CBSE Class 10 Maths Basic 2025 Question Paper 430/3/2 with Solutions

The distance of point $(-3,4)$ from y-axis is :

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

The value of $\frac{{\cot }^{2}A-{\text{cosec}}^{2}A}{\sin 30^{\circ }+\cos 60^{\circ }}$ is :

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

Which types of triangles are always similar ?

1. (A)Right-angled triangles
2. (B)Acute-angled triangles
3. (C)Isosceles triangles
4. (D)Equilateral triangles

What values of $x$ and $y$ will make $△ABC$ similar to $△QRP$ in the figures given below ?

1. (A)$x=6$, $y=5$
2. (B)$x=5$, $y=6$
3. (C)$x=6$, $y=6$
4. (D)$x=12$, $y=3.2$

In the given figure, chord AB of the larger circle touches the smaller circle at C. If both the circles have the same centre O, then the length of BD is :

1. (A)1 cm
2. (B)2 cm
3. (C)3 cm
4. (D)4 cm

In the given figure, the angle of elevation of point A from point C is :

1. (A)$30^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)Cannot be determined

The angle of the sector of a circle whose area is one-eighth of the area of the circle is :

1. (A)$22{\frac{1}{2}}^{\circ }$
2. (B)$45^{\circ }$
3. (C)$60^{\circ }$
4. (D)$90^{\circ }$

The perimeter of a quadrant of a circle of circumference 22 cm is :

1. (A)29 cm
2. (B)22 cm
3. (C)12.5 cm
4. (D)5.5 cm

A cone and cylinder have same height and same radius. The volume of the cone and the volume of the cylinder are in the ratio :

1. (A)1 : 1
2. (B)1 : 3
3. (C)3 : 1
4. (D)1 : 2

The following table shows the marks scored by 23 students of a class.
Marks: 0 – 10, 10 – 20, 20 – 30, 30 – 40, 40 – 50
Number of Students: 5, 3, 4, 8, 3
The lower limit of the modal class is :

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

For a distribution, if mean = 15 and mode = 12, then its median is :

1. (A)12
2. (B)13
3. (C)14
4. (D)15

A pair of dice is thrown simultaneously. Let E denote the event that “The sum of numbers obtained on both dice is at least 9.” The number of outcomes in favour of event E is :

1. (A)4
2. (B)6
3. (C)10
4. (D)26

If $p=2^3\times 3^2\times 5$ and $q=2^2\times 3^3$, then the LCM of $p$ and $q$ is :

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

$3^n$, where $n$ is a natural number, cannot end with the digit :

1. (A)3
2. (B)5
3. (C)7
4. (D)9

A prime number has :

1. (A)exactly two prime factors
2. (B)exactly one prime factor
3. (C)at least one prime factor
4. (D)at least two prime factors

For what value(s) of $k$, is the system of equations $kx+2y=3$ and $2x+y=5$ inconsistent ?

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

If $(\sqrt{x}+1{)}^2=x^2+2\sqrt{x}$ is expressed as a quadratic equation in the form of $a{x}^2+bx+c=0$, then the value of $a-b+c$ is :

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

If point $(1,2)$ divides the line segment joining the points $(3,5)$ and $(2p,q)$ in the ratio $1:1$, then $(p,q)$ is equal to :

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

Assertion (A) : Every quadratic equation has two real roots.
Reason (R) : A quadratic polynomial can have at most two zeroes.

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) : For an acute angle $\theta$, $\cot \theta =1\Rightarrow \text{cosec }\theta =2$.
Reason (R) : ${\text{cosec}}^2\theta -{\cot }^2\theta =1$.

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.

In the given figure, TP and TQ are two tangents. If $\angle PTQ=50^{\circ }$, then find the measure of $\angle OPQ$.

If $\sin 3A=1$, then find the value of $\cos 2A-{\tan }^{2}45^{\circ }$.

If $(\sec A+\tan A)(1-\sin A)=k\cos A$, then find the value of $k$.

In the given figure, OABC is a quadrant of a circle with centre O and radius 8 cm. If OD = 6 cm, then find then perimeter of the shaded region.

Solve the following system of equations graphically :
$x+2y=10$ and $y=3$

A vertical pole of height 10 m casts a shadow of 15 m on the ground and at the same time, a tower casts a shadow of 45 m on the ground. Find the height of the tower.

