CBSE Class 10 Maths Basic 2024 Question Paper 430/5/1 with Solutions

HCF $\times$ LCM for the numbers 40 and 30 is :

1. (A)12
2. (B)120
3. (C)1200
4. (D)40

The roots of the quadratic equation $x^2+3x-10=0$ are :

1. (A)5, 2
2. (B)$-5,2$
3. (C)$5,-2$
4. (D)$-5,-2$

The pair of linear equations $2kx+5y=7$, $6x+5y=11$ have a unique solution, if

1. (A)$k\ne 3$
2. (B)$k\ne -3$
3. (C)$k\ne \frac{1}{3}$
4. (D)$k\ne -\frac{1}{3}$

If the mean and mode of a frequency distribution are 28 and 16 respectively, then its median is :

1. (A)22
2. (B)23.5
3. (C)24
4. (D)24.5

A die is rolled once. What is the probability of getting an odd prime number ?

1. (A)$\frac{1}{6}$
2. (B)$\frac{1}{3}$
3. (C)$\frac{2}{3}$
4. (D)$\frac{3}{4}$

If the area of a sector of a circle is $\frac{1}{8}$ of the area of the circle, then the central angle of the sector is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

Prime factorisation of 424 is :

1. (A)$2\times 53\times 4$
2. (B)$2\times 53\times 2$
3. (C)$2^3\times 53$
4. (D)$2^4\times 53$

If x is a whole number, then $8^x$ ends with an even digit, except for which value of x ?

1. (A)6
2. (B)4
3. (C)2
4. (D)0

A tree casts a shadow 7 m long on the ground, when the angle of elevation of the Sun is $45^{\circ }$. The height of the tree is :

1. (A)$7\sqrt{3}$ m
2. (B)$\frac{7}{3}\sqrt{3}$ m
3. (C)7 m
4. (D)3.5 m

$\left(\frac{5}{{\cot }^2\theta }-\frac{5}{{\cos }^2\theta }\right)$ is equal to :

1. (A)1
2. (B)5
3. (C)$-5$
4. (D)0

If ${\tan }^2\theta =3$, where $\theta$ is an acute angle, then the value of $\theta$ is :

1. (A)$30^{\circ }$
2. (B)$60^{\circ }$
3. (C)$0^{\circ }$
4. (D)$45^{\circ }$

The length of an arc of a circle with radius 12 cm is $10\pi$ cm. The central angle subtended by this arc at the centre, is :

1. (A)$120^{\circ }$
2. (B)$6^{\circ }$
3. (C)$75^{\circ }$
4. (D)$150^{\circ }$

If the angle between the two radii of a circle is $130^{\circ }$, then the angle between the tangents at the ends of these radii, is :

1. (A)$50^{\circ }$
2. (B)$60^{\circ }$
3. (C)$90^{\circ }$
4. (D)$130^{\circ }$

The discriminant of the quadratic equation $x^2-4x+3=0$ is :

1. (A)28
2. (B)$-8$
3. (C)4
4. (D)2

The mid-point of the line segment AB joining $A(-2,8)$ and $B(-6,4)$ is :

1. (A)(2, 6)
2. (B)$(-4,12)$
3. (C)$(-4,6)$
4. (D)$(4,-6)$

AP and AQ are tangents drawn from an external point A to a circle with centre O and inclined to each other at an angle of $90^{\circ }$. If the length of each tangent is 2 cm, then the radius of the circle is :

1. (A)4 cm
2. (B)2 cm
3. (C)$2\sqrt{2}$ cm
4. (D)1 cm

It is given that $△ABC\sim △DEF$. If $\angle A=55^{\circ }$, $\angle E=45^{\circ }$, then $\angle C$ is :

1. (A)$80^{\circ }$
2. (B)$90^{\circ }$
3. (C)$55^{\circ }$
4. (D)$45^{\circ }$

In the given figure, in $△ABC$, DE $\parallel$ BC. If AD = 2x cm, AE = (x + 2) cm, DB = 4 cm, EC = 3 cm, then the value of x is :

1. (A)3
2. (B)2
3. (C)6
4. (D)4

Assertion (A) : The probability of getting number 8 on rolling a die is zero (0).
Reason (R) : The probability of an impossible event is zero (0).

