CBSE Class 10 Mathematics — practice questions
120 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice CBSE Class 10 Mathematics in the app →Which of the following fractions will have a non-terminating recurring decimal expansion?Which of the following rational numbers has a terminating decimal expansion?The decimal expansion of a rational number $\frac{a}{b}$ will terminate if, after reducing it to lowest terms,Why is $ qrt{p}$ irrational when $p$ is a prime number?Let $r$ be a non-zero rational number and $x$ be an irrational number. Which of the following must be irrationWhich statement is always true about the sum of a rational number and an irrational number?If $p$ is a prime number and $p$ divides $a^2$, then which statement must be true?Which of the following is a rational number?For any two positive integers $a$ and $b$, which relation is always true?If the prime factorisations of two numbers are $2^3\times 3^2\times 5$ and $2^2\times 3\times 5^2$, then theirWhat does the Fundamental Theorem of Arithmetic state?Using Euclid's division algorithm, what is the HCF of 135 and 225?According to Euclid's Division Lemma, for integers $a$ and $b$, the expression for division isWhich of the following best describes the set of real numbers?A student says: 'When two coins are tossed simultaneously, there are three outcomes — two heads, two tails, orTwo dice, one blue and one grey, are thrown together. Referring to the outcome table in Fig. 14.3, what is theA missing helicopter is equally likely to have crashed anywhere in the rectangular region shown in Fig. 14.2. In the musical-chair timing model shown on the number line in Fig. 14.1, the music may stop at any time from 0Harpreet tosses two different coins simultaneously. What is the probability of getting at least one head?A box contains 3 blue, 2 white and 4 red marbles. One marble is drawn at random. What is the probability that Savita and Hamida are friends. Ignoring leap year, what is the probability that they have the same birthday?One card is drawn from a well-shuffled deck of 52 cards. What is the probability that the card is not an ace?Which of the following is an impossible event when a fair die is thrown once?If $P(E)=0.62$, what is $P(\overline{E})$?A die is thrown once. What is the probability of getting a number greater than 4?An event having only one outcome of an experiment is calledA bag contains 4 red balls and 1 blue ball. One ball is drawn at random. Which statement is correct?Which of the following best states the theoretical probability of an event $E$ when all outcomes are equally lWhich statement correctly explains the difference between adding surface areas and adding volumes for a solid A right circular cylinder circumscribes the toy made of a cone on a hemisphere, shown in the figure. The toy hA solid toy consists of a hemisphere surmounted by a right circular cone. The cone height is $2\,\mathrm{cm}$ A cylindrical glass has inner diameter $5\,\mathrm{cm}$ and height $10\,\mathrm{cm}$, but its bottom has a hemIn the shed problem, machinery occupies $300\,\mathrm{m}^3$ and 20 workers occupy $0.08\,\mathrm{m}^3$ each onA shed is shaped like a cuboid surmounted by a half cylinder, as shown in the figure. The base of the cuboid iMayank's bird-bath is in the shape of a cylinder with a hemispherical depression at one end. The cylinder heigFor the rocket shown in the figure, what area is painted yellow? The cylindrical part has radius $1.5\,\mathrmA wooden toy rocket is made of a cone mounted on a cylinder, as shown. The total height is $26\,\mathrm{cm}$, The decorative block shown in the figure is made of a cube of edge $5\,\mathrm{cm}$ and a hemisphere of diametRasheed's playing top is shaped like a cone surmounted by a hemisphere. The entire top is $5\,\mathrm{cm}$ higA solid is formed by joining a cylinder with two hemispheres of the same radius, one at each end. Which part oWhen a cone and a hemisphere of the same radius are joined along their flat circular faces to make a toy, whicA medicine capsule is in the shape of a cylinder with two hemispheres stuck to each of its ends (see figure). A student claims that for three positive integers $p,q,r$, we always have $\operatorname{HCF}(p,q,r)\times \opWhich statement correctly justifies that $3 qrt{2}$ is irrational?Which statement is correct about the number $5- qrt{3}$?Which of the following best explains why $ qrt{3}$ is irrational?In the contradiction proof that $ qrt{2}$ is irrational, after assuming $ qrt{2}=\frac{a}{b}$ in lowest terms,If $p$ is a prime number and $p$ divides $a^2$, then which conclusion must be true?Given that $\operatorname{HCF}(306,657)=9$, what is $\operatorname{LCM}(306,657)$?For any two positive integers $a$ and $b$, which identity is always true?For the numbers 6, 72 and 120, which pair gives the HCF and LCM respectively?The prime factorizations of 96 and 404 are $96=2^5\times 3$ and $404=2^2\times 101$. What is their LCM?If $6=2\times 3$ and $20=2^2\times 5$, then their HCF and LCM respectively areWhy is there no natural number $n$ for which $4^n$ ends with the digit 0?Which statement correctly expresses the Fundamental Theorem of Arithmetic?Using the factor tree shown, what is the prime factorisation of 32760?
=3x^3-5x^2-11x-3$, which relFor the cubic polynomial $p(x)=2x^3-5x^2-14x+8$, what is the sum of the products of its zeroes taken two at a If $\alpha,\beta,\gamma$ are the zeroes of the cubic polynomial $ax^3+bx^2+cx+d$, then $\alpha\beta\gamma$ is A quadratic polynomial has sum of zeroes $-3$ and product of zeroes $2$. Which of the following is one such poThe zeroes of the quadratic polynomial $x^2+7x+10$ areIf $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $ax^2+bx+c$ with $a\neq 0$, then $\alpha+\bWhich statement is true for a polynomial of degree $n$?The graph of $y=x^3-4x$ is shown in the figure. How many zeroes does the polynomial $x^3-4x$ have?
