CBSE Class 10 Maths Basic 2025 Question Paper 430/5/3 with Solutions

PQ is tangent to the circle centred at O. If OQ = 3 cm, PQ = 5 cm, then OP is equal to

1. (A)5 cm
2. (B)4 cm
3. (C)$\sqrt{15}$ cm
4. (D)$\sqrt{34}$ cm

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

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

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)$(x+2{)}^2$

If sin A = cos A, then $\frac{1-\tan A}{1+\tan A}$ is equal to

1. (A)1
2. (B)–1
3. (C)0
4. (D)not defined

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)$\frac{1}{26}$

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

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)$45^{\circ }$

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

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)$\frac{1}{4}$

If the distance between the points (3, 0) and (2, y) is $\sqrt{5}$, then the value(s) of y is :

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

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)$90^{\circ }$

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

$10^{th}$ term of the A.P. : –12, –19, –26, .... is

1. (A)–75
2. (B)–65
3. (C)51
4. (D)–82

If E is an event such that P(E) = 0.1, then P($\overline{E}$) is equal to

1. (A)0.9
2. (B)$\frac{1}{2}$
3. (C)0.99
4. (D)–1

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

An arc of length '$l$' subtends an angle of $15^{\circ }$ at the centre of a circle of radius 8.4 cm. The value of $l$ is

1. (A)22 cm
2. (B)2.2 cm
3. (C)9.24 cm
4. (D)4.2 cm

The value of k for which the roots of the quadratic equation $6x^2+4kx+k=0$ are real and equal, is

1. (A)0
2. (B)$\frac{3}{4}$
3. (C)$\frac{-3}{2}$
4. (D)$\frac{2}{3}$

$\sqrt{2}(\sqrt{2}-1)$ is

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

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.

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 coordinates of the points of trisection of line segment joining the points (–4, 1) and (6, 5).

Using distance formula, show that the points (–1, 3), (6, 2) and (3, –1) are vertices of a right-angled triangle.

Check whether $15^n\times 2^n$, n being a natural number, ends with the digit zero.

If sec A = $\frac{25}{7}$, then find the value of cosec A and tan A.

Verify that sin (A + B) = sin A cos B + cos A sin B for A = $60^{\circ }$ and B = $30^{\circ }$.

Prove that : $(\sin \theta +\sec \theta {)}^2+(\cos \theta +\text{cosec }\theta {)}^2=(1+\sec \theta \text{cosec }\theta {)}^2$.

The traffic lights at three different road crossings change after every 45 seconds, 75 seconds and 60 seconds respectively. If they change together at 5.00 a.m., then at what time they will change together next ?

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.

It is given that $△ACD\cong △ABE$. Prove that $△ADE\sim △ABC$.

The sum of the squares of two consecutive odd numbers is 514. Find the numbers.

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.

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.

A statue 3 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is $60^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is $30^{\circ }$. Find the height of the pedestal and its distance from the point of observation on ground. (Use $\sqrt{3}$ = 1.73)

Solve the following pair of equations using graphical method :
$3x-4y+3=0$ and $-2x+5y=9$

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 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)

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)