The CBSE 2026 Class 10 Mathematics Standard (Set 3- 30/5/3) 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 3- 30/5/3)
| CBSE Class 10 Mathematics Standard Question Paper 2026 (Set 3- 30/5/3) | Download | Check Solutions |
A conical cavity of maximum volume is carved out from a wooden solid hemisphere of radius 10 cm. Curved surface area of the cavity carved out is (use \(\pi = 3.14\))
If \(a_n\) represents \(n^{th}\) term of the A.P. \(-\frac{15}{4}, -\frac{10}{4}, -\frac{5}{4}, \dots\) then value of \(a_{16} - a_{12}\) is
Meena calculates that the probability of her winning the first prize in a lottery is \(0.08\). If total \(800\) tickets were sold, the number of tickets bought by her, is
A camping tent in hemispherical shape of radius \(1.4\) m, has a door opening of area \(0.50\) \(m^2\). Outer surface area of the tent is
PQ is tangent to a circle with centre O. If \(OQ = a\), \(OP = a + 2\) and \(PQ = 2b\), then relation between \(a\) and \(b\) is
Simplest form of \(\frac{\sec A}{\sqrt{\sec^2 A - 1}}\) is
The line segment joining the points \(P(-4, -2)\) and \(Q(10, 4)\) is divided by y-axis in the ratio
A wire is attached from a point A on the ground to the top of a pole BC, making an angle of elevation as \(60^{\circ}\). If \(AB = 5\sqrt{3}\) m, then length of the wire is
In the given figure, \(AB \parallel EF\). If \(AB = 24\) cm, \(EF = 36\) cm and \(DA = 7\) cm, then \(AE\) equals
Devansh proved that \(\triangle ABC \sim \triangle PQR\) using SAS similarity criteria. If he found \(\angle C = \angle R\), then which of the following was proved true?
While calculating mean of a grouped frequency distribution, step deviation method was used \(u = \frac{x-a}{h}\). It was found that \(\bar{x} = 64\), \(h = 5\) and \(a = 62.5\). The value of \(\bar{u}\) is
For an acute angle \(\theta\), if \(\sin \theta = \frac{1}{9}\), then value of \(\frac{9 \csc \theta + 1}{9 \csc \theta - 1}\) is
Which of the following can not be the probability of an event?
The value of \(m\) for which the quadratic equation \(3x^2 - 7x + m = 0\) has real and equal roots, is
If the zeroes of a polynomial \(p(x)\) are \(-3\) and \(8\), then \(p(x)\) equals
The value of \(p\) for which roots of the quadratic equation \(x^{2} - px + 6 = 0\) are rational, is
An arc of length \(2.2\) cm subtends an angle \(\theta\) at the centre of the circle with radius \(2.8\) cm. The value of \(\theta\) is
Two dice are rolled together. The probability of getting an outcome \((x, y)\) where \(x > y\), is
Assertion (A) : H.C.F. \((36 m^{2}, 18 m) = 18 m\), where \(m\) is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
Assertion (A) : The system of linear equations \(3x - 5y + 7 = 0\) and \(-6x + 10y + 14 = 0\) is inconsistent.
Reason (R) : When two linear equations don't have unique solution, they always represent parallel lines.
In the given figure, point D divides the side BC of \(\triangle ABC\) in the ratio \(1 : 2\). Find length AD. (Given coordinates: \(A(1, 5), B(-2, 1), C(4, 2)\))
Evaluate : \(\frac{\sin^3 60^{\circ} - \tan 30^{\circ}}{\cos^2 45^{\circ}}\)
For acute angles A and B and \(A + 2B\) and \(2A + B\) are acute if \(\tan (A + 2B) = \sqrt{3}\) and \(\sin (2A + B) = \frac{1}{\sqrt{2}}\), then find the measures of angles A and B.
A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is \(3/5\), then find the number of yellow balls.
In the given figure, \(AB \parallel DE\) and \(AC \parallel DF\). Show that \(\triangle ABC \sim \triangle DEF\). If \(BC = 10\) cm, \(EB = CF = 5\) cm and \(AB = 7\) cm, then find the length DE.
Prove that \(14 - 2\sqrt{3}\) is an irrational number, given that \(\sqrt{3}\) is irrational.
A circle centered at (2, 1) passes through the points A(5, 6) and B(-3, K). Find the value(s) of K. Hence find length of chord AB.
Prove that the point P dividing the line segment joining the points A(-1, 7) and B(4, -3) in the ratio 3 : 2, lies on the line \(x - 3y = -1\). Also find length of PA and PB.
Use graphical method to solve the system of linear equations : \(x = -3\) and \(5x - 2y = -5\).
In an A.P., \(15^{th}\) term exceeds the \(8^{th}\) term by 21. If sum of first 10 terms is 55, then form the A.P.
The sum of first n terms of an A.P. is \(2n^{2} + 13n\). Find its \(n^{th}\) term and hence \(10^{th}\) term.
The dimensions of a window are 156 cm \(\times\) 216 cm. Arjun wants to put grill on the window creating complete squares of maximum size. Determine the side length of the square and hence find the number of squares formed.
Prove that :
\(\frac{\tan \theta}{1 - \cot \theta} + \frac{\cot \theta}{1 - \tan \theta} = 1 + \tan \theta + \cot \theta\).
A chord of a circle, of radius 14 cm, subtends an angle of \(60^{\circ}\) at the centre. Find the area of the smaller sector and perimeter of the smaller segment.
D is the mid-point of side BC of \(\triangle ABC\). CE and BF intersect at O, a point on AD. AD is produced to G such that \(OD = DG\). Prove that OBGC is a parallelogram.
In the same figure as 32(a), prove that \(EF \parallel BC\).
In the same figure as 32(a), prove that \(\triangle AEF \sim \triangle ABC\).
Through the mid-point Q of side CD of a parallelogram ABCD, the line AR is drawn which intersects BD at P and produced BC at R. Prove that \(AQ = QR\).
Using the conditions from 32(b), prove that \(AP = 2PQ\).
Using the conditions from 32(b), prove that \(PR = 2AP\).
The mean of the following distribution is 53. Find the missing frequency p.
\begin{tabular}{|l|c|c|c|c|c|}
\hline
Class Interval & 0-20 & 20-40 & 40-60 & 60-80 & 80-100
\hline
Frequency & 12 & 15 & p & 28 & 13
\hline
\end{tabular}
Hence, find mode of the distribution.
Compute median of the following data :
\begin{tabular}{|l|c|c|c|c|c|c|c|}
\hline
Mid-value & 115 & 125 & 135 & 145 & 155 & 165 & 175
\hline
Frequency & 12 & 15 & 20 & 16 & 10 & 16 & 11
\hline
\end{tabular}
PQ and PR are two tangents to a circle with centre O and radius 5 cm. AB is another tangent to the circle at C which lies on OP. If \(OP = 13\) cm, then find the length AB and PA.
Two water taps together can fill a tank in \(8\frac{8}{9}\) hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
Write a relation between \(d\) (the height of window) and \(y\).
Determine the value of \(h\).
Determine height of the water tank.
Find the value of \(x\) and height of the window above ground level.
Write the co-ordinates of point \(A\).
Find the span of the arch.
Write the zeroes of the polynomial using diagram and verify the relationship between sum of zeroes and polynomials.
Find the values of \(p(x)\) at \(x = 100\) and \(x = -100\). Are they same ?
Find the surface area of the bulb.
What could be the maximum diameter of the bulb if at least 1 cm space is left from each side ?
Find the area of the fabric used if there is a fold of 2 cm on top and bottom edges.
Find the space available inside the lamp.
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