Mathematics Questions

Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.

Q221
1. (i)A lot of 20 bulbs contain 4 defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
2. (ii)Suppose the bulb drawn in (i) is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?
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Q222
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
1. (i)a two-digit number,
2. (ii)a perfect square number,
3. (iii)a number divisible by $5$ .
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Q223
A child has a die whose six faces show the letters A, B, C, D, E, A. The die is thrown once. What is the probability of getting
1. (i) $A$ ?
2. (ii) $D$ ?
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Q224

Suppose you drop a die at random on the rectangular region shown in Fig. 14.6. What is the probability that it will land inside the circle with diameter $1 m$ ?
Rectangular region $3\,\text{m}\times 2\,\text{m}$ containing a circle of diameter $1\,\text{m}$.

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Q225
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
1. (i)She will buy it?
2. (ii)She will not buy it?
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Q226
Refer to Example 13.
1. (i)Complete the following table giving the probability for each possible sum when two dice are thrown together. Some entries are filled in to help you.
2. (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 $\frac{1}{11}$ . Do you agree with this argument? Justify your answer.
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Q227

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.

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Q228
A die is thrown twice. What is the probability that
1. (i) $5$ will not come up either time?
2. (ii) $5$ will come up at least once? [Hint: Throwing a die twice and throwing two dice simultaneously are treated as the same experiment.]
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Q229
Which of the following arguments are correct and which are not correct? Give reasons for your answer.
1. (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 $\frac{1}{3}$ .
2. (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 $\frac{1}{2}$ .
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Q230
State whether the following statements are always true, always false or ambiguous. Justify your answers.
1. (i)All mathematics textbooks are interesting.
2. (ii)The distance from the Earth to the Sun is approximately $1.5 \times 1 0^{8}$ km.
3. (iii)All human beings grow old.
4. (iv)The journey from Uttarkashi to Harsil is tiring.
5. (v)The woman saw an elephant through a pair of binoculars.
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Q231
State whether the following statements are true or false. Justify your answers.
1. (i)All hexagons are polygons.
2. (ii)Some polygons are pentagons.
3. (iii)Not all even numbers are divisible by 2.
4. (iv)Some real numbers are irrational.
5. (v)Not all real numbers are rational.
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Q232
Let $a$ and $b$ be real numbers such that $ab \neq = 0$ . Then which of the following statements are true? Justify your answers.
1. (i)Both $a$ and $b$ must be zero.
2. (ii)Both $a$ and $b$ must be non-zero.
3. (iii)Either $a$ or $b$ must be non-zero.
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Q233
Restate the following statements with appropriate conditions, so that they become true.
1. (i)If $a^{2} > b^{2}$ , then $a > b$ .
2. (ii)If $x^{2} = y^{2}$ , then $x = y$ .
3. (iii)If $(x + y)^{2} = x^{2} + y^{2}$ , then $x = 0$ .
4. (iv)The diagonals of a quadrilateral bisect each other.
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Q234

Given that all women are mortal, and suppose that A is a woman, what can we conclude about A?

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Q235

Given that the product of two rational numbers is rational, and suppose $a$ and $b$ are rationals, what can you conclude about $ab$ ?

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Q236

Given that the decimal expansion of irrational numbers is non-terminating, non-recurring, and $17$ is irrational, what can we conclude about the decimal expansion of $17$ ?

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Q237

Given that $y = x^{2} + 6$ and $x = - 1$ , what can we conclude about the value of $y$ ?

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Q238

Given that $A B C D$ is a parallelogram and $∠ B = 8 0^{\circ}$ . What can you conclude about the other angles of the parallelogram?

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Q239

Given that $P QR S$ is a cyclic quadrilateral and also its diagonals bisect each other. What can you conclude about the quadrilateral?

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Q240

Given that $p$ is irrational for all primes $p$ and also suppose that 3721 is a prime. Can you conclude that $3721$ is an irrational number? Is your conclusion correct? Why or why not?

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