Mathematics Basic - Delhi Set 3 2023-2024 English Medium Class 10 Question Paper Solution

For what value of k, the product of zeroes of the polynomial kx² − 4x − 7 is 2?

${\displaystyle -\frac{1}{14}}$

${\displaystyle -\frac{7}{2}}$

${\displaystyle \frac{7}{2}}$

${\displaystyle -\frac{2}{7}}$

In an A.P., if a = 8 and a₁₀ = −19, then value of d is ______.

3

${\displaystyle -\frac{11}{9}}$

${\displaystyle -\frac{27}{10}}$

−3

The mid-point of the line segment joining the points (−1, 3) and ${\displaystyle (8,\frac{3}{2})}$ is ______. 

${\displaystyle (\frac{7}{2},-\frac{3}{4})}$

${\displaystyle (\frac{7}{2},\frac{9}{2})}$

${\displaystyle (\frac{9}{2},-\frac{3}{4})}$

${\displaystyle (\frac{7}{2},\frac{9}{4})}$

The curved surface area of a right circular cone of radius 7 cm is 550 sq cm. The slant height of the cone is ______.

24 cm

25 cm

22 cm

20 cm

HCF (132, 77) is ______.

11

77

22

44

If the roots of quadratic equation 4x² − 5x + k = 0 are real and equal, then value of k is ______.

${\displaystyle \frac{5}{4}}$

${\displaystyle \frac{25}{16}}$

${\displaystyle -\frac{5}{4}}$

${\displaystyle -\frac{25}{16}}$

If probability of winning a game is p, then probability of losing the game is ______.

1 + p

−p

p − 1

1 − p

The distance between the points (2, −3) and (−2, 3) is ______.

${\displaystyle 2\sqrt{13}}$ units

5 units

${\displaystyle 13\sqrt{2}}$ units

10 units

If HCF (96, 404) = 4, then LCM (96, 404) is ______.

9600

96 × 404

404

9696

A card is drawn from a well shuffled deck of 52 playing cards. The probability that drawn card is a red queen, is______.

${\displaystyle \frac{1}{13}}$

${\displaystyle \frac{2}{13}}$

${\displaystyle \frac{1}{52}}$

${\displaystyle \frac{1}{26}}$

If a certain variable x divides a statistical data arranged in order into two equal parts, then the value of x is called the ______.

mean of the data

median

mode

range

The radius of a sphere is ${\displaystyle \frac{7}{2}}$ cm. The volume of the sphere is ______.

${\displaystyle \frac{231}{3}}$ cu cm

${\displaystyle \frac{539}{12}}$ cu cm

${\displaystyle \frac{539}{3}}$ cu cm

154 cu cm

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

52%

${\displaystyle \frac{1}{3}}$%

0.99

${\displaystyle \frac{1}{0.99}}$

The height and radius of a right circular cone are 24 cm and 7 cm respectively. The slant height of the cone is ______.

24 cm

31 cm

26 cm

25 cm

Two dice are rolled together. The probability of getting at least one 6, is ______.

${\displaystyle \frac{1}{3}}$

${\displaystyle \frac{11}{36}}$

${\displaystyle \frac{1}{6}}$

${\displaystyle \frac{10}{36}}$

The diameter of a circle is of length 6 cm. If one end of the diameter is (−4, 0), the other end on x-axis is at ______.

(0, 2)

(6, 0)

(2, 0)

(4, 0)

The value of k for which the pair of linear equations 5x + 2y − 7 = 0 and 2x + ky + 1 = 0 don't have a solution is ______.

5

${\displaystyle \frac{4}{5}}$

${\displaystyle \frac{5}{4}}$

${\displaystyle \frac{5}{2}}$

Two dice are rolled together. The probability of getting a double is ______.

${\displaystyle \frac{2}{36}}$

${\displaystyle \frac{1}{36}}$

${\displaystyle \frac{1}{6}}$

${\displaystyle \frac{5}{6}}$

Assertion (A): If PA and PB are tangents drawn to a circle with centre O from an external point P, then the quadrilateral OAPB is a cyclic quadrilateral.

Reason (R): In a cyclic quadrilateral, opposite angles are equal.

Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.

Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).

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

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

Assertion (A): Zeroes of a polynomial p(x) = x² − 2x − 3 are −1 and 3.

