The CBSE 2026 Class 10 Mathematics Standard (Set 1- 30/2/1) Question Paper with Solutions PDF is now available for students to evaluate their performance. Conducted from 10:30 AM to 1:30 PM, the exam was rated moderate in difficulty, featuring a balanced mix of MCQs, case-based studies, and theoretical problems.
Students who focused on NCERT fundamentals and high-weightage units like Algebra and Trigonometry found the paper manageable. This solved PDF serves as a vital resource for understanding the marking scheme and mastering the 2025-26 exam pattern.
CBSE 2026 Class 10 Mathematics Standard Question Paper with Solutions PDF- (Set 1- 30/2/1)
| CBSE Class 10 Mathematics Standard Question Paper 2026 (Set 1- 30/2/1) | Download | Check Solutions |
The LCM of 960 and 240 is :
The natural number 1 is :
For any natural number n, \( 5^n \) ends with the digit :
The graph of \( y = f(x) \) is given. The number of distinct zeroes of \( y = f(x) \) is :
If \( \alpha \) and \( \beta \) are two zeroes of a polynomial \( f(x) = px^2 - 2x + 3p \) and \( \alpha + \beta = \alpha\beta \), then value of p is :
If the pair of linear equations : \( a_1x + b_1y + c_1 = 0 \) and \( a_2x + b_2y + c_2 = 0 \) is consistent and dependent, then
Which of the following sequence is not an A.P. ?
In triangles ABC and PQR, \( \angle A = \angle Q \) and \( \angle B = \angle R \), then \( AB : AC \) is equal to :
The distance of the point \( A(4a, 3a) \) from x-axis is :
If \( \cos A = \frac{4}{5} \), then the value of \( \tan A \) is :
If \( 2 \sin A = 1 \), then the value of \( \tan A + \cot A \) is :
From a point on the ground, which is 60 m away from the foot of a vertical tower, the angle of elevation of the top of the tower is found to be \( 45^\circ \). The height (in metres) of the tower is :
In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle OAB = 15^\circ \), then \( \angle APB \) equals :
In the given figure, PA and PB are tangents to a circle centred at O. If \( \angle AOB = 130^\circ \), then \( \angle APB \) is equal to :
Area of a segment of a circle of radius 'r' and central angle \( 60^\circ \) is :
A hemispherical bowl is made of steel of thickness 1 cm. The outer radius of the bowl is 6 cm. The volume of steel used (in \( cm^3 \)) is :
The mean and median of a frequency distribution are 43 and 43.4 respectively. The mode of the distribution is :
The probability for a randomly selected number out of 1, 2, 3, 4, ..., 25 to be a composite number is :
Assertion (A) : The surface area of the cuboid formed by joining two cubes of sides 4 cm each, end-to-end, is \( 160 cm^2 \).
Reason (R) : The surface area of a cuboid of dimensions \( l \times b \times h \) is \( (lb + bh + hl) \).
Assertion (A) : The mean of first 'n' natural numbers is \( \frac{n - 1}{2} \).
Reason (R) : The sum of first 'n' natural numbers is \( \frac{n(n + 1)}{2} \).
If \( \alpha, \beta \) are the zeroes of the quadratic polynomial \( px^2 + qx + r \), then find the value of \( \alpha^3\beta + \beta^3\alpha \).
In the given figure, \( \triangle AHK \sim \triangle ABC \). If \( AK = 10 cm \), \( BC = 3.5 cm \) and \( HK = 7 cm \), find the length of \( AC \).
In the given figure, \( XY \parallel QR \), \( \frac{PQ}{XQ} = \frac{7}{3} \) and \( PR = 6.3 cm \). Find the length of \( YR \).
If the points \( A(4, 5), B(m, 6), C(4, 3) \) and \( D(1, n) \) taken in this order are the vertices of a parallelogram ABCD, then find the values of \( m \) and \( n \).
If \( \tan \theta + \frac{1}{\tan \theta} = 2 \), find the value of \( \tan^2 \theta + \frac{1}{\tan^2 \theta} \).
Prove that : \( \sqrt{\frac{1 - \sin \theta}{1 + \sin \theta}} = \sec \theta - \tan \theta \)
In the given figure, O is the centre of the circle. PQ and PR are tangents. Show that the quadrilateral PQOR is cyclic.
Prove that \( \sqrt{5} \) is an irrational number.
Find the coordinates of the points of trisection of the line segment joining the points \( A(-1, 4) \) and \( B(-3, -2) \).
Prove that : \( \frac{\sec^3 \theta}{\sec^2 \theta - 1} + \frac{cosec^3 \theta}{cosec^2 \theta - 1} = \sec \theta \cdot cosec \theta (\sec \theta + cosec \theta) \)
If \( \frac{\sec \alpha}{cosec \beta} = p \) and \( \frac{\tan \alpha}{cosec \beta} = q \), then prove that \( (p^2 - q^2) \sec^2 \alpha = p^2 \).
Prove that the lengths of tangents drawn from an external point to a circle are equal.
Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that \( \angle PTQ = 2 \angle OPQ \).
Find the area of the sector of a circle of radius 42 cm and of central angle \( 30^\circ \). Also, find the area of the corresponding major sector. [Use \( \pi = \frac{22}{7} \)]
Two dice are thrown at the same time. Determine the probability that the sum of the numbers on the two dice is 5.
Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 3.
Aarush bought 2 pencils and 3 chocolates for Rs 11 and Tanish bought 1 pencil and 2 chocolates for Rs 7 from the same shop. Represent this situation in the form of a pair of linear equations. Find the price of 1 pencil and 1 chocolate, graphically.
A person on a tour has Rs 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs 70. Find the original duration of the tour.
The area of a right-angled triangle is \( 600 cm^2 \). If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.
Prove that if a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio.
As shown in the given figure, a girl of height 90 cm is walking away from the base of a lamp post at a speed of 1.2 m/s. If the lamp is 3.6 m above the ground, find the length of her shadow after 4 seconds.
An SBI health insurance agent found the following data for distribution of ages of 100 policy holders. Find the modal age and median age of the policy holders.
Case Study - 1
Your elder brother wants to buy a car and plans to take a loan from a bank for his car. He repays his total loan of 1,18,000 by paying every month, starting with the first instalment of1,000 and he increases the instalment by 100 every month.
36(i).
Find the amount paid by him in the \( 30^{th} \) instalment.
If the total number of instalments is 40, what is the amount paid in the last instalment ?
What amount does he still have to pay after the \( 30^{th} \) instalment ?
Find the ratio of the tenth instalment to the last instalment.
Case Study - 2
Tejas is standing at the top of a building and observes a car at an angle of depression of 30° as it approaches the base of the building at a uniform speed. 6 seconds later, the angle of depression increases to 60", and at that moment, the car is 25 m away from the building.
37(i).
What is the height of the building ?
What is the distance between the two positions of the car ?
What would be the total time taken by the car to reach the foot of the building from the starting point ?
What is the distance of the observer from the car when it makes an angle of \( 60^\circ \) ?
Case Study - 3
On a Sunday your parents took you to a fair. You could see lot of toys displayed and you wanted them to buy a Rubik's cube and a strawberry ice-cream for you.
38(i).
Find the length of the diagonal of Rubik's cube if each edge measures 6 cm.
Find the volume of Rubik's cube if the length of the edge is 7 cm.
What is the curved surface area of hemisphere (ice-cream) if the base radius is 7 cm ?
If two cubes of edges 4 cm are joined end-to-end, then find the surface area of the resulting cuboid.
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