CBSE Class 10 Mathematics Standard Set 1 - (30/1/1) Question Paper 2026 with Solution PDF

The HCF of 960 and 432 is :

• (a) 48
• (b) 54
• (c) 72
• (d) 36

The natural number 2 is :

• (a) a prime number
• (b) a composite number
• (c) prime as well as composite
• (d) neither prime nor composite

For any natural number n, \(6^n\) ends with the digit :

• (a) 0
• (b) 6
• (c) 3
• (d) 2

The graph of y = f(x) is given.
The number of zeroes of f(x) is :

• (a) 0
• (b) 1
• (c) 2
• (d) 3

If a pair of linear equations in two variables is represented by two coincident lines, then the pair of equations has :

• (a) a unique solution
• (b) two solutions
• (c) no solution
• (d) an infinite number of solutions

The common difference of the AP : \(\sqrt{2}, 2\sqrt{2}, 3\sqrt{2}, 4\sqrt{2}, \dots\) is :

• (a) \(\sqrt{2}\)
• (b) 1
• (c) \(2\sqrt{2}\)
• (d) \(-\sqrt{2}\)

If \(\Delta ABC\) and \(\Delta DEF\) are similar such that \(2 AB = DE\) and \(BC = 8\) cm, then \(EF\) is equal to :

• (a) 4 cm
• (b) 8 cm
• (c) 12 cm
• (d) 16 cm

The mid-point of the line segment joining the points (5, -4) and (6, 4) lies on :

• (a) x-axis
• (b) y-axis
• (c) origin
• (d) neither x-axis nor y-axis

Given that \(\sin \theta = a/b\), then \(\cos \theta\) is equal to :

• (a) \(\frac{\sqrt{b^2 - a^2}}{b}\)
• (b) \(b/a\)
• (c) \(a/b\)
• (d) \(\frac{\sqrt{b^2 - a^2}}{a}\)

If \(\cos A = 1/2\), then the value of \(\sin^2 A + \cos^2 A\) is :

• (a) \(3/2\)
• (b) \(5/4\)
• (c) \(-1\)
• (d) \(1/2\)

A car is moving away from the base of a 30 m high tower. The angle of elevation of the top of the tower from the car at an instant, when the car is \(10\sqrt{3}\) m away from the base of the tower, is :

• (a) 30°
• (b) 45°
• (c) 90°
• (d) 60°

If TP and TQ are two tangents to a circle with centre O from an external point T so that \(\angle POQ = 120^\circ\), then \(\angle PTQ\) is equal to :

• (a) 60°
• (b) 70°
• (c) 80°
• (d) 90°

In the given figure, PA is a tangent from an external point P to a circle with centre O. If \(\angle POB = 125^\circ\), then \(\angle APO\) is equal to :

• (a) 25°
• (b) 65°
• (c) 90°
• (d) 35°

The length of the arc of the sector of a circle with radius 21 cm and of central angle 60°, is :

• (a) 22 cm
• (b) 44 cm
• (c) 88 cm
• (d) 11 cm

The hour hand of a clock is 7 cm long. The angle swept by it between 7:00 a.m. and 8:10 a.m. is :

• (a) \(\frac{35}{4}^\circ\)
• (b) \(\frac{35}{2}^\circ\)
• (c) 35°
• (d) 70°

The total surface area of a solid hemisphere of diameter ‘2d’ is :

• (a) \(3\pi d^2\)
• (b) \(2\pi d^2\)
• (c) \(\frac{1}{2}\pi d^2\)
• (d) \(\frac{3}{4}\pi d^2\)

If the mean and mode of a data are 12 and 21 respectively, then its median is :

• (a) 6
• (b) 13.5
• (c) 15
• (d) 14

A die is thrown once. Probability of getting a number other than 3 is :

• (a) \(\frac{1}{6}\)
• (b) \(\frac{3}{6}\)
• (c) \(\frac{5}{6}\)
• (d) 1

Assertion (A) : The probability that a leap year has 53 Mondays is \(\frac{2}{7}\).

Reason (R) : The probability that a non-leap year has 53 Mondays is \(\frac{5}{7}\).

Assertion (A) : The polynomial \(p(y) = y^2 + 4y + 3\) has two zeroes.

Reason (R) : A quadratic polynomial can have at most two zeroes.

If \(\alpha, \beta\) are the zeroes of the polynomial \(p(x) = x^2 - 3x - 1\), then find the value of \(\frac{1}{\alpha} + \frac{1}{\beta}\).

In \(\triangle ABC\), \(DE \parallel BC\). If \(AD = x\), \(DB = x - 2\), \(AE = x + 2\) and \(EC = x - 1\), then find the value of \(x\).

In the figure given above, \(\triangle ABC \sim \triangle XYZ\), then find the values of \(x\) and \(y\).

The coordinates of the centre of a circle are \((x - 7, 2x)\). Find the value(s) of ‘x’, if the circle passes through the point \((-9, 11)\) and has radius \(5\sqrt{2}\) units.

If \(\tan \theta = \frac{24}{7}\), then find the value of \(\sin \theta + \cos \theta\).

If \(\cot \theta = \frac{7}{8}\), then find the value of \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\).

Two concentric circles are of radii 5 cm and 4 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Prove that \(\sqrt{3}\) is an irrational number.

Find the ratio in which the x-axis divides the line segment joining the points \((-6, 5)\) and \((-4, -1)\). Also, find the point of intersection.

If \(x = h + a \cos \theta\), \(y = k + b \sin \theta\), then prove that : \(\left( \frac{x - h}{a} \right)^2 + \left( \frac{y - k}{b} \right)^2 = 1\)

Prove that : \(\frac{\tan A}{1 + \sec A} - \frac{\tan A}{1 - \sec A} = 2 \csc A\)

In the given figure, \(\triangle ABC\) is a right triangle in which \(\angle B = 90^\circ\), \(AB = 4\) cm and \(BC = 3\) cm. Find the radius of the circle inscribed in the triangle ABC.

Prove that : \(PM = \frac{1}{2} (PQ + QR + PR)\)

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid. (Use \(\pi = \frac{22}{7}\))

Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :
(i) same number appears on both the dice?
(ii) different number appears on both the dice?

Determine graphically, the coordinates of vertices of a triangle whose equations are \(2x - 3y + 6 = 0\); \(2x + 3y - 18 = 0\) and \(x = 0\). Also, find the area of this triangle.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

The sum of areas of two squares is 640 m\(^2\). If the difference in perimeters is 64 m, find the sides.

State and prove Basic Proportionality Theorem.