Class 10 Maths Standard

Very Short Answer practice across CBSE Class 10 Maths Standard chapters.

Practice coverage:155 published questions across 6 formats.

ChapterTopic

Base

For $x^{2} - 6 x + 9 = 0$ , what is the value of the discriminant?

Answer

A. 0

Quick solution

Here $a = 1$ , $b = - 6$ , $c = 9$ . So $D = b^{2} - 4 a c = 36 - 36 = 0$ .

FAQ

What does $D = 0$ mean?

$D = 0$ means the quadratic equation has two equal real roots.

Base

Write the prime factorisation of $180$ .

Answer

$2^{2} \times 3^{2} \times 5$

Quick solution

$180 = 18 \times 10 = (2 \times 3^{2}) (2 \times 5) = 2^{2} \times 3^{2} \times 5$ .

FAQ

What is prime factorisation?

It expresses a number as a product of prime numbers.

Base

Is $3 + 5$ rational or irrational?

Answer

Irrational

Quick solution

$3$ is rational and $5$ is irrational. The sum of a non-zero rational number and an irrational number is irrational.

FAQ

Can a rational number plus an irrational number be rational?

No. The sum is irrational.

Base

Find the sum of the zeroes of $2 x^{2} - 7 x + 3$ .

Answer

$\frac{7}{2}$

Quick solution

For $a x^{2} + b x + c$ , sum of zeroes is $- \frac{b}{a}$ . Here it is $- \frac{- 7}{2} = \frac{7}{2}$ .

FAQ

What is the sum of zeroes of $ax^2+bx+c$?

It is $- b / a$ .

Base

If one zero of $x^{2} - 5 x + k$ is $2$ , find $k$ .

Answer

$6$

Quick solution

Put $x = 2$ : $2^{2} - 5 (2) + k = 0$ . Thus $4 - 10 + k = 0$ , so $k = 6$ .

FAQ

How do you use a known zero to find an unknown coefficient?

Substitute the zero into the polynomial and set the result equal to zero.

Base

How many solutions does $2 x + 3 y = 6$ and $4 x + 6 y = 12$ have?

Answer

Infinitely many

Quick solution

The second equation is twice the first, so both represent the same line and have infinitely many common points.

FAQ

When do two linear equations have infinitely many solutions?

When all corresponding coefficients, including constants, are proportional.

Base

Solve $x + y = 9$ and $x - y = 3$ .

Answer

$x = 6, y = 3$

Quick solution

Add the equations: $2 x = 12$ , so $x = 6$ . Substituting in $x + y = 9$ gives $y = 3$ .

FAQ

Which method is quick when signs of one variable are opposite?

Adding the equations eliminates that variable.

Base

Find the roots of $x^{2} - 7 x + 12 = 0$ .

Answer

$3$ and $4$

Quick solution

$x^{2} - 7 x + 12 = (x - 3) (x - 4)$ . Therefore $x = 3$ or $x = 4$ .

FAQ

How can a quadratic be solved by factorisation?

Factor it into two linear factors and set each factor equal to zero.

Base

Find the common difference of $7, 11, 15, 19, \dots$ .

Answer

$4$

Quick solution

Subtract consecutive terms: $11 - 7 = 4$ and $15 - 11 = 4$ .

FAQ

How do you find the common difference of an AP?

Subtract any term from the next term.

Base

Find the $10$ th term of the A.P. $3, 8, 13, \dots$ .

Answer

$48$

Quick solution

Here $a = 3$ , $d = 5$ . $a_{10} = 3 + (10 - 1) 5 = 48$ .

FAQ

What is the nth-term formula of an AP?

$a_{n} = a + (n - 1) d$ .

Base

In $△ A B C$ , $D E ∥ B C$ , $A D = 3$ cm, $D B = 6$ cm and $A E = 4$ cm. Find $E C$ .

Answer

$8$ cm

Quick solution

$A B = 9$ . By BPT, $\frac{A D}{A B} = \frac{A E}{A C}$ , so $\frac{3}{9} = \frac{4}{4 + E C}$ . Hence $E C = 8$ cm.