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Assertion (A) : Common difference of the A.P. $5,1,-3,-7$ .... is 4.
Reason (R) : Common difference of the A.P. $a_1,a_2,a_3$ ...., $a_n$ is obtained by $d=a_n-a_{n-1}$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Evaluate : ${\sin }^{2}30^{\circ }+{\cos }^{2}45^{\circ }-\cos 0^{\circ }\cdot \tan 45^{\circ }$

Find the ratio in which the point $(3,y)$, divides the line segment joining the points $(-2,-5)$ and $(6,3)$. Also, find the value of y.

Find a point on y-axis which is equidistant from the points $A(6,5)$ and $B(-4,3)$.

If $\frac{2}{3}$ is a root of the quadratic equation $k{x}^2-x-2=0$, then find the value of k.

The length of a tangent drawn to a circle from a point A, at a distance of 10 cm from the centre of the circle, is 6 cm. Find the radius of the circle.

If $\alpha$, $\beta$ are zeroes of the quadratic polynomial $2x^2+7x+5$, then find the value of ${\alpha }^2+{\beta }^2+\alpha \beta$.

If one zero of the quadratic polynomial $6x^2+37x-(p-2)$ is reciprocal of the other, then find the value of p.

Prove that $6+3\sqrt{2}$ is an irrational number, given that $\sqrt{2}$ is an irrational number.

Find the zeroes of the quadratic polynomial $6x^2-7x-3$ and verify the relationship between the zeroes and the coefficients of the polynomial.

Prove that : $(\sin \theta +\text{cosec}\theta {)}^2+(\cos \theta +\sec \theta {)}^2=7+{\tan }^2\theta +{\cot }^2\theta$.

Prove that the parallelogram circumscribing a circle is a rhombus.

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

A horse is tied with a 14 m long rope at one corner of an equilateral triangular field having side 20 m. Find the area of the field where the horse cannot graze.

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand between 8:00 am and 8:05 am.

Find the coordinates of the points of trisection of the line segment joining the points $A(5,-3)$ and $B(-4,3)$.

A toy is in the form of a cone of radius 7 cm mounted on a hemisphere of same radius. The total height of the toy is 31 cm. Find the surface area of the toy.

A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is 15 cm and its base is of radius 4.2 cm, then find the total surface area of the article.

The ratio of monthly incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save ₹ 2,000 per month, then find their monthly incomes.

Sides AB, BC and median AD of $△ABC$ are respectively proportional to sides PQ, QR and median PM of $△PQR$. Show that $△ABC\sim △PQR$.

Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides at distinct points, then the other two sides are divided in the same ratio.

The following frequency distribution table gives the monthly consumption of electricity of 70 consumers of a locality. Find the median of the data.
Monthly consumption (in units): 65 – 85, 85 – 105, 105 – 125, 125 – 145, 145 – 165, 165 – 185, 185 – 205
Number of consumers: 7, 8, 7, 20, 14, 9, 5

Family structure : In a recent survey of this year, 51% of the families in the United States of America had no children, 20% had one child, 19% had two children, 7% had three children and 3% had four or more children.
A family is selected at random.
Based on the above information, answer the following questions :
(i) Find the probability that the selected family has two or three children. (1)
(ii) Find the probability that the selected family has more than one child. (1)
(iii) (a) Find the probability that the selected family has less than three children. (2)
OR
(b) Find the probability that the selected family has more than two children. (2)

Sumant's mother started a new shoe shop. To display the shoes, she put 3 pairs of shoes in the 1st row, 5 pairs in the 2nd row, 7 pairs in the 3rd row and so on.
Based on the above information, answer the following questions :
(i) How many pairs of shoes are displayed in the 6th row ? (1)
(ii) What is the difference of pairs of shoes in the 1st row and the 6th row ? (1)
(iii) (a) Find the total number of pairs of shoes displayed in the first 15 rows. (2)
OR
(b) If the pairs of shoes displayed in the 4th row are 'on sale' at price of ₹ 500 for each pair, then find the total amount (money) earned by Sumant's mother if all shoes displayed in the 4th row are sold out. (2)

Two poles of different heights stand on level ground and at a distance of 40 m. Both poles are supported by wires attached from the top of each pole to the bottom of the other. A coupling is placed at point C, where the two wires cross (as shown in the figure).
Based on the above information, answer the following questions :
(i) Find the height of pole AB. (1)
(ii) Find the height of pole PQ. (1)
(iii) (a) If the angle of elevation of the top of the pole PQ from the top of the pole AB is $30^{\circ }$, find the distance BQ. (2)
OR
(b) If the coupling is at a height of 20 m from the ground, how far down the wire from the smaller pole AB is the coupling ? (2)