CBSE Class 10 Maths Basic 2024 Question Paper 430/2/3 with Solutions

The total surface area of a cube of side 20 cm is

1. (A)240 cm${}^2$
2. (B)160 cm${}^2$
3. (C)2400 cm${}^2$
4. (D)1600 cm${}^2$

The zeroes of the polynomial $3x^2+8x-3$ are :

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

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)$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

The distance of the point (5, 4) from the origin is

1. (A)41
2. (B)$\sqrt{41}$
3. (C)3
4. (D)9

$\frac{2\tan 30^{\circ }}{1-{\tan }^{2}30^{\circ }}$ is equal to

1. (A)$\cos 60^{\circ }$
2. (B)$\sin 60^{\circ }$
3. (C)$\tan 60^{\circ }$
4. (D)$\sin 30^{\circ }$

If a pole 6 m high casts a shadow $2\sqrt{3}$ 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)$90^{\circ }$

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)$-1\le P(A)\le 1$

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

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

If n is any natural number, then which of the following numbers ends with digit 0 ?

1. (A)$(3\times 2{)}^n$
2. (B)$(5\times 2{)}^n$
3. (C)$(6\times 2{)}^n$
4. (D)$(4\times 2{)}^n$

If $5\cos A-4=0$, then the value of $\tan A$ is

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

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)$50^{\circ }$

Which of the following equations has 2 as a root ?

1. (A)$x^2-4x+5=0$
2. (B)$x^2+3x-12=0$
3. (C)$2x^2-7x+6=0$
4. (D)$3x^2-6x-2=0$

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)$-x^2+5x+6$

The value of ‘p’ for which the pair of equations $-2x+3y-9=0$ and $4x+py+7=0$ has a unique solution is

1. (A)$p\ne 6$
2. (B)$p=6$
3. (C)$p=-6$
4. (D)$p\ne -6$

$\frac{{\text{cosec}}^{2}A-{\cot }^{2}A}{1-{\sin }^{2}A}$ is equal to

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

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

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${}^2$

In an A.P., if $d=-4$ and $a_7=4$, then the first term ‘a’ is equal to

1. (A)6
2. (B)7
3. (C)20
4. (D)28

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.

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.

15 defective pens are accidentally mixed with 145 good ones. One pen is taken out at random from this lot. Determine the probability that the pen taken out is a good one.

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

Find the LCM of 231 and 396 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 :
$x-3y=7$
$3x-3y=5$

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.

Zeroes of the quadratic polynomial $x^2-3x+2$ are $\alpha$ and $\beta$. Construct a quadratic polynomial whose zeroes are $2\alpha +1$ and $2\beta +1$.

Find the zeroes of the polynomial $4x^2-4x+1$ and verify the relationship between the zeroes and the coefficients.

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.

All the kings and queens are removed from a deck of 52 playing cards. Remaining cards are well shuffled and then a card is drawn at random. Find the probability that the drawn card is
(a) an ace of hearts
(b) a black card
(c) a jack of spades

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.

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

Prove that $5\sqrt{2}-3$ is an irrational number, given that $\sqrt{2}$ is an irrational number.

As observed from the top of a 75 m light house from the sea-level, the angles of depression of two ships are $30^{\circ }$ and $45^{\circ }$. If one ship is exactly behind the other on the same side of the light house, find the distance between the two ships. [Use $\sqrt{3}=1.732$]

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 $\pi =3.14$)

The area of a rectangular plot is 528 m${}^2$. The length of the plot (in metres) is one more than twice the breadth. Find the length and breadth of the plot. Also, find the cost of levelling the plot at the rate of ₹ 80 per square metre.

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)

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)