FAQ

What does the Basic Proportionality Theorem state?

A line parallel to one side of a triangle divides the other two sides proportionally.

Base

Two similar triangles have corresponding sides $4$ cm and $10$ cm. Find their ratio in simplest form.

Answer

$2 : 5$

Quick solution

The ratio is $4 : 10$ . Divide both terms by $2$ to get $2 : 5$ .

FAQ

How are corresponding sides of similar triangles related?

Their ratios are equal.

Base

Find the distance between $(0, 0)$ and $(6, 8)$ .

Answer

$10$ units

Quick solution

Distance $= (6 - 0)^{2} + (8 - 0)^{2} = 36 + 64 = 10$ units.

FAQ

What formula gives the distance between two points?

$(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}$ .

Base

Find the midpoint of the line segment joining $(2, 4)$ and $(8, 10)$ .

Answer

$(5, 7)$

Quick solution

Midpoint $= (\frac{2 + 8}{2}, \frac{4 + 10}{2}) = (5, 7)$ .

FAQ

What is the midpoint formula?

$((x_{1} + x_{2}) /2, (y_{1} + y_{2}) /2)$ .

Base

If $sin θ = \frac{3}{5}$ for an acute angle $θ$ , find $cos θ$ .

Answer

$\frac{4}{5}$

Quick solution

$sin^{2} θ + cos^{2} θ = 1$ . Thus $cos^{2} θ = 1 - \frac{9}{25} = \frac{16}{25}$ , so $cos θ = \frac{4}{5}$ .

FAQ

Which identity relates sine and cosine?

$sin^{2} θ + cos^{2} θ = 1$ .

Base

Evaluate $sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ}$ .

Answer

$1$

Quick solution

The identity $sin^{2} θ + cos^{2} θ = 1$ applies directly.

FAQ

What is $\sin^2\theta+\cos^2\theta$ equal to?

It is always $1$ .

Base

A pole casts a $10$ m shadow when the sun's angle of elevation is $4 5^{\circ}$ . Find the height of the pole.

Answer

$10$ m

Quick solution

$tan 4 5^{\circ} = \frac{h}{10} = 1$ , so $h = 10$ m.

FAQ

Which trigonometric ratio relates height and shadow?

Tangent equals perpendicular height divided by base distance.

Base

A person stands $20$ m from a building. The angle of elevation to its top is $3 0^{\circ}$ . Write the building height in exact form.

Answer

$\frac{20 3}{3}$ m

Quick solution

$tan 3 0^{\circ} = \frac{h}{20} = \frac{1}{3}$ . Thus $h = \frac{20}{3} = \frac{20 3}{3}$ m.

FAQ

What is $\tan30^\circ$?

$tan 3 0^{\circ} = 1/ 3$ .

Base

What is the angle between a tangent and the radius at the point of contact?

Answer

$9 0^{\circ}$

Quick solution

A tangent to a circle is perpendicular to the radius drawn to the point of contact.

FAQ

How is a tangent related to the radius at the contact point?

They are perpendicular.

Base

From an external point $P$ , tangents $P A$ and $P B$ touch a circle. If $P A = 7$ cm, find $P B$ .

Answer

$7$ cm

Quick solution

Tangents drawn from the same external point to a circle are equal, so $P B = P A = 7$ cm.

FAQ

Are two tangents from the same external point equal?

Yes, their lengths are equal.

Base

Find the area of a $9 0^{\circ}$ sector of a circle of radius $7$ cm. Use $π = \frac{22}{7}$ .

Answer

$38.5$ cm $^{2}$

Quick solution

Area $= \frac{90}{360} \times \frac{22}{7} \times 7^{2} = \frac{1}{4} \times 154 = 38.5$ cm $^{2}$ .

FAQ

What fraction of a circle is a $90^\circ$ sector?

One-fourth.

