Nootan solutions for Mathematics [English] Class 10 ICSE chapter • - Competency focused practice questions [Latest edition]

A retailer buys an article at its listed price from a wholesaler and sells it to a consumer in the same state after marking up the price by 20%. The list price of the article is 2500 and the rate of GST is 12%. What is the tax liability of the retailer to the central government?

Dev bought an electrical fan which has a marked price of ₹ 800. If the GST on the goods is 7%, then the SGST is ______.

₹ P is deposited for n number of months in a recurring deposit account which pays interest at the rate of r % per annum. The nature and time of interest calculated is ______.

Anwesha intended to open a Recurring Deposit account of ₹ 1000 per month for 1 year in a Bank, paying a 5% per annum rate of simple interest. The bank reduced the rate to 4% per annum. How much must Anwesha deposit monthly for 1 year so that her interest remains the same?

Mr. Das invests in ₹ 100, 12% shares of Company А available at ₹ 60 each. Mr. Singh invests in ₹ 50, 16% shares of Company B available at ₹ 40 each. Use this information to state which of the following statements is true?

Amit invested a certain sum of money in ₹ 100 shares, paying a 7.5% dividend. The rate of return on his investment is 10%. The money invested by Amit to purchase 10 shares is ______.

If – 3 ≤ – 4x + 5 and x ε W, then the solution set is ______.

If – 4x > 8y, then

The value/s of ‘k’ for which the quadratic equation 2x² – kx + k = 0 has equal roots is (are):

If x = –2 is one of the solutions of the quadratic equation x² + 3a – x = 0, then the value of ‘a’ is ______.

In solving a quadratic equation, one of the values of the variable x is 233.356. The solution rounded to two significant figures is ______.

In the adjoining diagram, AB = x cm, BC = у cm and x – y = 7 cm. Area of ΔABC = 30 cm². The length of AC is:

If p, q and r are in continued proportion, then:

The ratio of diameter to height of a Borosil cylindrical glass is 3 : 5. If the actual diameter of the glass is 6 cm, then the curved surface area of the glass is ______.

If the polynomial 2x³ + 3x² – 2x – 3 is completely divisible by (2x + a) and the quotient is equal to (x² – 1), then one of the values of a is ______.

If A = [a b] and B = `[(c), (d)]`, then:

Matrix A = `[(6, 9),(-4, k)]` such that A² = `[(0, 0),(0, 0)]`. Then k is ______.

If the sum of n terms of an arithmetic progression S_n = n² – n, then the third term of the series is ______.

Which of the following is NOT a geometric progression?

In the adjoining diagram, G is the centroid of ΔABC. A(3, –3), В(2, –6), C(x, y) and G(5, –5). The coordinates of point D are:

In the given diagram, O is the origin and P is the midpoint of AB. The equation of OP is:

In the given figure Line l₁ is a parallel to Line l₂. If line l₃ is perpendicular to Line l₁, then the slopes of lines l₂ and l₃ respectively are:

Which of the following lines cut the positive x-axis and positive y-axis at equal distances from the origin?

In the given diagram (not drawn to scale), railway stations A, B, C, P and Q are connected by straight tracks. Track PQ is parallel to BC. The time taken by a train travelling at 90km/hr to reach B from A by the shortest route is:

In the given diagram, ΔABC and ΔDEF (not drawn to scale) are such that ∠C = ∠F and `(AB)/(DE) = (BC)/(EF)`, then

In the adjoining diagram, ST is not parallel to PQ. The necessary and sufficient conditions for ΔPQR ~ ΔTSR is:

The scale factor of a picture and the actual height of Sonia is 20 cm: 1.6 m. If her height in the picture is 18 cm, then her actual height is ______.

In the adjoining figure, O is the centre of the circle and a semicircle is drawn on OA as the diameter. ∠APQ = 20°. The degree measure of ∠OAQ is:

In the given diagram, O is the centre of the circle and DE is a tangent at B. If ∠ABC = 50°, then values of x, y and z respectively are:

In the given figure, PT and QT are tangents to a circle such that ∠TPS = 45° and ∠TQS = 30°. Then, the value of x is:

A cylindrical metallic wire is stretched to double its length. Which of the following will NOT change for the wire after stretching?

A right circular cone has the radius of the base equal to the height of the cone. If the volume of the cone is 9702 cu. cm, then the diameter of the base of the cone is ______.

A solid sphere with a radius of 4 cm is cut into 4 identical pieces by two mutually perpendicular planes passing through its centre. Find the total surface area of one-quarter piece.

Two identical solid hemispheres are kept in contact to form a sphere. The ratio of the total surface areas of the two hemispheres to the surface area of the sphere formed is:

cosec²θ + sec²θ is equal to ______.

Given a = 3 sec² θ and b = 3 tan² θ – 2. The value of (a – b) is ______.

At a certain time of day, the ratio of the height of the pole to the length of its shadow is `1 : sqrt(3)`, then the angle of elevation of the sun at that time of the day is ______.

A man standing on a ship approaching the port towards the lighthouse is observing the top of the lighthouse. In 10 minutes, the angle of elevation of the top of the lighthouse changes from α to β. Then:

Assertion (A): The difference in class marks of the modal class and the median class of the following frequency distribution table is 0.

Reason (R): Modal class and median class are always the same for a given frequency distribution.

