CBSE Class 10 Maths Basic 2024 Question Paper 430/5/3 with Solutions

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)$45^{\circ }$

The area of a sector of a circle of radius 16 cm cut off by an arc, which is 18.5 cm long, is :

1. (A)168 cm${}^2$
2. (B)148 cm${}^2$
3. (C)154 cm${}^2$
4. (D)176 cm${}^2$

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)$45^{\circ }$

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

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

A lamp post 15 m high, casts a shadow $5\sqrt{3}$ m long on the ground. The Sun's elevation at this moment is :

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

If $x=4\sin \theta$, $y=4\cos \theta$, then the value of $(x^2+y^2)$ is :

1. (A)4
2. (B)$\frac{1}{4}$
3. (C)$\frac{1}{16}$
4. (D)16

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)$-5,-2$

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

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

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

In a frequency distribution, the mid-value of a class is 10 and the width of the class is 6. The lower limit of the class is :

1. (A)6
2. (B)7
3. (C)8
4. (D)12

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)$2^4\times 53$

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)$k\ne -\frac{1}{3}$

The roots of the quadratic equation $a{x}^2+bx+c=0$ are real and distinct, if :

1. (A)$b^2-4ac>0$
2. (B)$b^2-4ac=0$
3. (C)$b^2-4ac<0$
4. (D)$b^2-4ac\ge 0$

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 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)$150^{\circ }$

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)$(4,-6)$

A letter is chosen at random from the word 'MATHEMATICS'. What is the probability that it will be a 'vowel' ?

1. (A)$\frac{3}{11}$
2. (B)$\frac{4}{11}$
3. (C)$\frac{5}{11}$
4. (D)$\frac{7}{11}$

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.

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

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.

If $x=\sin 60^{\circ }\cos 30^{\circ }+\cos 60^{\circ }\sin 30^{\circ }$, then find the value of x.

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 $B(-4,3)$.

Find the zeroes of the polynomial $3x^2-5x-2$ and verify the relationship between the zeroes and the coefficients of the polynomial.

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

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.

Prove that $\sqrt{\frac{1+\sin A}{1-\sin A}}=\sec A+\tan A$.

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

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 data gives the information about the lifetimes (in hours) of 225 neon lamps :
Lifetime (in hours): 1500 – 2000, 2000 – 2500, 2500 – 3000, 3000 – 3500, 3500 – 4000, 4000 – 4500
Number of lamps: 10, 35, 52, 61, 38, 29
Find the median lifetime of a lamp.

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 sum of the digits of a 2-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

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)

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)