Base

Find the length of a $6 0^{\circ}$ arc of a circle of radius $21$ cm. Use $π = \frac{22}{7}$ .

Answer

$22$ cm

Quick solution

Arc length $= \frac{60}{360} \times 2 π r = \frac{1}{6} \times 2 \times \frac{22}{7} \times 21 = 22$ cm.

FAQ

What is the arc-length formula?

$\frac{θ}{36 0 ^{\circ}} \times 2 π r$ .

Base

A hemisphere of radius $3$ cm is attached to a cylinder of radius $3$ cm and height $5$ cm. Find the total volume in terms of $π$ .

Answer

$63 π$ cm $^{3}$

Quick solution

Cylinder volume $= π (3)^{2} (5) = 45 π$ . Hemisphere volume $= \frac{2}{3} π (3)^{3} = 18 π$ . Total $= 63 π$ cm $^{3}$ .

FAQ

What is the volume of a hemisphere?

$\frac{2}{3} π r^{3}$ .

Base

A cone of radius $3$ cm and height $4$ cm is attached to a cylinder of the same radius and height $10$ cm. Find the total volume in terms of $π$ .

Answer

$102 π$ cm $^{3}$

Quick solution

Cylinder volume $= π (3)^{2} (10) = 90 π$ . Cone volume $= \frac{1}{3} π (3)^{2} (4) = 12 π$ . Total $= 102 π$ cm $^{3}$ .

FAQ

What is the volume of a cone?

$\frac{1}{3} π r^{2} h$ .

Base

Find the class mark of the interval $20$ - $30$ .

Answer

$25$

Quick solution

Class mark $= \frac{20 + 30}{2} = 25$ .

FAQ

How is class mark calculated?

Add the upper and lower class limits and divide by two.

Base

In a grouped frequency table, the total frequency is $30$ . Find $N /2$ , used to locate the median class.

Answer

$15$

Quick solution

Here $N = 30$ , so $N /2 = 15$ .

FAQ

Why is $N/2$ used in grouped-data median?

It helps locate the median class through cumulative frequency.

Base

A fair die is rolled once. Find the probability of obtaining a prime number.

Answer

$\frac{1}{2}$

Quick solution

Prime outcomes are $2, 3, 5$ : three favourable outcomes out of six. Probability $= \frac{3}{6} = \frac{1}{2}$ .

FAQ

Which prime numbers appear on a die?

$2, 3,$ and $5$ .

Base

A bag contains $3$ red and $2$ blue balls. One ball is drawn at random. Find the probability that it is blue.

Answer

$\frac{2}{5}$

Quick solution

There are $5$ balls in total and $2$ blue balls. Probability $= \frac{2}{5}$ .

FAQ

What is the basic probability formula?

Probability equals favourable outcomes divided by total equally likely outcomes.

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Class 10 Maths Standard

Very Short Answer practice across CBSE Class 10 Maths Standard chapters.

Practice coverage:155 published questions across 6 formats.

ChapterTopic

Class 10 Maths Standard

For x2−6x+9=0, what is the value of the discriminant?

Write the prime factorisation of 180.

Is 3+5​ rational or irrational?

Find the sum of the zeroes of 2x2−7x+3.

If one zero of x2−5x+k is 2, find k.

How many solutions does 2x+3y=6 and 4x+6y=12 have?

Solve x+y=9 and x−y=3.

Find the roots of x2−7x+12=0.

Find the common difference of 7,11,15,19,….

Find the 10th term of the A.P. 3,8,13,….

In △ABC, DE∥BC, AD=3 cm, DB=6 cm and AE=4 cm. Find EC.

Two similar triangles have corresponding sides 4 cm and 10 cm. Find their ratio in simplest form.

Find the distance between (0,0) and (6,8).

Find the midpoint of the line segment joining (2,4) and (8,10).

If sinθ=53​ for an acute angle θ, find cosθ.

Evaluate sin230∘+cos230∘.

A pole casts a 10 m shadow when the sun's angle of elevation is 45∘. Find the height of the pole.