=x^2-3x-4$, what is the value of $p(-1)$?The zero of the linear polynomial $ax+b$ with $a\neq 0$ isWhich of the following is not a polynomial in the variable $x$?In the circular park shown, $AB$ is a diameter of length $13$ m and the pole is placed at point $P$ on the bouIf the discriminant of a quadratic equation is negative, what can be concluded about its roots?For the quadratic equation $ax^2+bx+c=0$, what is the discriminant?The breadth of a prayer hall is $x$ m and its length is $(2x+1)$ m. If its area is $300\text{ m}^2$, what are The equation $3x^2-2 qrt{6}x+2=0$ has repeated factors after factorisation. What are its roots?Find the roots of $2x^2-5x+3=0$ by factorisation.What is the maximum number of real roots a quadratic equation can have?If $\alpha$ is a root of the quadratic equation $ax^2+bx+c=0$ with $a\neq 0$, then which statement must be truWhich equation appears cubic at first glance but actually simplifies to a quadratic equation?Which of the following is NOT a quadratic equation after simplification?A cottage industry produces $x$ toys in a day, and the cost of producing each toy on that day is ₹$(55-x)$. IfIf John originally had $x$ marbles and Jivanti had $45-x$, and both lost 5 marbles each, then their remaining The rectangular hall shown has area $300\text{ m}^2$, breadth $x$ m and length $(2x+1)$ m. Which quadratic equA quadratic equation in the variable $x$ is an equation of which form?In a potato race, a bucket is placed at the starting point, which is $5\text{ m}$ from the first potato, and tA spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A,Find the sum of the first $40$ positive integers divisible by $6$.If the sum of the first $n$ terms of an AP is $S_n=4n-n^2$, what is the $n$th term of the AP?If the sum of the first $7$ terms of an AP is $49$ and that of the first $17$ terms is $289$, what is the sum Find the sum of the first $51$ terms of an AP whose second and third terms are $14$ and $18$ respectively.Find the sum of first $22$ terms of an AP in which $d=7$ and the $22$nd term is $149$.The first term of an AP is $5$, the last term is $45$ and the sum is $400$. Find the number of terms and the cHow many terms of the AP $9, 17, 25, \ldots$ must be taken to give a sum of $636$?How many terms of the AP $24, 21, 18, \ldots$ must be taken so that their sum is 78?The numbers of pairs of rabbits shown in the figure are $1, 1, 2, 3, 5, 8, \ldots$. Why is this pattern not anWhich term of the AP $21, 18, 15, \ldots$ is $-81$?Reena's monthly salary forms an AP: ₹8000, ₹8500, ₹9000, $\ldots$. What will be her monthly salary in the 15thIf an AP has first term $a=6$ and common difference $d=-3$, which of the following is the correct AP?Which of the following best explains why $1, 1, 2, 3, 5, 8, \ldots$ is not an arithmetic progression?The list $-1.0, -1.5, -2.0, -2.5, \ldots$ is an AP. What is its common difference?Using the ladder shown in the figure, if the bottom rung is 45 cm long and each successive rung is 2 cm shorteWhich of the following lists is an arithmetic progression?In Fig. 6.33, $CM$ and $RN$ are medians of $\triangle ABC$ and $\triangle PQR$ respectively, and $\triangle ABA girl of height $0.9\text{ m}$ is standing so that her distance from a lamp-post is $4.8\text{ m}$. If the laIn the lamp-post and shadow setup of Fig. 6.32, why are $\triangle ABE$ and $\triangle CDE$ similar?
![](httpA girl of height $90\text{ cm}$ walks away from the base of a lamp-post at a speed of $1.2\text{ m/s}$. If theIn Fig. 6.31, given $OA\cdot OB = OC\cdot OD$, which conclusion follows from the similarity of the relevant trIn Fig. 6.31, if $OA\cdot OB = OC\cdot OD$, which pair of triangles is used to apply the SAS similarity criterIn Fig. 6.30, $\angle A=80^\circ$ and $\angle B=60^\circ$ in $\triangle ABC$. If $\triangle ABC im \triangle Using the side lengths shown in the two triangles of Fig. 6.30, which statement is correct?
![](https://qalleIn two triangles, if the corresponding sides are in the same ratio, which similarity criterion is used to concIn Fig. 6.29, if $PQ \parallel RS$, which pair of triangles is similar?
![](https://qallery.app/diagrams/v2_7If two angles of one triangle are respectively equal to two angles of another triangle, then the triangles areIn $\triangle ABC$, points D and E lie on AB and AC respectively. If $\dfrac{AD}{DB}=\dfrac{AE}{EC}$, then whiIn $\triangle ABC$, a line through points D on AB and E on AC is drawn parallel to BC. According to the Basic In Fig. 6.7, the square and the rhombus are not similar because
![](https://qallery.app/diagrams/v2_70b17897dIn Fig. 6.6, the two quadrilaterals shown are not similar because
![](https://qallery.app/diagrams/v2_70b1789Two polygons having the same number of sides are similar ifUsing Fig. 6.1, which one of the following pairs is always similar?
![](https://qallery.app/diagrams/v2_70b17