CBSE Class 10 Maths Basic 2025 Question Paper 430/5/2 with Solutions

The point ($x$, 0) divides the line segment joining the points (–4, 5) and (0, –10) in the ratio

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

A black card is lost from a deck of 52 playing cards. Rest of the cards are shuffled and one card is drawn at random from the available cards. The probability that drawn card is 'king of hearts', is

1. (A)$\frac{1}{52}$
2. (B)$\frac{1}{4}$
3. (C)$\frac{1}{51}$
4. (D)$\frac{1}{26}$

$(2-5\sqrt{3}{)}^2$ is

1. (A)a negative integer
2. (B)an irrational number
3. (C)a rational number
4. (D)a positive integer

The $16^{th}$ term of the A.P. : $5\sqrt{3}$, $2\sqrt{3}$, $-\sqrt{3}$, ... is

1. (A)$-25\sqrt{3}$
2. (B)$-40\sqrt{3}$
3. (C)$50\sqrt{3}$
4. (D)$-45+5\sqrt{3}$

The roots of the equation $x^2-8=0$ are

1. (A)rational and distinct
2. (B)irrational and distinct
3. (C)real and equal
4. (D)not real

Tangent BC makes an angle of $x^{\circ }$ with the chord AB of circle centered at O. If $\angle AOB=100^{\circ }$, then value of $x$ is

1. (A)40
2. (B)80
3. (C)90
4. (D)50

In the given figure, AB is diameter of the circle with centre O. CD is tangent to the circle so that $\angle ACD=40^{\circ }$. The value of $\angle CBA$ is

1. (A)$50^{\circ }$
2. (B)$40^{\circ }$
3. (C)$80^{\circ }$
4. (D)$45^{\circ }$

A quadratic polynomial having only zero (–2) is

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

PQ and PR are tangents to a circle with centre O such that OQ = QP. The value of $\angle OPQ$ is equal to

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

If tan A = 1, then 3 sin A + cos A is equal to

1. (A)$4\sqrt{2}$
2. (B)4
3. (C)$2\sqrt{2}$
4. (D)$4\times 45^{\circ }$

Which of the following depends on all observations of a given data ?

1. (A)Median
2. (B)Mean
3. (C)Range
4. (D)Mode

The value of k for which roots of quadratic equation k$x$($x$ – 2) + 6 = 0 are real and equal, is

1. (A)0 only
2. (B)0, 6
3. (C)6 only
4. (D)–6 only

An arc of length 22 cm subtends an angle of $x^{\circ }$ at the centre of the circle. If radius of circle is 36 cm, the value of $x$ is

1. (A)35
2. (B)40
3. (C)60
4. (D)30

Two dice are rolled together. The probability that only one die shows number 4, is

1. (A)$\frac{11}{36}$
2. (B)$\frac{1}{3}$
3. (C)$\frac{5}{18}$
4. (D)$\frac{1}{4}$

The distance between the points (2, 3) and (–2, –3) is

1. (A)$4\sqrt{13}$
2. (B)$\sqrt{40}$
3. (C)$2\sqrt{13}$
4. (D)5

Observe the given graph of polynomial p($x$). The number of zeroes of p($x$) is

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

If E is an event such that P(E) = 1%, then P($\overline{E}$) is equal to

1. (A)0.09
2. (B)0.99
3. (C)$\frac{1}{99}$
4. (D)0.90

The largest possible cone is just fitted inside a hollow cube of edge 25 cm. The radius of the base of the cone is

1. (A)5 cm
2. (B)12.5 cm
3. (C)25 cm
4. (D)10 cm

Assertion (A) : In a right angle triangle ABC, $\angle B=90^{\circ }$. Therefore the value of cos (A + C) is equal to 0.
Reason (R) : $A+B+C=180^{\circ }$ and $\cos 90^{\circ }=0$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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) : When a hemisphere of same radius (r) is carved out from one side of a solid wooden cylinder, the total surface area of remaining solid is increased by $2\pi r^2$.
Reason (R) : Curved surface area of hemisphere is $2\pi r^2$.

1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. (C)Assertion (A) is true, but Reason (R) is false.
4. (D)Assertion (A) is false, but Reason (R) is true.

Establish a relation between $x$ and y such that point ($x$, y) is equidistant from points (–2, 5) and (3, 9).

Using distance formula, prove that the points (1, 5), (2, 3) and (3, 1) are collinear.

Prove that, for a natural number n, $6^n$ can not end with the digit 0. Which prime number must be multiplied with $6^n$ so that the resultant ends with the digit zero ?

Evaluate : $2{\tan }^{2}45^{\circ }+{\cos }^{2}30^{\circ }-{\sin }^{2}90^{\circ }$.

