CBSE Class 10 Maths Basic 2024 Question Paper 430/2/2 with Solutions

The difference of the areas of a minor sector of angle $120^{\circ }$ and its corresponding major sector of a circle of radius 21 cm, is

1. (A)231 cm${}^2$
2. (B)462 cm${}^2$
3. (C)346.5 cm${}^2$
4. (D)693 cm${}^2$

The annual rainfall record of a city for 66 days is given in the following table :
Rainfall (in cm) : 0–10, 10–20, 20–30, 30–40, 40–50, 50–60
Number of days : 22, 10, 8, 15, 5, 6
The difference of upper limits of modal and median classes is :

1. (A)10
2. (B)15
3. (C)20
4. (D)30

In the given figure, tangents PA and PB from a point P to a circle with centre O are inclined to each other at an angle of $80^{\circ }$. $\angle ABO$ is equal to

1. (A)$40^{\circ }$
2. (B)$80^{\circ }$
3. (C)$100^{\circ }$
4. (D)$50^{\circ }$

$\frac{1+{\tan }^{2}A}{1+{\cot }^{2}A}$ is equal to

1. (A)${\sec }^{2}A$
2. (B)$-1$
3. (C)${\cot }^{2}A$
4. (D)${\tan }^{2}A$

If ${\sin }^2\theta =\frac{3}{4}$, then $\theta$ is

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

The zeroes of the polynomial $3x^2-5x-2$, are :

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

A pole $7\sqrt{3}$ m high casts a shadow 21 m long on the ground, then the sun’s elevation is :

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

The HCF of smallest 2 – digit number and the smallest composite number is :

1. (A)2
2. (B)20
3. (C)40
4. (D)4

The total surface area of a solid hemisphere of radius 7 cm is :

1. (A)$98\pi$ cm${}^2$
2. (B)$147\pi$ cm${}^2$
3. (C)$196\pi$ cm${}^2$
4. (D)$228\frac{2}{3}\pi$ cm${}^2$

If $\sin A=\frac{3}{5}$, then value of $\cot A$ is :

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

The graph of a pair of linear equations $a_{1}x+b_{1}y=c_1$ and $a_{2}x+b_{2}y=c_2$ in two variables $x$ and y represents parallel lines, if

1. (A)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}$
2. (B)$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$
3. (C)$\frac{a_1}{a_2}\ne \frac{b_1}{b_2}=\frac{c_1}{c_2}$
4. (D)$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

A line intersecting a circle in two distinct points is called a

1. (A)secant
2. (B)chord
3. (C)diameter
4. (D)tangent

The value of ‘k’ for which the pair of linear equations $x+y-4=0$ and $2x+ky-8=0$ has infinitely many solutions, is

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

A quadratic polynomial, the sum of whose zeroes is $-5$ and their product is 6, is

1. (A)$x^2+5x+6$
2. (B)$x^2-5x+6$
3. (C)$x^2-5x-6$
4. (D)$-x^2+5x+6$

If P(A) denotes the probability of an event A, then

1. (A)$P(A)<0$
2. (B)$P(A)>1$
3. (C)$0\le P(A)\le 1$
4. (D)$-1\le P(A)\le 1$

Which of the following quadratic equations has $-1$ as a root ?

1. (A)$x^2-4x-5=0$
2. (B)$-x^2-4x+5=0$
3. (C)$x^2+3x+4=0$
4. (D)$x^2-5x+6=0$

The distance of the point (3, 4) from the origin is

1. (A)25
2. (B)5
3. (C)7
4. (D)1

If the first term of an AP is $-3$ and common difference $-2$, then the seventh term is

1. (A)$-9$
2. (B)9
3. (C)$-17$
4. (D)$-15$

Assertion (A) : The point (0, 4) lies on y – axis.
Reason (R) : The $x$-coordinate of a point, lying on y – axis, is zero.

1. (A)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are correct 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) : A line drawn parallel to any one side of a triangle intersects the other two sides in the same ratio.
Reason (R) : Parallel lines cannot be drawn to any side of a triangle.

1. (A)Both Assertion (A) and Reason (R) are correct and Reason (R) is the correct explanation of Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are correct 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.

In the given figure, $OA\cdot OB=OC\cdot OD$. Prove that $△AOD\sim △COB$.

In the given figure, $\angle D=\angle E$ and $\frac{AD}{DB}=\frac{AE}{EC}$. Prove that $△ABC$ is isosceles.

A lot consists of 165 ball pens of which 30 are defective and the others are good. Rakshita will buy a pen if it is good. The shopkeeper draws one pen at random and gives it to Rakshita. What is the probability that she will buy it ?

