CBSE Class 10 Maths Basic 2024 Question Paper 430/4/1 with Solutions

The distance between the points $(2,-1)$ and $(-1,-5)$ is :

1. (A)15 units
2. (B)5 units
3. (C)25 units
4. (D)41 units

If $C(1,-1)$ is the mid-point of the line segment AB joining points $A(4,x)$ and $B(-2,4)$, then value of $x$ is :

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

Which of the following relationship is correct ?

1. (A)$P(E)=1+P(\overline{E})$
2. (B)$P(\overline{E})-P(E)=1$
3. (C)$P(E)+P(\overline{E})=1$
4. (D)$P(E)=2P(\overline{E})$

The following distribution gives the daily income of 50 workers of a factory :
Income (in ₹): 400–424, 425–449, 450–474, 475–499, 500–524
Number of workers: 12, 14, 8, 6, 10
The lower limit of the modal class is :

1. (A)425
2. (B)449
3. (C)$424.5$
4. (D)$425.5$

A lamp post 9 m high casts a shadow $3\sqrt{3}$ m long on the ground. The Sun’s elevation at this moment is :

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

If one zero of a quadratic polynomial $k{x}^2+4x+k$ is 1, then the value of $k$ is :

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

The number of quadratic polynomials having zeroes $-1$ and 3 is :

1. (A)1
2. (B)2
3. (C)3
4. (D)more than 3

The roots of the quadratic equation $x^2-4=0$ is/are :

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

Which of the following is not a quadratic equation ?

1. (A)$(x-2{)}^2+1=2x-3$
2. (B)$(2x-1)(x-3)=(x+5)(x-1)$
3. (C)$x(x+1)+8=(x+2)(x-2)$
4. (D)$2x+\frac{3}{x}=5$

The common difference of an A.P., if $a_{23}-a_{19}=32$, is :

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

$\left(\frac{1}{{\tan }^2\theta }-\frac{1}{{\sin }^2\theta }\right)$ is equal to :

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

The region between a chord and either of the two arcs of a circle is called :

1. (A)an arc
2. (B)a sector
3. (C)a segment
4. (D)a semicircle

If $1080=2^x\times 3^y\times 5$, then $(x-y)$ is equal to :

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

In the given figure, PA is a tangent from an external point P to a circle with centre O. If $\angle AOP=70^{\circ }$, then the measure of $\angle APO$ is :

1. (A)$70^{\circ }$
2. (B)$90^{\circ }$
3. (C)$110^{\circ }$
4. (D)$20^{\circ }$

The median group in the following frequency distribution is :
Class: 0–10, 10–20, 20–30, 30–40, 40–50, 50–60
Frequency: 5, 8, 20, 15, 7, 5

1. (A)10–20
2. (B)20–30
3. (C)30–40
4. (D)40–50

In a circle of radius 21 cm, if an arc subtends an angle of $60^{\circ }$ at the centre of the circle, then the length of the arc is :

1. (A)11 cm
2. (B)44 cm
3. (C)$\frac{22}{7}$ cm
4. (D)22 cm

A tangent to a circle is a line that touches the circle at :

1. (A)one point only
2. (B)two points
3. (C)three points
4. (D)infinite number of points

In the given figure, if $△ABC\sim △QPR$, then the value of $x$ is :

1. (A)$5.3$ cm
2. (B)$4.6$ cm
3. (C)$2.3$ cm
4. (D)4 cm

Assertion (A): The pair of linear equations $5x+2y+6=0$ and $7x+6y+18=0$ have infinitely many solutions.
Reason (R): The pair of linear equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$ have infinitely many solutions, if $\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$.

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): 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.

Given that HCF (306, 1314) = 18, find LCM of (306, 1314).

XY and PQ are two tangents drawn at the end points of the diameter AB of a circle. Prove that $XY\parallel PQ$.

In the given figure, $PQ\parallel RS$. Prove that $OP\times OR=OQ\times OS$.

In the given figure, $LM\parallel CB$ and $LN\parallel CD$. Prove that $\frac{AM}{AN}=\frac{AB}{AD}$.

If $\alpha$, $\beta$ are zeroes of the polynomial $8x^2+14x+3$, then find the value of $\left(\frac{1}{\alpha }+\frac{1}{\beta }\right)$.

Find a quadratic polynomial whose zeroes are $-9$ and 6.