Assertion (A): For a collection of 11 arrayed data, the median is the middle number.

Reason (R): For the data 5, 9, 7, 13, 10, 11, 10, the median is 13.

Ankit had the option of investing in company A, where 7%, ₹ 100 shares are available at ₹ 120 or in company B, where 8%, ₹ 1000 shares are available at ₹ 1620.

Assertion (A): Investment in Company A is better than Company B.

Reason (R): The rate of income in Company A is better than in Company B.

Assertion (A): x³ + 2x² – x – 2 is a polynomial of degree 3.

Reason (R): x + 2 is a factor of the polynomial.

Assertion (A): The point (–2, 8) is invariant under reflection in line x = –2.

Reason (R): If a point has its x-coordinate 0, it is invariant under reflection in both axes.

When a die is cast with numbering on its faces, as shown, the ratio of the probability of getting a composite number to the probability of getting a prime number is ______.

The product of `A = [(1, -2),(-3, 4)]` and matrix M, AM = B where `B = [(2), (24)]`, then the order of matrix M is ______.

Given, a₁, а₂, а₃, ....... and b₁, b₂, b₃, ....... are real numbers such that a₁ – b₁ = a₂ – b₂ = a₃ – b₃ = .......... are all equal. a₁ – b₁, a₂ – b₂, a₃ – b₃ .......... forms a ______ progression.

Locus of a moving point is ______ if it moves such that it keeps a fixed distance from a fixed point.

The point of concurrence of the angle bisectors of a triangle is called the ______ of the triangle.

A shopkeeper marked a pressure cooker at ₹ 1800. The rate of GST on pressure cooker is 12%. The customer has only ₹ 1792 with him and he requests the shopkeeper to reduce the price so that he can buy the cooker in ₹ 1792. What percent discount must the shopkeeper give?

A man opened a recurring deposit account in a branch of PNB. The man deposits certain amount of money per month such that after 2 years, the interest accumulated is equal to his monthly deposits. Find the rate of interest per annum that the bank was paying for the recurring deposit account.

Akshay buys 350 shares of ₹ 50 par value of a company. The dividend declared by the company is 14%. If his return percent from the shares is 10%, find the market value of each share.

Solve for x, if `5/x + 4sqrt(3) = (2sqrt(3))/x^2, x = 0`

The marked price of a toy is same as the percentage of GST that is charged. The price of the toy is ₹ 24 including GST. Taking the marked price as x, form an equation and solve it to find x.

The mean proportion between two numbers is 6 and their third proportion is 48. Find the two numbers.

Pamela factorized the following polynomial:

2x³ + 3x² – 3x – 2

She found the result as (x + 2) (x – 1) (x – 2). Using remainder and factor theorem, verify whether her result is correct. If incorrect, give the correct result.

`A = [(-6, 0),(4, 2)]` and `B = [(1, 0),(1, 3)]`. Find matrix M, if `M = 1/2 A - 2B + 5l`, where l is the identity matrix.

(a) Write the nth term (T_n) of an Arithmetic Progression (A.P.) consisting of all whole numbers which are divisible by 3 and 7.

(b) How many of these are two-digit numbers? Write them.

(c) Find the sum of first 10 terms of this A.P.

Write the first five terms of the sequence given by `(sqrt(3))^n, n ∈ N`.

1. Is the sequence an A.P. or G.P?
2. If the sum of its first ten terms is `p(3 + sqrt(3))`, find the value of p.

ABC is a triangle as shown in the figure below.

1. Write down the coordinates of A, B and C on reflecting through the origin. 
2. Write down the coordinates of the point/s which remain invariant on reflecting the triangle ABC on the x-axis and y-axis respectively.

Determine the ratio in which the line y = 2 + 3x divides the line segment AB joining the points A(–3, 9) and B(4, 2).

Square ABCD lies in the third quadrant of a XY plane such that its vertex A is at (–3, –1) and the diagonal DB produced is equally inclined to both the axes. The diagonals AC and BD meets at P(–2, –2). Find the:

1. slope of BD
2. equation of AC

ABCD is a rectangle where side BC is twice side AB. If ΔACQ ~ ΔBAP, find area of ΔBAP : area of ΔACQ.

Given a triangle ABC and D is a point on BC such that BD = 4 cm and DC = x cm. If ∠BAD = ∠C and AB = 8 cm, then, 

1. prove that triangle ABD is similar to triangle CBA. 
2. find the value of ‘x’.

In the extract of Survey of India map G43S7, prepared on a scale of 2 cm to 1 km, a child finds the length of the cart track between two settlements is 7.6 cm. Find:

1. the actual length of the cart track on the ground. 
2. actual area of a grid square, if each has an area of 4 cm².

Construct a triangle ABC such that AB = 7 cm, BC = 6 cm and CA = 5 cm. (use ruler and compass to do so).

(a) Draw the locus of the points such that

(i) it is equidistant from BC and BA.

(ii) it is equidistant from points A and B. 

(b) Mark P where the loci (i) and (ii) meet, measure and write length of PA.

In the given figure O is the centre of the circle. ABCD is a quadrilateral where sides AB, BC, CD and DA touch the circle at E, F, G and H respectively. If AB = 15 cm, BC = 18 cm and AD = 24 cm, find the length of CD.