Prove that the tangents drawn at the ends of a diameter of a circle are parallel to each other.

Find the HCF of 84 and 144 by prime factorisation method.

The sum of two natural numbers is 70 and their difference is 10. Find the natural numbers.

Solve for $x$ and y :
$x-3y=7$
$3x-3y=5$

To warn ships for underwater rocks, a light house spreads a red coloured light over a sector of angle $80^{\circ }$ to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use $\pi =3.14$)

Zeroes of the quadratic polynomial $x^2+x-6$ are ‘$\alpha$’ and ‘$\beta$’. Construct a quadratic polynomial whose zeroes are $\frac{1}{\alpha }$ and $\frac{1}{\beta }$.

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

Prove that $\frac{\tan \theta }{1-\cot \theta }+\frac{\cot \theta }{1-\tan \theta }=1+\sec \theta \text{cosec}\theta$

Two dice are tossed simultaneously. Find the probability of getting
(a) an even number on both the dice.
(b) the sum of two numbers more than 9.

A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of $120^{\circ }$. Find the area cleaned at each sweep of the blades.

In two concentric circles, a chord of length 24 cm of larger circle touches the smaller circle, whose radius is 5 cm. Find the radius of the larger circle.

Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segment joining the points of contact at the centre.

In the given figure, altitudes CE and AD of $△ABC$ intersect each other at the point P.
Show that
(i) $△AEP\sim △CDP$
(ii) $△ABD\sim △CBE$
(iii) $△AEP\sim △ADB$

AD and PM are medians of triangles ABC and PQR, respectively, where $△ABC\sim △PQR$. Prove that $\frac{AB}{PQ}=\frac{AD}{PM}$.

A textile industry runs in a shed. This shed is in the shape of a cuboid surmounted by a half cylinder. If the base of the industry is of dimensions 14 m $\times$ 20 m and the height of the cuboidal portion is 7 m, find the volume of air that the industry can hold. Further, suppose the machinery in the industry occupies a total space of 400 m${}^3$. Then, how much space is left in the industry ?

From a solid cylinder of height 8 cm and radius 6 cm, a conical cavity of the same height and same radius is carved out. Find the total surface area of the remaining solid. (Take $\pi =3.14$)

From the top of a 7 m high building, the angle of elevation of the top of a cable tower is $60^{\circ }$ and the angle of depression of its foot is $45^{\circ }$. Determine the height of the tower. (Use $\sqrt{3}=1.732$)

A cottage industry produces a certain number of pottery articles in a day. It was observed that 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 ₹ 90, find the number of articles produced and the cost of each article.

Heart Rate : The heart rate is one of the ‘vital signs’ of health in the human body. It measures the number of times per minute that the heart contracts or beats. While a normal heart rate does not guarantee that a person is free of health problems, it is a useful benchmark for identifying a range of health issues.
Thirty women were examined by doctors of AIIMS and the number of heart beats per minute were recorded and summarized as follows :
Number of heart beats per minute : 65–68, 68–71, 71–74, 74–77, 77–80, 80–83, 83–86
Number of Women : 2, 4, 3, 8, 7, 4, 2
Based on the above information, answer the following questions :
(i) How many women are having heart beat in the range 68 – 77 ? (1)
(ii) What is the median class of heart beats per minute for these women ? (1)
(iii) Find the modal value of heart beats per minute for these women. (2)
OR (iii) Find the median value of heart beats per minute for these women. (2)

The top of a table is hexagonal in shape.
On the basis of the information given above, answer the following questions :
(i) Write the coordinates of A and B. (1)
(ii) Write the coordinates of the mid-point of line segment joining C and D. (1)
(iii) Find the distance between M and Q. (2)
OR (iii) Find the coordinates of the point which divides the line segment joining M and N in the ratio 1:3 internally. (2)

Saving money is a good habit and it should be inculcated in children right from the beginning. Rehan’s mother brought a piggy bank for Rehan and puts one ₹ 5 coin of her savings in the piggy bank on the first day. She increases his savings by one ₹ 5 coin daily.
Based on the above information, answer the following questions :
(i) How many coins were added to the piggy bank on 8th day ? (1)
(ii) How much money will be there in the piggy bank after 8 days ? (1)
(iii) If the piggy bank can hold one hundred twenty ₹ 5 coins in all, find the number of days she can contribute to put ₹ 5 coins into it. (2)
OR (iii) Find the total money saved, when the piggy bank is full. (2)