In the given figure, $\frac{QR}{QS}=\frac{QT}{PR}$ and $\angle 1=\angle 2$. Prove that $△PQS\sim △TQR$.

A fraction becomes $\frac{1}{3}$, when 1 is subtracted from the numerator and it becomes $\frac{1}{4}$, when 8 is added to its denominator. Find the fraction.

Find the value of $k$ for which the following pair of linear equations will have infinitely many solutions :
$kx+3y-(k-3)=0$ and $12x+ky-k=0$
Hence, find any two solutions of the given pair of equations.

Prove the following trigonometric identity :
$\frac{1+\sec A}{\sec A}=\frac{{\sin }^{2}A}{1-\cos A}$

A box contains 6 blue, 4 white and 8 red marbles. A marble is drawn at random from this box. Find the probability that the marble so drawn is :
(i) white
(ii) white or red
(iii) not red

In the given figure, a circle is inscribed in a quadrilateral ABCD which touches the sides AB, BC, CD and DA at P, Q, R and S respectively. Prove that $\angle AOB+\angle COD=180^{\circ }$.

Prove that $\sqrt{2}$ is an irrational number.

Find which among the following numbers a, b and c is/are composite numbers.
$a=7\times 11\times 13+13$
$b=6\times 5\times 4+4$
$c=7\times 13+6$

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

State and Prove “Basic Proportionality Theorem”.

In the given figure, CM and RN are respectively, the medians of $△ABC$ and $△PQR$. If $△ABC\sim △PQR$, prove that :
(i) $△AMC\sim △PNR$
(ii) $\angle BCM=\angle QRN$
(iii) $△BMC\sim △QNR$

From a solid wooden cylinder of height 10 cm and radius 14 cm, a cylinder of radius 7 cm and height 5 cm is scooped out to form a cavity inside the solid cylinder. Find the total surface area of the remaining solid.

The following distribution shows the weekly pocket allowance (in ₹) of some children of a locality. The mean pocket allowance is ₹ 180.
Weekly Pocket Allowance (in ₹): 110 – 130, 130 – 150, 150 – 170, 170 – 190, 190 – 210, 210 – 230, 230 – 250
Number of Children: 7, 6, 9, 13, f, 5, 4
Find the value of f. Hence find the mode of given data.

Find two consecutive odd integers, sum of whose squares is 290.

A charity trust decides to build a rectangular hall having an area of 300 ${\text{m}}^2$. The length of the hall is one metre more than twice its width. Find the length and breadth of the hall.

Two motorboats A and B are waiting at the opposite banks of a river in order to reach the opposite side. From a point P on the bridge, 20 m above the river, the angles of depression of the boats are $30^{\circ }$ and $45^{\circ }$ respectively, as shown in the figure given below. Both the boats leave at the same time at the speed of 10 m/s and 5 m/s, respectively
Based on the above information, answer the following questions :
(i) Find the distance travelled by boat A to reach point D in the river, vertically below the point P. (Use $\sqrt{3}=1.73$) (1)
(ii) What is the width of the river ? (1)
(iii) (a) Which boat will reach point D first, and how much earlier, than the other boat ? (2)
OR
(b) What is the distance between the two boats after 3 seconds ? (2)

There is a semicircular park in Aman’s society. He wishes to plant saplings along the boundary of the park. There is a borewell at the centre O of the park along the diameter AB as shown in the figure below.
Based on the above information, answer the following questions :
(i) Find the coordinates of point O. (1)
(ii) Find the radius of the semicircular park. (1)
(iii) (a) One sapling is kept at point C(12, y). Find the coordinates of C. (2)
OR
(b) One sapling is kept at point P along AB so that PA = $\frac{1}{3}$ PB. Find the coordinates of P. (2)

In a society, a yoga instructor was hired to train the people of the society to live a healthy lifestyle. Yoga sessions were held daily from 5 p.m. to 7 p.m. in the society park. On day one, 5 people joined the yoga session, on day two, 3 more people joined, on day three, another 3 people joined and in this manner every next day, 3 more people kept on joining.
Based on the given information, answer the following questions :
(i) On which day did 59 people join the yoga session ? (1)
(ii) How many people joined the yoga session on the 31st day ? (1)
(iii) (a) The yoga instructor was paid ₹100 for each person attending the yoga session. On which day would he earn ₹5,000 ? (2)
OR
(b) What was the total amount earned by the yoga instructor in 16 days ? (2)