A person stands 20 m from a building. The angle of elevation to its top is 30∘. Write the building height in exact form.

What is the angle between a tangent and the radius at the point of contact?

From an external point P, tangents PA and PB touch a circle. If PA=7 cm, find PB.

Find the area of a 90∘ sector of a circle of radius 7 cm. Use π=722​.

Find the length of a 60∘ arc of a circle of radius 21 cm. Use π=722​.

A hemisphere of radius 3 cm is attached to a cylinder of radius 3 cm and height 5 cm. Find the total volume in terms of π.

A cone of radius 3 cm and height 4 cm is attached to a cylinder of the same radius and height 10 cm. Find the total volume in terms of π.

Find the class mark of the interval 20-30.

In a grouped frequency table, the total frequency is 30. Find N/2, used to locate the median class.

A fair die is rolled once. Find the probability of obtaining a prime number.

A bag contains 3 red and 2 blue balls. One ball is drawn at random. Find the probability that it is blue.

Class 10 Maths Standard

For x2−6x+9=0, what is the value of the discriminant?

Write the prime factorisation of 180.

Is 3+5​ rational or irrational?

Find the sum of the zeroes of 2x2−7x+3.

If one zero of x2−5x+k is 2, find k.

How many solutions does 2x+3y=6 and 4x+6y=12 have?

Solve x+y=9 and x−y=3.

Find the roots of x2−7x+12=0.

Find the common difference of 7,11,15,19,….

Find the 10th term of the A.P. 3,8,13,….

In △ABC, DE∥BC, AD=3 cm, DB=6 cm and AE=4 cm. Find EC.

Two similar triangles have corresponding sides 4 cm and 10 cm. Find their ratio in simplest form.

Find the distance between (0,0) and (6,8).

Find the midpoint of the line segment joining (2,4) and (8,10).

If sinθ=53​ for an acute angle θ, find cosθ.

Evaluate sin230∘+cos230∘.

A pole casts a 10 m shadow when the sun's angle of elevation is 45∘. Find the height of the pole.

A person stands 20 m from a building. The angle of elevation to its top is 30∘. Write the building height in exact form.

What is the angle between a tangent and the radius at the point of contact?

From an external point P, tangents PA and PB touch a circle. If PA=7 cm, find PB.

Find the area of a 90∘ sector of a circle of radius 7 cm. Use π=722​.

Find the length of a 60∘ arc of a circle of radius 21 cm. Use π=722​.

A hemisphere of radius 3 cm is attached to a cylinder of radius 3 cm and height 5 cm. Find the total volume in terms of π.

A cone of radius 3 cm and height 4 cm is attached to a cylinder of the same radius and height 10 cm. Find the total volume in terms of π.

Find the class mark of the interval 20-30.

In a grouped frequency table, the total frequency is 30. Find N/2, used to locate the median class.

A fair die is rolled once. Find the probability of obtaining a prime number.

A bag contains 3 red and 2 blue balls. One ball is drawn at random. Find the probability that it is blue.

For $x^{2} - 6 x + 9 = 0$ , what is the value of the discriminant?

Write the prime factorisation of $180$ .

Is $3 + 5$ rational or irrational?

Find the sum of the zeroes of $2 x^{2} - 7 x + 3$ .

If one zero of $x^{2} - 5 x + k$ is $2$ , find $k$ .

How many solutions does $2 x + 3 y = 6$ and $4 x + 6 y = 12$ have?

Solve $x + y = 9$ and $x - y = 3$ .

Find the roots of $x^{2} - 7 x + 12 = 0$ .

Find the common difference of $7, 11, 15, 19, \dots$ .

Find the $10$ th term of the A.P. $3, 8, 13, \dots$ .

In $△ A B C$ , $D E ∥ B C$ , $A D = 3$ cm, $D B = 6$ cm and $A E = 4$ cm. Find $E C$ .

Two similar triangles have corresponding sides $4$ cm and $10$ cm. Find their ratio in simplest form.

