     Maths | ICSE Board | Grade 10 | 2015
Q. Find the value of k for which x=3 is a solution of the quadratic equation, (k+2)x2kx+6=0.
Thus find the other root of the equation.
View Solution  Q. A bag contains 5 white balls, 6 red balls and 9 green balls. A ball is drawn at random from the bag. Find the probability that the ball drawn is :
(i) a green ball.
(ii) a white or a red ball.
(iii) is neither a green ball nor a white ball.
View Solution  Q. Use a graph paper for this question taking 1cm=1 unit along both the x and y axis :
(i) Plot the points A(0, 5), B(2, 5), C(5, 2), D(5, 2), E(2, 5) and F(0, 5)
(ii) Reflect the points B, C, D and E on the y-axis and name them respectively as B, C, D and E.
(iii) Write the coordinates of B, C, D and E.
(iv) Name the figure formed by BCDEEDCB.
(v) Name a line of symmetry for the figure formed.
View Solution  Q. Virat opened a Saving Bank account in a bank on 16th April, 2010. His pass book shows the following entries:
 Date Particulars Withdrawal (Rs.) Deposit (Rs.) Balance (Rs.) April 16th By cash ___ 2500 2500 April 28th By cheque ___ 3000 5500 May 9th To cheque 850 ___ 4650 May 15th By cash ___ 1600 6250 May 24th To cash 1000 ___ 5250 June 4th To cash 500 ___ 4750 June 30th By cheque ___ 2400 7150 July 3rd By cash ___ 1800 8950
Calculate the interest Virat earned at the end of 31st July, 2010 at 4% per annum interest. What sum of money will he receive if he closes the account on 1st August, 2010?
View Solution  Q. Sum of two natural numbers is 8 and the difference of their reciprocal is 215. Find the numbers.
View Solution  Q. Prove that sinθ1cotθ+cosθ1tanθ=cosθ+sinθ.
View Solution  Q. If A=, B= and C=. Find AB5C.
View Solution  Q.
Without using trigonometric tables evaluate :
sin63cos27+cos39sin51sin23sec67+csc230
View Solution  Q. Solve the following inequation and write the solution set :
13x5<15x+4<7x+12, xR
Represent the solution on a real number line.
View Solution  Q. A wholesaler buys a TV from the manufacturer for Rs. 25, 000. He marks the price of the TV 20% above his cost price and sell it to a retailer at 10% discount on the marked price. If the rate of VAT is 8%, find the:
(i) marked price.
(ii) retailer's cost price inclusive of tax.
(iii) VAT paid by the wholesaler.
View Solution  Q. In the given figure, ABCD is a square of side 21cm. AC and BD are two diagonals of the square. Two semi circles are drawn with AD and BC as diameters. Find the area of the shaded region (in cm2). (Take π=227) View Solution  Q. Find a if the two polynomials ax3+3x29 and 2x3+4x+a, leaves the same remainder when divided by x+3.
View Solution  Q. The horizontal distance between two towers is 120m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower is 30o and 24o respectively.
Find the height of the two towers. Give your answer correct to 4 significant figures. View Solution  Q. If a, b, c are in continued proportion, prove that
(a+b+c)(ab+c)=a2+b2+c2
View Solution  Q. Rohit invested Rs. 9, 600 on Rs. 100 shares at Rs. 20 premium paying 8% dividend. Rohit sold the shares when the price rose to Rs. 160. He invested the proceeds (excluding dividend) in 10% Rs. 50 shares at Rs. 40. Find the :
(i) original number of shares.
(ii) sale proceeds.
(iii) new number of shares.
(iv) change in the two dividends.
View Solution  Q. The weight of 50 workers is given below:
 Weight in Kg. 50−60 60−70 70−80 80−90 90−100 100−110 110−120 No. workers 4 7 11 14 6 5 3
Draw an ogive of the given distribution using a graph sheet. Take 2 cm=10 kg on one axis and 2 cm=5 workers along the other axis. Use a graph to estimate the following:
(i) the upper and lower quartiles.
(ii) if weighing 95 kg and above is considered overweight find the number of workers who are overweight.
View Solution  Q. Katrina opened a recurring deposit account with a Nationalised Bank for a period of 2 years. If the bank pays interest at the rate of 6% per annum and the monthly installment is Rs. 1, 000, find the:
(i) interest earned in 2 years
(ii) matured value.
View Solution  Q. ABC is a right angled triangle with ABC=90o. D is any point on AB and DE is perpendicular to AC. Prove that :
(ii) If AC=13cm, BC=5cm and AE=4cm. Find DE and AD. View Solution  Q. Given x3+12x6x2+8=y3+27y9y2+27. Using componendo and dividendo find x:y.
View Solution  Q. Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone (in cm) so formed.
View Solution  Q. In the figure given below, O is the centre of the circle and SP is a tangent. If SRT=65o, find the value of x, y and z. View Solution  Q. The present population of a town is 2, 00, 000. Its population increases by 10% in the first year and 15% in the second year. Find the population of the town at the end of the two years.
View Solution  Q. Calculate the mean of the following distribution:
 Class Interval 0−10 10−20 20−30 30−40 40−50 50−60 Frequency 8 5 12 35 24 16
View Solution  Q. If A=[3x01] and B=[9160y], find x and y when A2=B.
View Solution  Q. In the given figure ABC is a triangle and BC is parallel to the y-axis. AB and AC intersects the y-axis at P and Q respectively.
(i) Write the coordinates of A.
(ii) Find the length of AB and AC.
(iii) Find the ratio in which Q divides AC.
(iv) Find the equation of the line AC. View Solution  Q. A shopkeeper bought an article for Rs. 3, 450. He marks the price of the article 16% above the cost price. The rate of sales tax charged on the article is 10%. Find the :
(i) marked price of the article
(ii) price paid by a customer who buys the article.
View Solution  Q. Three vertices of a parallelogram ABCD taken in order are A(3, 6), B(5, 10) and C(3, 2) find :
(i) the coordinates of the fourth vertex D.
(ii) length of diagonal BD.
View Solution  Q. The marks obtained by 30 students in a class assessment of 5 marks is given below :
 Marks 0 1 2 3 4 5 Number of Students 1 3 6 10 5 5
Calculate the mean, median and mode of the above distribution.
View Solution  Q. AB and CD are two chords of a circle intersecting at P. Prove that AP×PB=CP×PD. View Solution  