ICSE 10th Maths question paper - 2017

If b is the mean proportion between a and c, show that (a⁴ + a²b² + b⁴)/(b⁴ + b²c² + c⁴) = a²/c² is a true statement.

Solve the quadratic equation 4x² - 5x - 3 = 0 and give your answer correct to two decimal places.

AB and CD are two parallel chords of a circle such that AB = 24 cm and CD = 10 cm. If the radius of the circle is 13 cm, find the distance between the two chords.

Evaluate without using trigonometric tables: sin²28° + sin²62° + tan²38° - cot²52° + (1/4)sec²30°.

Jaya borrowed Rs. 50,000 for 2 years. The rates of interest for two successive years are 12% and 15% respectively. She repays Rs. 33,000 at the end of the first year. Find the amount she must pay at the end of the second year to clear her debt.

The catalogue price of a computer set is Rs. 42,000. The shopkeeper gives a discount of 10% on the listed price. He further gives an off-season discount of 5% on the discounted price. Sales tax at 8% is charged on the remaining price. Find the amount of sales tax a customer has to pay.

P(1,-2) is a point on the line segment A(3,-6) and B(x,y) such that AP : PB is equal to 2 : 3. Find the coordinates of B.

The marks of 10 students of a class in an examination arranged in ascending order is as follows: 13, 35, 43, x, x+4, 55, 61, 71, 80. If the median marks is 48, find the value of x.

In the given figure ABCD is a rectangle. It consists of a circle and two semi-circles each of which are of radius 5 cm. Find the area of the shaded region. Give your answer correct to three significant figures.

Solve the following inequation: -8½ < -½ - 4x ≤ 7½, where x is an integer. Write the solution set.

Given matrix B = [[1, 1], [8, 3]], find the matrix X if X = B² - 4B.

How much should a man invest in Rs. 50 shares selling at Rs. 60 to obtain an income of Rs. 450, if the rate of dividend declared is 10%?

Sixteen cards are labeled as a, b, c, ..., p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is a vowel?

Sixteen cards are labeled as a, b, c, ..., p. They are put in a box and shuffled. A boy is asked to draw a card from the box. What is the probability that the card drawn is a consonant?

A conical tent is to accommodate 77 persons. Each person must have 16 m³ of air to breathe. Given the radius of the tent as 7 m, find the height of the tent.

If (7m+2n)/(7m-2n) = 5/3, use properties of proportion to find the ratio m:n.

A page from a savings bank account passbook is given. Calculate the interest for the 6 months from January to June 2016, at 6% per annum.

If the account is closed on 1st July 2016, find the amount received by the account holder.

The histogram represents scores of 25 students. Frame a frequency distribution table from the given histogram.

The printed price of an air conditioner is Rs. 45000/-. The wholesaler allows a discount of 10% to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find the VAT paid by the shopkeeper to the government.

The printed price of an air conditioner is Rs. 45000/-. The wholesaler allows a discount of 10% to the shopkeeper. The shopkeeper sells the article to the customer at a discount of 5% of the marked price. Sales tax (under VAT) is charged at the rate of 12% at every stage. Find the total amount paid by the customer inclusive of tax.

In the figure given, O is the centre of the circle. ∠DAE = 70°. Find the measure of ∠BCD.

In the figure given, O is the centre of the circle. ∠DAE = 70°. Find the measure of ∠BOD.

In the figure given, O is the centre of the circle. ∠DAE = 70°. Find the measure of ∠OBD.

A(-1,3) B(4,2) and C(3,-2) are the vertices of a triangle. Find the coordinates of the centroid G of the triangle.

Prove that (sinθ - 2sin³θ)/(2cos³θ - cosθ) = tanθ is a true statement.

The sum of the ages of Vivek and his younger brother Amit is 47 years. The product of their ages in years is 550. Find their ages.

An aeroplane at an altitude of 1500 metres, finds that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.

PQR is a triangle. S is a point on the side QR of ΔPQR such that ∠PSR = ∠QPR. Given QP = 8 cm, PR = 6 cm and SR = 3 cm. Find the length of QR.

Mr. Richard has a recurring deposit account in a bank for 3 years at 7.5% p. a. simple interest. If he gets Rs. 8325 as interest at the time of maturity, find the monthly deposit.

Mr. Richard has a recurring deposit account in a bank for 3 years at 7.5% p. a. simple interest. If he gets Rs. 8325 as interest at the time of maturity, find the maturity value.

If (3a+2b) : (5a+3b) = 18 : 29, find the ratio a : b.

The mean of the following numbers is 68. Find the value of 'x': 45, 52, 60, x, 69, 70, 26, 81, and 94. Then, estimate the median.

The slope of a line joining P(6,k) and Q(1-3k,3) is 1/2. Find the value of k.

Without using trigonometric tables, evaluate: csc²57° - tan²33° + cos44° csc46° - √2cos45° - tan²60°.

A certain number of metallic cones, each of radius 2 cm and height 3 cm are melted and recast into a solid sphere of radius 6 cm. Find the number of cones.

Solve the following inequation: -3(x-7) ≥ 15 - 7x > (x+1)/3, where x is a real number. Write the solution set.

In the figure given, AD is a diameter. O is the centre of the circle. AD is parallel to BC and ∠CBD = 32°. Find ∠ABD.

A game of numbers has cards marked with 11, 12, 13, ..., 40. A card is drawn at random. What is the probability that the number on the card is a perfect square?

A line AB meets X-axis at A and Y-axis at B. P(4,-1) divides AB in the ratio 1:2. Find the coordinates of A and B.

Mr. Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate the rate of interest.

Mr. Lalit invested Rs. 5000 at a certain rate of interest, compounded annually for two years. At the end of the first year, it amounts to Rs. 5325. Calculate the amount at the end of the second year, to the nearest rupee.

Solve the quadratic equation x² - 3(x+3)=0, giving the answer correct to two significant figures.

In what time will Rs. 1500 yield Rs. 496.50 as compound interest at 10% per annum compounded annually?

In the given figure, PQRS is a cyclic quadrilateral. PQ and SR produced meet at T. If area of ΔPTS = 27 cm², and TP = 18 cm, RQ = 4 cm and TR = 6 cm, find the area of quadrilateral PQRS.

A bus covers a distance of 240 km at a uniform speed. Due to heavy rain, its speed gets reduced by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be x km/h, form an equation and solve it to evaluate 'x'.

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the number of shares he bought.

Ashok invested Rs. 26,400 on 12%, Rs. 25 shares of a company. If he receives a dividend of Rs. 2,475, find the market value of each share.

Prove that cosA/(1+sinA) + tanA = secA is a true statement.

Mohan has a recurring deposit account in a bank for 2 years at 6% p.a. simple interest. If he gets Rs. 1200 as interest at the time of maturity, find the monthly installment.