Find the distance between $(0, 0)$ and $(6, 8)$ .

Find the midpoint of the line segment joining $(2, 4)$ and $(8, 10)$ .

If $sin θ = \frac{3}{5}$ for an acute angle $θ$ , find $cos θ$ .

Evaluate $sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ}$ .

A pole casts a $10$ m shadow when the sun's angle of elevation is $4 5^{\circ}$ . Find the height of the pole.

A person stands $20$ m from a building. The angle of elevation to its top is $3 0^{\circ}$ . Write the building height in exact form.

From an external point $P$ , tangents $P A$ and $P B$ touch a circle. If $P A = 7$ cm, find $P B$ .

Find the area of a $9 0^{\circ}$ sector of a circle of radius $7$ cm. Use $π = \frac{22}{7}$ .

Find the length of a $6 0^{\circ}$ arc of a circle of radius $21$ cm. Use $π = \frac{22}{7}$ .

A hemisphere of radius $3$ cm is attached to a cylinder of radius $3$ cm and height $5$ cm. Find the total volume in terms of $π$ .

A cone of radius $3$ cm and height $4$ cm is attached to a cylinder of the same radius and height $10$ cm. Find the total volume in terms of $π$ .

Find the class mark of the interval $20$ - $30$ .

In a grouped frequency table, the total frequency is $30$ . Find $N /2$ , used to locate the median class.

A bag contains $3$ red and $2$ blue balls. One ball is drawn at random. Find the probability that it is blue.

For $x^{2} - 6 x + 9 = 0$ , what is the value of the discriminant?

Write the prime factorisation of $180$ .

Is $3 + 5$ rational or irrational?

Find the sum of the zeroes of $2 x^{2} - 7 x + 3$ .

If one zero of $x^{2} - 5 x + k$ is $2$ , find $k$ .

How many solutions does $2 x + 3 y = 6$ and $4 x + 6 y = 12$ have?

Solve $x + y = 9$ and $x - y = 3$ .

Find the roots of $x^{2} - 7 x + 12 = 0$ .

Find the common difference of $7, 11, 15, 19, \dots$ .

Find the $10$ th term of the A.P. $3, 8, 13, \dots$ .

In $△ A B C$ , $D E ∥ B C$ , $A D = 3$ cm, $D B = 6$ cm and $A E = 4$ cm. Find $E C$ .

Two similar triangles have corresponding sides $4$ cm and $10$ cm. Find their ratio in simplest form.

Find the distance between $(0, 0)$ and $(6, 8)$ .

Find the midpoint of the line segment joining $(2, 4)$ and $(8, 10)$ .

If $sin θ = \frac{3}{5}$ for an acute angle $θ$ , find $cos θ$ .

Evaluate $sin^{2} 3 0^{\circ} + cos^{2} 3 0^{\circ}$ .

A pole casts a $10$ m shadow when the sun's angle of elevation is $4 5^{\circ}$ . Find the height of the pole.

A person stands $20$ m from a building. The angle of elevation to its top is $3 0^{\circ}$ . Write the building height in exact form.

From an external point $P$ , tangents $P A$ and $P B$ touch a circle. If $P A = 7$ cm, find $P B$ .

Find the area of a $9 0^{\circ}$ sector of a circle of radius $7$ cm. Use $π = \frac{22}{7}$ .

Find the length of a $6 0^{\circ}$ arc of a circle of radius $21$ cm. Use $π = \frac{22}{7}$ .

A hemisphere of radius $3$ cm is attached to a cylinder of radius $3$ cm and height $5$ cm. Find the total volume in terms of $π$ .

A cone of radius $3$ cm and height $4$ cm is attached to a cylinder of the same radius and height $10$ cm. Find the total volume in terms of $π$ .

Find the class mark of the interval $20$ - $30$ .

In a grouped frequency table, the total frequency is $30$ . Find $N /2$ , used to locate the median class.

A bag contains $3$ red and $2$ blue balls. One ball is drawn at random. Find the probability that it is blue.