find the slope and Y- intercept of the lines 2x + 3y = 4 Find the distance between the points (6, 5)and (4, 4) Find the distance between the origin and the point (5, 12) Find the co-ordinates of the midpoint of the line joining the points (-3, 10) and (6, -8) Find the co-ordinaties of point p which divides the line joining A(4, -5) and B(6, 3) in the ratio 2:5. The radii of two right circular cylinders are in the ratio 2:3 and the ratio of their curved surface careas is 5:6. Find the ratio of their lights. A rectangular sheet of paper 44cm x 20cm is rolled along its length to from a cylinder. Find the volume of the cylinder so formed. The CSA of a right circular cylinder of height 14cm is 88cm2. Find the radius of the base of the cylinder. How many metres of cloth 5m wide will be required to make a conical tent the radius of the base is 7m and whose height is 24m? The radii of two circular ends of a frustum shaped dustbin are 15cm and 8cm. If its depth is 63cm, find volume of dustbin. A capsule of medicine is in the shape of a sphere of diameter 3.5mm. How much medicine is needed to fill this capsule? Plan out the field from the data given from the surveyor’s field book. Metre to E 350 To D 100 300 150 to F To C 75 250 150 100 to G To B 50 50 From A
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Craft teacher of a school taught the students to prepare cylindrical pen holders out of cardboard. In a class of strength 42 if each child prepared a pen holder of radius 5cm and height 14cm, how much cardboard was consumed? A right angled triangle of which the sides containing the right angle are 6.3cm and 10cm in length is made to turn around on the longer side. Find the volume of the solid thus generated. A right circulars metallic cone of height 20cm and base radius 5cm is melted and recast in to a sphere. Find the radius of the sphere. The diameter of a roller 120cm long is 84cm. If it takes 500 complete revolutions to level a play ground determine the cost of levelling it at the rate of Rs. 2.50per square metre. A toy is in the form of a cone mounted on a hemisphere with the same radius. The diameter of the conical portion is 6cm and its height is 4cm. Determine the surface area and volume of the solid. A storage tank consists of a circular cylinder with a hemisphere adjoined on either ends. The external diameter of the cylinder is 1-4m and length is 8m, find the cost of painting it on the outside at the rate of Rs. 10per m2
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