List of top Mathematics Questions asked in CBSE X

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.[Use \(\pi=\frac{22 }{7}\) ]

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use \(\pi=\frac{22 }{7}\) ]

2 cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboids.

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
(i) If two coins are tossed simultaneously there are three possible outcomes - - two heads, two tails or one of each. Therefore, for each of these outcomes, the probability is \(\frac{1}{3}\).
(ii) If a die is thrown, there are two possible outcomes - - an odd number or an even number. Therefore, the probability of getting an odd number is \(\frac{1}{2}\)

A die is thrown twice. What is the probability that
(i) 5 will not come up either time?
(ii) 5 will come up at least once?
[Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment].

A game consists of tossing a one rupee coin 3 times and noting its outcome each time. Hanif wins if all the tosses give the same result i.e., three heads or three tails, and loses otherwise. Calculate the probability that Hanif will lose the game.

Two dice, one blue and one grey, are thrown at the same time.
(i) Write down all the possible outcomes and complete the following table:

(ii) A student argues that 'there are 11 possible outcomes 2, 3, 4, 5, 6, 7, 8, 9, 10, 11 and 12. Therefore, each of them has a probability \(\frac{1}{11}\)

A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good but will not buy if it is defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that
(i) She will buy it.
(ii) She will not buy it.

Suppose you drop a die at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?

A child has a die whose six faces shows the letters as given below:

A child has a die whose six faces shows the letters as given below:
The die is thrown once. What is the probability of getting (i) A? (ii) D?

A box contains 90 discs which are numbered from 1 to 90. If one disc is drawn at random from the box, find the probability that it bears
(i) a two-digit number
(ii) a perfect square number
(iii) a number divisible by 5.

Is it possible to design a rectangular park of perimeter 80 m and area 400 \(m^2\) ? If so, find its length and breadth.

Ramkali saved Rs. 5 in the first week of a year and then increased her weekly savings by Rs 1.75. If in the \(n^{th}\)week, her weekly savings become Rs 20.75, find n.

Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 \(m^2\)? If so, find its length and breadth.

Find the values of k for each of the following quadratic equations, so that they have two equal roots.
(i) \(2x^2 + kx + 3 = 0\) (ii) \(kx (x – 2) + 6 = 0\)

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:
(i) \(2x^2 – 3x + 5 = 0\) (ii) \(3x^2 – 4\sqrt3 x + 4 = 0\) (iii) \(2x^2 – 6x + 3 = 0\)

In the following figure, if ΔABE≅ΔACD, show that ΔADE ~ ΔABC.

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Find two consecutive positive integers, sum of whose squares is 365.

Find two numbers whose sum is 27 and product is 182.

Solve the problems given in Example 1:-

(i) John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 124. Find out how many marbles they had to start with.

(ii) A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. Find out the number of toys produced on that day.

Find the roots of the following quadratic equations by factorisation:
(i) \(x^2 – 3x – 10 = 0\)

(ii) \(2x^2 + x – 6 = 0\)

(iii) \(\sqrt2x^2+7x+5\sqrt2 = 0\)

(iv) \(2x^2 – x + \frac{1}8\)\( = 0\)

(v) \(100x^2 – 20x + 1 = 0\)

Represent the following situations in the form of quadratic equations.

(i) The area of a rectangular plot is 528 \(m^2\). The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.

(ii) The product of two consecutive positive integers is 306. We need to find the integers.

(iii) Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

(iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.