Class 10 Maths Basic

Assertion Reason practice across CBSE Class 10 Maths Basic chapters.

Practice coverage:155 published questions across 6 formats.

ChapterTopic

Base

Assertion: $\frac{13}{40}$ has a terminating decimal expansion. Reason: After simplification, the denominator $40 = 2^{3} \times 5$ has no prime factors other than $2$ and $5$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

When does a rational number have a terminating decimal expansion?

After simplification, its denominator must have only the prime factors $2$ and/or $5$ .

Base

Assertion: If one zero of $x^{2} - 5 x + 6$ is $2$ , the other zero is $3$ . Reason: For $a x^{2} + b x + c$ , the sum of zeroes is $- \frac{b}{a}$ and their product is $\frac{c}{a}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What are the relations between zeroes and coefficients of a quadratic polynomial?

For $a x^{2} + b x + c$ , sum of zeroes is $- b / a$ and product is $c / a$ .

Base

Assertion: The pair $2 x + 3 y = 6$ and $4 x + 6 y = 15$ has no solution. Reason: If $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What condition gives no solution for two linear equations?

No solution occurs when $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .

Base

Assertion: The equation $x^{2} - 4 x + 4 = 0$ has equal roots. Reason: Its discriminant is $b^{2} - 4 a c = 0$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What discriminant gives equal roots?

A quadratic equation has equal real roots when its discriminant is zero.

Base

Assertion: The $21$ st term of the A.P. $3, 7, 11, \dots$ is $83$ . Reason: The $n$ th term of an A.P. is $a_{n} = a + (n - 1) d$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the formula for the nth term of an AP?

The nth term is $a_{n} = a + (n - 1) d$ .

Base

Assertion: If two angles of one triangle are respectively equal to two angles of another triangle, the triangles are similar. Reason: This is the AA similarity criterion.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

Which similarity criterion uses two equal angles?

The AA similarity criterion uses two pairs of equal corresponding angles.

Base

Assertion: The distance of the point $(3, - 4)$ from the x-axis is $- 4$ units. Reason: The distance of a point $(x, y)$ from the x-axis is $∣ y ∣$ units.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

How do you find the distance of a point from the x-axis?

For $(x, y)$ , the distance from the x-axis is $∣ y ∣$ .

Base

Assertion: For an acute angle $θ$ , $sin^{2} θ + cos^{2} θ = 1$ . Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the fundamental trigonometric identity?

The fundamental identity is $sin^{2} θ + cos^{2} θ = 1$ .

Base

Assertion: When an observer looks upward at the top of a tower, the angle made by the line of sight with the horizontal is an angle of elevation. Reason: An angle of elevation is measured from the horizontal line upward to the line of sight.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

From which line is an angle of elevation measured?

It is measured from the horizontal line upward to the line of sight.

Base

Assertion: The lengths of two tangents drawn from an external point to a circle are equal. Reason: A tangent to a circle is perpendicular to the radius at the point of contact.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the theorem about tangents from an external point?

The two tangent segments drawn from the same external point to a circle are equal in length.

Base

Assertion: The area of a $9 0^{\circ}$ sector of a circle of radius $r$ is $\frac{π r ^{2}}{4}$ . Reason: The area of a sector of angle $θ$ is $\frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the formula for area of a sector?

Area of sector $= \frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Base

Assertion: The total surface area of a sphere of radius $r$ is $4 π r^{2}$ . Reason: The curved surface area of a hemisphere of the same radius is $2 π r^{2}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the total surface area of a sphere?

The total surface area of a sphere of radius $r$ is $4 π r^{2}$ .

Base

Assertion: The median of $3, 5, 7, 9, 11$ is $7$ . Reason: For an odd number of observations arranged in order, the median is the middle observation.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

How is the median found for an odd number of ordered observations?

It is the single middle observation.

Base

Assertion: The probability of getting an even number on a fair die is $\frac{1}{2}$ . Reason: A fair die has three even outcomes out of six equally likely outcomes.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the probability of an even number on a fair die?

There are three even outcomes out of six, so the probability is $1/2$ .