Reason (R): The graph of polynomial p(x) = x² − 2x − 3 intersects x-axis at (−1, 0) and (3, 0).

Both, Assertion (A) and Reason (R) are true. Reason (R) explains Assertion (A) completely.

Both, Assertion (A) and Reason (R) are true. Reason (R) does not explain Assertion (A).

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

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

D is a point on the side BC of ${\displaystyle △}$ABC such that ${\displaystyle \angle }$ADC = ${\displaystyle \angle }$BAC. Show that AC² = BC × DC.

Solve the following pair of linear equations for x and y algebraically:

x + 2y = 9 and y − 2x = 2

Check whether the point (−4, 3) lies on both the lines represented by the linear equations x + y + 1 = 0 and x − y = 1.

Prove that ${\displaystyle 6-4\sqrt{5}}$ is an irrational number, given that ${\displaystyle \sqrt{5}}$ is an irrational number.

Show that 11 × 19 × 23 + 3 × 11 is not a prime number.

If sin A = ${\displaystyle \frac{1}{2}}$ and cos B = ${\displaystyle \frac{1}{\sqrt{2}}}$, then find the value of sin A sin B + cos A cos B.

In the given figure, in ΔABC, BD and CE are perpendiculars to AC and AB respectively. Prove that: AE × BD = AD × CE.

Two alarm clocks ring their alarms at regular intervals of 20 minutes and 25 minutes respectively. If they first beep together at 12 noon, at what time will they beep again together next time?

The greater of two supplementary angles exceeds the smaller by 18°. Find measures of these two angles.

Find the co-ordinates of the points of trisection of the line segment joining the points (−2, 2) and (7, −4).

Prove that:

sin⁶ θ  + cos⁶ θ  + 3 sin² θ cos² θ = 1

A solid is in the form of a cylinder with hemispherical ends of same radii. The total height of the solid is 20 cm and the diameter of the cylinder is 14 cm. Find the surface area of the solid.

A juice glass is cylindrical in shape with hemispherical raised up portion at the bottom. The inner diameter of glass is 10 cm and its height is 14 cm. Find the capacity of the glass. (use π = 3.14)

If A(2, −1), B(a, 4), C(−2, b) and D(−3, −2) are vertices of a parallelogram ABCD taken in order, then find the values of a and b. Also, find the length of the sides of the parallelogram.

In the given figure, two concentric circles with centre O have radii 14 cm and 7 cm. If ∠AOB = 30°, find the area of the shaded region.

How many terms of the A.P. 27, 24, 21, ..... must be taken so that their sum is 105? Which term of the A.P. is zero?

In an A.P. of 50 terms, the sum of first 10 terms is 250 and the sum of its last 15 terms is 2625. Find the A.P. so formed.

A chord of a circle of radius 14 cm subtends an angle of 90° at the centre. Find the area of the corresponding minor and major segments of the circle.

To keep the lawn green and cool, Sadhna uses water sprinklers which rotate in circular shape and cover a particular area.

The diagram below shows the circular areas covered by two sprinklers:

Two circles touch externally. The sum of their areas is 130π sq m and the distance between their centres is 14 m.

Based on the above information, answer the following questions:

1. Obtain a quadratic equation involving R and r from above.    1
2. Write a quadratic equation involving only r.    1
3. 1. Find the radius r and the corresponding area irrigated.    2
      OR
   2. Find the radius R and the corresponding area irrigated.    2

Gurpreet is very fond of doing research on plants. She collected some leaves from different plants and measured their lengths in mm.

The data obtained is represented in the following table:

Based on the above information, answer the following questions:

1. Write the median class of the data.    1
2. How many leaves are of length equal to or more than 10 cm?    1
3. 1. Find median of the data.    2
      OR
   2. Write the modal class and find the mode of the data.    2

The picture given below shows a circular mirror hanging on the wall with a cord. The diagram represents the mirror as a circle with centre O. AP and AQ are tangents to the circle at P and Q, respectively such that AP = 30 cm and ∠PAQ = 60°.

Based on the above information, answer the questions:

1. Find the length PQ.    1
2. Find m ∠POQ.    1
   1. Find the length OA.    2
      OR
   2. Find the radius of the mirror.    2