Class 10 Mathematics • Sample Paper Set 3

The probability of getting a sum of at least 10 when two dice are thrown simultaneously is:

If the mean of the first $n$ natural numbers is 15, then the value of $n$ is:

The mode of a frequency distribution can be determined graphically from:

If $P(E) = 0.05$, what is the probability of 'not E'?

The distance between the points $(a \cos \theta + b \sin \theta, 0)$ and $(0, a \sin \theta - b \cos \theta)$ is:

If $\tan A = \cot B$, then the value of $(A + B)$ is:

The decimal expansion of the rational number $\frac{14587}{1250}$ will terminate after:

If the circumference of a circle and the perimeter of a square are equal, then:

The roots of the equation $x^2 + 7x + 10 = 0$ are:

In a $\triangle ABC$, right angled at B, if $\tan A = \frac{1}{\sqrt{3}}$, then the value of $\sin A \cos C + \cos A \sin C$ is:

If the lines $3x + 2ky = 2$ and $2x + 5y + 1 = 0$ are parallel, then the value of $k$ is:

The value of $c$ for which the pair of equations $cx - y = 2$ and $6x - 2y = 3$ will have infinitely many solutions is:

The area of a circle that can be inscribed in a square of side 6 cm is:

The sum of the first 20 odd natural numbers is:

If the radius of a sphere is doubled, its volume becomes ____ times the original volume:

The point of intersection of the x-axis and the line $2x + 3y = 6$ is:

Which of the following cannot be the probability of an event?

The median class of the following distribution is:

Class	0-10	10-20	20-30	30-40	40-50
Freq	5	8	12	15	10

Two dice are thrown at the same time. Find the probability of getting different numbers on the dice.

Find the mode of the following distribution:

Marks	0-10	10-20	20-30	30-40	40-50
Students	4	6	10	8	2

In the given figure, $DE \parallel BC$. If $AD = 1.5$ cm, $DB = 3$ cm and $AE = 1$ cm, find $EC$.

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.

Find the value of $k$ if the points $A(2, 3)$, $B(4, k)$ and $C(6, -3)$ are collinear.

A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, determine the number of blue balls in the bag.

The mean of the following distribution is 53. Find the missing frequency $p$:

Class	0-20	20-40	40-60	60-80	80-100
Freq	12	15	32	$p$	13

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

If $\tan(A+B) = \sqrt{3}$ and $\tan(A-B) = \frac{1}{\sqrt{3}}$; $0^\circ < A+B \le 90^\circ$; $A > B$, find $A$ and $B$.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the corresponding: (i) minor segment (ii) major sector. (Use $\pi = 3.14$)

Solve for $x$ and $y$: $\frac{2}{x} + \frac{3}{y} = 13$ and $\frac{5}{x} - \frac{4}{y} = -2$.

The median of the following data is 525. Find the values of $x$ and $y$, if the total frequency is 100.

A box contains cards bearing numbers from 6 to 70. If one card is drawn at random from the box, find the probability that it bears: (i) a one-digit number, (ii) a number divisible by 5, (iii) an odd number less than 30, (iv) a composite number between 50 and 70.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder.

Case Study: Probability (Cards)
Two friends, Rahul and Ravi, are playing a game with a standard deck of 52 playing cards. Rahul draws a card at random.

Case Study: Statistics (Sports)
A coach is analyzing the performance of a batsman in 10 matches. The runs scored are: 12, 25, 38, 56, 12, 45, 78, 12, 34, 60.

Case Study: Trigonometry
A lighthouse is a tower, building, or other type of structure designed to emit light from a system of lamps and lenses and to serve as a navigational aid. A guard on top of a 100m high lighthouse observes a ship coming towards it. The angle of depression changes from $30^\circ$ to $45^\circ$.