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Class 10 Maths Basic

Assertion Reason practice across CBSE Class 10 Maths Basic chapters.

Practice coverage:155 published questions across 6 formats.

ChapterTopic

Base

Assertion: $\frac{13}{40}$ has a terminating decimal expansion. Reason: After simplification, the denominator $40 = 2^{3} \times 5$ has no prime factors other than $2$ and $5$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

When does a rational number have a terminating decimal expansion?

After simplification, its denominator must have only the prime factors $2$ and/or $5$ .

Base

Assertion: If one zero of $x^{2} - 5 x + 6$ is $2$ , the other zero is $3$ . Reason: For $a x^{2} + b x + c$ , the sum of zeroes is $- \frac{b}{a}$ and their product is $\frac{c}{a}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What are the relations between zeroes and coefficients of a quadratic polynomial?

For $a x^{2} + b x + c$ , sum of zeroes is $- b / a$ and product is $c / a$ .

Base

Assertion: The pair $2 x + 3 y = 6$ and $4 x + 6 y = 15$ has no solution. Reason: If $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What condition gives no solution for two linear equations?

No solution occurs when $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ .

Base

Assertion: The equation $x^{2} - 4 x + 4 = 0$ has equal roots. Reason: Its discriminant is $b^{2} - 4 a c = 0$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What discriminant gives equal roots?

A quadratic equation has equal real roots when its discriminant is zero.

Base

Assertion: The $21$ st term of the A.P. $3, 7, 11, \dots$ is $83$ . Reason: The $n$ th term of an A.P. is $a_{n} = a + (n - 1) d$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the formula for the nth term of an AP?

The nth term is $a_{n} = a + (n - 1) d$ .

Base

Assertion: If two angles of one triangle are respectively equal to two angles of another triangle, the triangles are similar. Reason: This is the AA similarity criterion.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

Which similarity criterion uses two equal angles?

The AA similarity criterion uses two pairs of equal corresponding angles.

Base

Assertion: The distance of the point $(3, - 4)$ from the x-axis is $- 4$ units. Reason: The distance of a point $(x, y)$ from the x-axis is $∣ y ∣$ units.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

How do you find the distance of a point from the x-axis?

For $(x, y)$ , the distance from the x-axis is $∣ y ∣$ .

Base

Assertion: For an acute angle $θ$ , $sin^{2} θ + cos^{2} θ = 1$ . Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the fundamental trigonometric identity?

The fundamental identity is $sin^{2} θ + cos^{2} θ = 1$ .

Base

Assertion: When an observer looks upward at the top of a tower, the angle made by the line of sight with the horizontal is an angle of elevation. Reason: An angle of elevation is measured from the horizontal line upward to the line of sight.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

From which line is an angle of elevation measured?

It is measured from the horizontal line upward to the line of sight.

Base

Assertion: The lengths of two tangents drawn from an external point to a circle are equal. Reason: A tangent to a circle is perpendicular to the radius at the point of contact.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the theorem about tangents from an external point?

The two tangent segments drawn from the same external point to a circle are equal in length.

Base

Assertion: The area of a $9 0^{\circ}$ sector of a circle of radius $r$ is $\frac{π r ^{2}}{4}$ . Reason: The area of a sector of angle $θ$ is $\frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the formula for area of a sector?

Area of sector $= \frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Base

Assertion: The total surface area of a sphere of radius $r$ is $4 π r^{2}$ . Reason: The curved surface area of a hemisphere of the same radius is $2 π r^{2}$ .

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the total surface area of a sphere?

The total surface area of a sphere of radius $r$ is $4 π r^{2}$ .

Base

Assertion: The median of $3, 5, 7, 9, 11$ is $7$ . Reason: For an odd number of observations arranged in order, the median is the middle observation.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

How is the median found for an odd number of ordered observations?

It is the single middle observation.

Base

Assertion: The probability of getting an even number on a fair die is $\frac{1}{2}$ . Reason: A fair die has three even outcomes out of six equally likely outcomes.

Choose the correct assertion-reasoning relation.

Select an option first. The solution will unlock after your attempt.

FAQ

What is the probability of an even number on a fair die?

