Mathematics Standard - Outside Delhi Set 2 2022-2023 English Medium Class 10 Question Paper Solution

If p² = `32/50`, then p is a/an ______.

whole number

integer

rational number

irrational number

The distance of the point (–6, 8) from x-axis is ______.

6 units

– 6 units

8 units

10 units

The number of quadratic polynomials having zeroes –5 and –3 is ______.

1

2

3

more than 3

The point of intersection of the line represented by 3x – y = 3 and y-axis is given by ______.

(0, –3)

(0, 3)

(2, 0)

(–2, 0)

The circumferences of two circles are in the ratio 4 : 5. What is the ratio of their radii?

16 : 25

25 : 16

`2 : sqrt(5)`

4 : 5

The LCM of smallest 2-digit number and smallest composite number is ______.

12

4

20

40

The distance of the point (–4, 3) from y-axis is ______.

–4

4

3

5

If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is ______.

10

- 10

5 

- 5

If the quadratic equation ax² + bx + c = 0 has two real and equal roots, then 'c' is equal to ______.

`(-b)/(2a)`

`b/(2a)`

`(-b^2)/(4a)`

`b^2/(4a)`

In the given figure, DE || BC. If AD = 3 cm, AB = 7 cm and EC = 3 cm, then the length of AE is ______.

2 cm

2.25 cm

3.5 cm

4 cm

A bag contains 5 pink, 8 blue and 7 yellow balls. One ball is drawn at random from the bag. What is the probability of getting neither a blue nor a pink ball?

`1/4`

`2/5`

`7/20`

`13/20`

The volume of a right circular cone whose area of the base is 156 cm² and the vertical height is 8 cm, is ______.

2496 cm³

1248 cm³

1664 cm³

416 cm³

3 chairs and 1 table cost ₹ 900; whereas 5 chairs and 3 tables cost ₹ 2,100. If the cost of 1 chair is ₹ x and the cost of 1 table is ₹ y, then the situation can be represented algebraically as ______.

3x + y = 900, 3x + 5y = 2100

x + 3y = 900, 3x + 5y = 2100

3x + y = 900, 5x + 3y = 2100

x + 3y = 900, 5x + 3y = 2100

In the given figure, PA and PB are tangents from external point P to a circle with centre C and Q is any point on the circle. Then the measure of ∠AQB is ______.

`62 (1/2)^circ`

125°

55°

90°

A card is drawn at random from a well shuffled deck of 52 playing cards. The probability of getting a face card is ______.

`1/2`

`3/13`

`4/13`

`1/13`

A box contains 90 discs, numbered from 1 to 90. If one disc is drawn at random from the box, the probability that it bears a prime number less than 23, is ______.

`7/90`

`9/90`

`1/9`

`10/90`

`4/15`

`4/45`

`8/89`

\[\frac{9}{89}\]

The coordinates of the point where the line 2y = 4x + 5 crosses x-axis is ______.

`(0, (-5)/4)`

`(0, 5/2)`

`((-5)/4, 0)`

`((-5)/2, 0)`

cos⁴ A − sin⁴ A is equal to ______.

2 cos² A + 1

2 cos² A − 1

2 sin² A − 1

2 sin² A + 1

Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.

Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.

Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).

Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).

Assertion (A) is true but Reason (R) is false.

Assertion (A) is false but Reason (R) is true.

Statement A (Assertion): For 0 < θ ≤ 90°, cosec θ – cot θ and cosec θ + cot θ are reciprocal of each other.

Statement R (Reason): cosec² θ – cot² θ = 1

Both Assertion (A) and Reason (R) are true; and Reason (R) is the correct explanation of Assertion (A).

Both Assertion (A) and Reason (R) are true; but Reason (R) is not the correct explanation of Assertion (A).

Assertion (A) is true but Reason (R) is false.

Assertion (A) is false but Reason (R) is true.

Show the 6ⁿ cannot end with digit 0 for any natural number 'n'.

Find the HCF and LCM of 72 and 120.

A line intersects y-axis and x-axis at point P and Q, respectively. If R(2, 5) is the mid-point of line segment PQ, them find the coordinates of P and Q.

Find the length of the shadow on the ground of a pole of height 18m when angle of elevation θ of the sun is such that tan θ = `6/7`.

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using similarity criterion for two triangles, show that `"OA"/"OC"="OB"/"OD"`.

In the given figure, AB and CD are diameters of a circle with centre O perpendicular to each other. If OA = 7 cm, find the area of shaded region.

If sin θ + cos θ = p and sec θ + cosec θ = q, then prove that q(p² – 1) = 2p.

In the following figure, E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC, prove that ΔABD ∼ ΔECF.

The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.

If α and β are roots of the quadratic equation x² – 7x + 10 = 0, find the quadratic equation whose roots are α² and β².

Proved that `(1 + secA)/secA = (sin^2A)/(1 - cos A)`.

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector formed by the arc. (Use π = `22/7`)

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the length of the arc.  (Use π = `22/7`)

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Prove that ∠PTQ = 2∠OPQ.

A circle touches the side BC of a ΔABC at a point P and touches AB and AC when produced at Q and R respectively. As shown in the figure that AQ = `1/2` (Perimeter of ΔABC).

A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.

A solid is in the shape of a cone surmounted on a hemisphere, the radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

Find the sum of the integers between 100 and 200 that are

1. divisible by 9
2. not divisible by 9

[Hint (ii) : These numbers will be : Total numbers – Total numbers divisible by 9]

Find the sum of the integers between 100 and 200 that are not divisible by 9.

Solve the equation:

– 4 + (–1) + 2 + 5 + ... + x = 437

Read the following passage:

Based on the above information, answer the following questions:

1. Represent the information given above in terms of x and y.
2. Find the monthly fee paid by a poor child.
   OR
   Find the difference in the monthly fee paid by a poor child and a rich child.
3. If there are 10 poor and 20 rich children in batch II, what is the total monthly collection of fees from batch II?

Read the following passage:

Based on the above information, answer the following questions:

1. Find the length of the wire from the point O to the top of Section B. 
2. Find the distance AB.
   OR
   Find the area of ∠OPB.
3. Find the height of the Section A from the base of the tower.

Read the following passage:

Based on the above information, answer the following questions:

1. What is the probability that the drawn ball bears number 8?
2. What is the probability that the drawn ball bears an even number?
   OR
   What is the probability that the drawn ball bears a number, which is a multiple of 3?
3. What is the probability that the drawn ball is a solid coloured and bears an even number?