Verify that $\cos 2A=\frac{1-{\tan }^{2}A}{1+{\tan }^{2}A}$ for $A=30^{\circ }$.

A bag contains 40 marbles out of which some are white and others are black. If the probability of drawing a black marble is $\frac{3}{5}$, then find the number of white marbles.

In a pre-primary class, a teacher put cards numbered 20 to 59 in a bowl. A student picked up a card at random and read the number. Find the probability that the number read was (i) a prime number (ii) a perfect square.

Find the smallest number which when increased by 20, is exactly divisible by 72, 90 and 150.

A spherical glass vessel has a cylindrical neck 7 cm long and 8 cm in diameter. The radius of spherical part is 10 cm. Find the volume of the vessel.

From each end of a solid cylinder of height 20 cm and base radius 7 cm, a cone of base radius 2.1 cm and height 5 cm is scooped out. Find the volume of the remaining solid.

Point E lies on the extended side AD of parallelogram ABCD. BE intersects CD at F. Show that (i) $△DFE\sim △CFB$ (ii) $△AEB\sim △CBF$.

Prove that : $\frac{\cos \theta }{1-\tan \theta }+\frac{\sin \theta }{1-\cot \theta }=\cos \theta +\sin \theta$.

If $\alpha$, $\beta$ are zeroes of the polynomial $3x^2-8x+4$, then form a quadratic polynomial in $x$ whose zeroes are $\frac{1}{\alpha }$ and $\frac{1}{\beta }$.

Find zeroes of the polynomial $6x^2-7x-3$ and verify the relationship between zeroes and its coefficients.

A rectangular field is 16 m long and 10 m wide. There is a path of equal width all around it, having an area of 120 sq.m. Find the width of the path.

From a point on the ground, the angle of elevation of the top of a tree observed by a person is $60^{\circ }$. When moved back by 28 m, in the same line, the angle of elevation from another point on ground becomes $30^{\circ }$. Find the height of the tree and its distance from the initial point. (Use $\sqrt{3}$ = 1.73)

Find 'mean' and 'mode' of the following data :
Class: 10-25, 25-40, 40-55, 55-70, 70-85, 85-100
Number of Students: 12, 10, 15, 13, 8, 12

The following table shows the ages of patients admitted in a hospital during a year :
Age (in years): 5-15, 15-25, 25-35, 35-45, 45-55, 55-65
Number of Patients: 7, 10, 21, 22, 15, 5
Find 'mode' and 'median' of the above data.

The sum of a 2-digit number and the number obtained by reversing the order of its digits, is 121. The two digits differ by 3.
(i) Represent the above information in the form of pair of linear equations.
(ii) Show that the equations have unique solution.
(iii) Solve the equations and find the number.

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

It is given that sides AB and AC and median AD of $△ABC$ are respectively proportional to sides PQ and PR and median PM of another $△PQR$. Show that $△ABC\sim △PQR$.

A tent house owner provides furniture on rent. He stacks chairs in his shop to save space.
In the diagram, the height of seat of chair from ground is represented by $h_1$, $h_2$, $h_3$, .... The height of first seat is 44 cm from ground level and gap between every two seats is 10 cm.
(i) Write the values of $h_1$, $h_2$, $h_3$, $h_4$ and $h_5$ in this order only. (1)
(ii) Show that the above values form an A.P. Write its first term and common difference. (1)
(iii) (a) If chairs can be stacked up to the maximum height of 160 cm, then find the maximum number of chairs in a stack. (2)
OR
(iii) (b) Is it possible to stack 15 chairs if maximum height of the stack can not be more than 180 cm ? Justify your answer. (2)

In a Fine Arts class, students were asked to design triangular tiles in geometric pattern.
Neelima made a circular design inside an equilateral triangle ABC. The radius of the circle is 4 cm. Observe the diagram and answer the following questions :
(i) Determine the length OB. (1)
(ii) Is DE $\parallel$ CA ? Give reason for your answer. (1)
(iii) (a) Write all angles of quadrilateral OEBD and show that it is a cyclic quadrilateral. (2)
OR
(iii) (b) Find the perimeter of $△ABC$. (Use $\sqrt{3}=1.73$) (2)

A farmer has put up a decorative windmill in his farm in which there are eight blades of equal width and equally placed in a circular arrangement. A circular wire goes through them.
The diagram shows two blades OAB and OPQ in a quarter circle with centre O. $\angle AOB=\angle POQ=30^{\circ }$, OA = 28 cm, OC = 21 cm.
O is the centre of both the circles.
(i) Determine the measure of $\angle BOP$. (1)
(ii) Find length of arc CD. (1)
(iii) (a) Find the area of region CABD. (2)
OR
(iii) (b) Find perimeter of region CABD. (2)