There are three even outcomes out of six, so the probability is $1/2$ .

Class 10 Maths Basic

Assertion: 4013​ has a terminating decimal expansion. Reason: After simplification, the denominator 40=23×5 has no prime factors other than 2 and 5.

Assertion: If one zero of x2−5x+6 is 2, the other zero is 3. Reason: For ax2+bx+c, the sum of zeroes is −ab​ and their product is ac​.

Assertion: The pair 2x+3y=6 and 4x+6y=15 has no solution. Reason: If a2​a1​​=b2​b1​​=c2​c1​​, the lines are parallel.

Assertion: The equation x2−4x+4=0 has equal roots. Reason: Its discriminant is b2−4ac=0.

Assertion: The 21st term of the A.P. 3,7,11,… is 83. Reason: The nth term of an A.P. is an​=a+(n−1)d.

Assertion: If two angles of one triangle are respectively equal to two angles of another triangle, the triangles are similar. Reason: This is the AA similarity criterion.

Assertion: The distance of the point (3,−4) from the x-axis is −4 units. Reason: The distance of a point (x,y) from the x-axis is ∣y∣ units.

Assertion: For an acute angle θ, sin2θ+cos2θ=1. Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Assertion: When an observer looks upward at the top of a tower, the angle made by the line of sight with the horizontal is an angle of elevation. Reason: An angle of elevation is measured from the horizontal line upward to the line of sight.

Assertion: The lengths of two tangents drawn from an external point to a circle are equal. Reason: A tangent to a circle is perpendicular to the radius at the point of contact.

Assertion: The area of a 90∘ sector of a circle of radius r is 4πr2​. Reason: The area of a sector of angle θ is 360∘θ​πr2.

Assertion: The total surface area of a sphere of radius r is 4πr2. Reason: The curved surface area of a hemisphere of the same radius is 2πr2.

Assertion: The median of 3,5,7,9,11 is 7. Reason: For an odd number of observations arranged in order, the median is the middle observation.

Assertion: The probability of getting an even number on a fair die is 21​. Reason: A fair die has three even outcomes out of six equally likely outcomes.

Class 10 Maths Basic

Assertion: 4013​ has a terminating decimal expansion. Reason: After simplification, the denominator 40=23×5 has no prime factors other than 2 and 5.

Assertion: If one zero of x2−5x+6 is 2, the other zero is 3. Reason: For ax2+bx+c, the sum of zeroes is −ab​ and their product is ac​.

Assertion: The pair 2x+3y=6 and 4x+6y=15 has no solution. Reason: If a2​a1​​=b2​b1​​=c2​c1​​, the lines are parallel.

Assertion: The equation x2−4x+4=0 has equal roots. Reason: Its discriminant is b2−4ac=0.

Assertion: The 21st term of the A.P. 3,7,11,… is 83. Reason: The nth term of an A.P. is an​=a+(n−1)d.

Assertion: If two angles of one triangle are respectively equal to two angles of another triangle, the triangles are similar. Reason: This is the AA similarity criterion.

Assertion: The distance of the point (3,−4) from the x-axis is −4 units. Reason: The distance of a point (x,y) from the x-axis is ∣y∣ units.

Assertion: For an acute angle θ, sin2θ+cos2θ=1. Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Assertion: When an observer looks upward at the top of a tower, the angle made by the line of sight with the horizontal is an angle of elevation. Reason: An angle of elevation is measured from the horizontal line upward to the line of sight.

Assertion: The lengths of two tangents drawn from an external point to a circle are equal. Reason: A tangent to a circle is perpendicular to the radius at the point of contact.

Assertion: The area of a 90∘ sector of a circle of radius r is 4πr2​. Reason: The area of a sector of angle θ is 360∘θ​πr2.

Assertion: The total surface area of a sphere of radius r is 4πr2. Reason: The curved surface area of a hemisphere of the same radius is 2πr2.

Assertion: The median of 3,5,7,9,11 is 7. Reason: For an odd number of observations arranged in order, the median is the middle observation.

Assertion: The probability of getting an even number on a fair die is 21​. Reason: A fair die has three even outcomes out of six equally likely outcomes.

