CBSE Class 10 Maths Basic 2024 Question Paper 430/2/1 with Solutions

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 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)$k=-2$

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)$3x^2-6x-2=0$

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

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

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

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)$\frac{5}{4}$

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

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

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

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

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 zeroes of the polynomial $3x^2+11x-4$ are :

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

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

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

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${}^2$

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

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)$50^{\circ }$

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 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)$90^{\circ }$

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.

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 :
$x-3y=7$
$3x-3y=5$

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.

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.

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

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.

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 $7-3\sqrt{5}$ is an irrational number, given that $\sqrt{5}$ is an irrational number.

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.

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

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.

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was ₹ 750. Find the total number of toys produced on that day.

A TV tower stands vertically on a bank of a canal. From a point on the other bank exactly opposite the tower, the angle of elevation of the top of the tower is $60^{\circ }$. From another point 20 m away from this point on the line joining this point to the foot of the tower, the angle of elevation of the top of the tower is $30^{\circ }$. Find the height of the tower and the width of the canal. [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 $\pi =3.14$)

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)

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)