Evaluate :
$\sin 30^{\circ }\cos 60^{\circ }+\cos 30^{\circ }\sin 60^{\circ }-\cot 45^{\circ }$

A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding (i) minor sector (ii) major sector. (Use $\pi =3.14$)

Prove that opposite sides of a quadrilateral circumscribing a circle subtends supplementary angles at the centre of the circle.

If O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of $40^{\circ }$ with PQ, then find the measure of $\angle POQ$.

Using quadratic formula, find the real roots of the equation $2x^2+2x+9=0$, if they exist.

Find the values of ‘k’ for which the quadratic equation $k{x}^2-2kx+6=0$ has real and equal roots. Also, find the roots.

One card is drawn at random from a well-shuffled deck of 52 playing cards. Find the probability that the card drawn is :
(i) a red king.
(ii) not a black card.
(iii) an ace of hearts.

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

Prove that :
$(\tan A+\sec A{)}^2+(\tan A-\sec A{)}^2=2\left(\frac{1+{\sin }^{2}A}{1-{\sin }^{2}A}\right)$

Two cubes each of volume 125 cm${}^3$ are joined end to end. Find the volume and the surface area of the resulting cuboid.

A solid is in the shape of a cone surmounted on a hemisphere with both their diameters being equal to 7 cm and the height of the cone is equal to its radius. Find the volume of the solid.

A contractor plans to install two slides for the children to play in a park. For the children below the age of 6 years, he prefers to have a slide whose top is at a height of 2.0 m and is inclined at an angle of $30^{\circ }$ to the ground, whereas for older children, he wants to have a steep slide at a height of 4.0 m and inclined at an angle of $60^{\circ }$ to the ground. What would be the length of the slide in each case ?

If BD and QM are medians of triangles ABC and PQR, respectively, where $△ABC\sim △PQR$, prove that $\frac{AB}{PQ}=\frac{BD}{QM}$.

CD and GH are respectively the bisectors of $\angle ACB$ and $\angle EGF$ such that D and H lie on sides AB and FE of $△ABC$ and $△FEG$ respectively. If $△ABC\sim △FEG$, show that :
(i) $\frac{CD}{GH}=\frac{AC}{FG}$
(ii) $△DCB\sim △HGE$

A manufacturer of TV sets produced 720 TV sets in the fourth year and 880 TV sets in the eighth year. Assuming that the production increases uniformly by a fixed number every year, find the production in the tenth year and the total production in the first seven years.

Mutual Fund : A mutual fund is a type of investment vehicle that pools money from multiple investors to invest in securities like stocks, bonds or other securities. Mutual funds are operated by professional money managers, who allocate the fund’s assets and attempt to produce capital gains or income for the fund’s investors.
Net Asset Value (NAV) represents a fund’s per share market value. It is the price at which the investors buy fund shares from a fund company and sell them to a fund company.
The following table shows the Net Asset Value (NAV) per unit of mutual fund of ICICI mutual funds :
NAV (in ₹): 0–5, 5–10, 10–15, 15–20, 20–25
Number of mutual funds: 13, 16, 22, 18, 11
Based on the above information, answer the following questions :
(i) What is the upper limit of modal class of the data ? (1)
(ii) What is the median class of the data ? (1)
(iii) (a) What is the mode NAV of mutual funds ? (2)
OR (b) What is the median NAV of mutual funds ? (2)

Resident Welfare Association (RWA) of Gulmohar Society in Delhi, have installed three electric poles A, B and C in the society’s common park. Despite these three poles, some parts of the park are still in the dark. So, RWA decides to have one more electric pole D in the park. The park can be modelled as a coordinate system given below.
On the basis of the above information, answer the following questions :
(i) What is the position of the pole C ? (1)
(ii) What is the distance of the pole B from the corner O of the park ? (1)
(iii) (a) Find the position of the fourth pole D so that the four points A, B, C and D form a parallelogram ABCD. (2)
OR (b) Find the distance between poles A and C. (2)

Deepankar bought 3 notebooks and 2 pens for ₹ 80 and his friend Suryansh bought 4 notebooks and 3 pens for ₹ 110 from the school bookshop.
Based on the above information, answer the following questions.
(i) If the price of one notebook be ₹ $x$ and the price of one pen be ₹ $y$, write the given situation algebraically. (1)
(ii) (a) What is the price of one notebook ? (2)
OR (b) What is the price of one pen ? (2)
(iii) What is the total amount to be paid by Suryansh, if he purchases 6 notebooks and 3 pens ? (1)