Assertion: $\frac{13}{40}$ has a terminating decimal expansion. Reason: After simplification, the denominator $40 = 2^{3} \times 5$ has no prime factors other than $2$ and $5$ .

Assertion: If one zero of $x^{2} - 5 x + 6$ is $2$ , the other zero is $3$ . Reason: For $a x^{2} + b x + c$ , the sum of zeroes is $- \frac{b}{a}$ and their product is $\frac{c}{a}$ .

Assertion: The pair $2 x + 3 y = 6$ and $4 x + 6 y = 15$ has no solution. Reason: If $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel.

Assertion: The equation $x^{2} - 4 x + 4 = 0$ has equal roots. Reason: Its discriminant is $b^{2} - 4 a c = 0$ .

Assertion: The $21$ st term of the A.P. $3, 7, 11, \dots$ is $83$ . Reason: The $n$ th term of an A.P. is $a_{n} = a + (n - 1) d$ .

Assertion: The distance of the point $(3, - 4)$ from the x-axis is $- 4$ units. Reason: The distance of a point $(x, y)$ from the x-axis is $∣ y ∣$ units.

Assertion: For an acute angle $θ$ , $sin^{2} θ + cos^{2} θ = 1$ . Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Assertion: The area of a $9 0^{\circ}$ sector of a circle of radius $r$ is $\frac{π r ^{2}}{4}$ . Reason: The area of a sector of angle $θ$ is $\frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Assertion: The total surface area of a sphere of radius $r$ is $4 π r^{2}$ . Reason: The curved surface area of a hemisphere of the same radius is $2 π r^{2}$ .

Assertion: The median of $3, 5, 7, 9, 11$ is $7$ . Reason: For an odd number of observations arranged in order, the median is the middle observation.

Assertion: The probability of getting an even number on a fair die is $\frac{1}{2}$ . Reason: A fair die has three even outcomes out of six equally likely outcomes.

Assertion: $\frac{13}{40}$ has a terminating decimal expansion. Reason: After simplification, the denominator $40 = 2^{3} \times 5$ has no prime factors other than $2$ and $5$ .

Assertion: If one zero of $x^{2} - 5 x + 6$ is $2$ , the other zero is $3$ . Reason: For $a x^{2} + b x + c$ , the sum of zeroes is $- \frac{b}{a}$ and their product is $\frac{c}{a}$ .

Assertion: The pair $2 x + 3 y = 6$ and $4 x + 6 y = 15$ has no solution. Reason: If $\frac{a _{1}}{a _{2}} = \frac{b _{1}}{b _{2}} \neq = \frac{c _{1}}{c _{2}}$ , the lines are parallel.

Assertion: The equation $x^{2} - 4 x + 4 = 0$ has equal roots. Reason: Its discriminant is $b^{2} - 4 a c = 0$ .

Assertion: The $21$ st term of the A.P. $3, 7, 11, \dots$ is $83$ . Reason: The $n$ th term of an A.P. is $a_{n} = a + (n - 1) d$ .

Assertion: The distance of the point $(3, - 4)$ from the x-axis is $- 4$ units. Reason: The distance of a point $(x, y)$ from the x-axis is $∣ y ∣$ units.

Assertion: For an acute angle $θ$ , $sin^{2} θ + cos^{2} θ = 1$ . Reason: The identity follows by applying Pythagoras theorem to the sides of a right triangle.

Assertion: The area of a $9 0^{\circ}$ sector of a circle of radius $r$ is $\frac{π r ^{2}}{4}$ . Reason: The area of a sector of angle $θ$ is $\frac{θ}{36 0 ^{\circ}} π r^{2}$ .

Assertion: The total surface area of a sphere of radius $r$ is $4 π r^{2}$ . Reason: The curved surface area of a hemisphere of the same radius is $2 π r^{2}$ .

Assertion: The median of $3, 5, 7, 9, 11$ is $7$ . Reason: For an odd number of observations arranged in order, the median is the middle observation.

Assertion: The probability of getting an even number on a fair die is $\frac{1}{2}$ . Reason: A fair die has three even outcomes out of six equally likely outcomes.