Solved maths problems — page 9
1518 problems, newest first. Browse by chapter at NCERT solutions by class.
- Lali tosses two different coins simultaneously. The probability that she gets at most one head is:
The probability that she gets at most one head is (3)/(4).
- If a bicycle wheel makes 5000 revolutions in moving 11 km, then the diameter of the wheel is:
The diameter of the wheel is 70 cm.
- The length of the tangent drawn from a point P, whose distance from the centre of a circle is 25 cm, and the radius of the circle is 7 cm, is:
24 cm
- In the figure, PA and PB are two tangents to the circle with centre O such that APB = 50^°. Then, the measure of OAB is:
The measure of OAB is 25^°.
- OACB is a quadrant of a circle with centre O and radius 7 cm where ACB is the arc. Then the perimeter of the quadrant is:
25 cm
- Using empirical relationship, the mode of a distribution whose mean is 7.2 and the median 7.1, is:
6.9
- The height of a tower is 20 m. The length of its shadow made on the level ground, when the sun's elevation is 60^°, is:
The length of the shadow is (20√3)/(3) m.
- If x, 2x + 9, 4x + 3 are three consecutive terms of an A.P., then the value of x is:
The value of x is 15.
- The coordinates of the point A, where AB is the diameter of the circle whose centre is (3, 2) and B (7, 4) is:
The coordinates of point A are (-1, 0).
- cot² θ - (1)/(sin² θ) is equal to:
-1
- The zeroes of the polynomial 3x² + 11x - 4 are:
The zeroes of the polynomial are (1)/(3) and -4.
- The condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines is:
The condition for which the pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines is ab = 6.
- In a family of two children, the probability of having at least one girl is:
The probability of having at least one girl is (3)/(4).
- The distance of the point (4, 7) from the x-axis is:
7 units
- The values of k for which the equation 4x² + kx + 9 = 0 has real and equal roots are:
k = ± 12
- Sukesh is having a garden at the back of his house with trees and flower plants. One day, due to heavy rain and storm, one of the trees broke such that the heig
(i) The length of the broken part of the tree is 25 m. (ii) The total height of the full tree was 40 m. (iii) (a) The perimeter of the triangle formed is 60 m.
- The following table shows the age distribution of patients admitted during a day in two different hospitals: | Age (in years): | 5 - 15 | 15 - 25 | 25 - 35 | 35
(i) The upper limit of the modal class for Hospital I is 45. (ii) The lower limit of the modal class for Hospital II is 25. (iii) The mode of the data for Hospi
- Ashok and Harish are very close friends. They decided to go on a long drive with their families in separate cars. Ashok's car travels at a speed of x km/h, whil
(i) The distance covered by Harish's car in two hours is 2(x+5) km. (ii) The quadratic equation describing the speed of Ashok's car is x² + 5x - 500 = 0. (iii)
- (a) The perimeter of a sector of a circle of radius 7 cm is 25 cm. Find the area of the sector. OR (b) In a circle of radius 35 cm, an arc subtends an angle of
(a) The area of the sector is 38.5 cm². (b) The area of the minor segment is 350 cm².
- (a) Find the sum of all multiples of 9 lying between 300 and 700. OR (b) The 26^(th), 11^(th) and the last term of an A.P. are 0, 3 and -51 respectively. Find t
The common difference is -(1)/(5) and the number of terms is 281.
- From a point on the ground, the angles of elevation of the bottom and the top of a transmission tower fixed at the top of a 25 m high building are 30^° and 60^°
The height of the transmission tower is 50 m.
- (a) Find the relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). OR (b) Find the coordinates of the points
The relation between x and y is x - y = 2.
- Prove that (3 + 2√5) is an irrational number, given that √5 is an irrational number.
Therefore, 3 + 2√5 is an irrational number.
- From a solid cone, whose height is 16 cm and radius 12 cm, and conical cavity of height 3 cm and base radius 4 cm is hollowed out such that the bases of the con
388π cm²
- (a) The product of the digits of a 2-digit number is 18. When 27 is subtracted from the number, the digits interchange their places. Find the number. OR (b) Two
(a) The number is 63. (b) The numbers are 40 and 48.
- Solve the following pair of linear equations: x + y = 5 2x - 3y = 4
x = (19)/(5), y = (6)/(5)
- Find the greatest number which divides 65 and 117 completely.
13
- (a) An unbiased die is thrown once. Find the probability of getting (i) a number greater than 3 (ii) an even prime number. OR (b) A box contains 5 red, 8 white
(a) (i) (1)/(2) (ii) (1)/(6) OR (b) (i) (8)/(17) (ii) (13)/(17)
- E and F are points on the sides PQ and PR respectively of a PQR and EF || QR. If PE = 2·5 cm, PQ = 6 cm and PF = 4·5 cm, find the lengths of RF and PR.
RF = 6.3 cm, PR = 10.8 cm
- (a) If cos θ = (3)/(5), find the value of (tan θ + sin θ)/(cosec θ - cot θ). OR (b) For θ = 30^°, verify that cos 2θ = cos² θ - sin² θ.
(64)/(15)
- Assertion (A): The probability of drawing a red face card, at random, from a well-shuffled pack of 52 playing cards is (3)/(26). Reason (R): The number of face
Assertion (A) is true, but Reason (R) is false.
- Assertion (A): If surface areas of the two spheres are in the ratio 16: 9, then their volumes are in the ratio 64: 27. Reason (R): If S_1 and S_2 are the surfac
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
- A solid is hemispherical at the bottom and conical above (of same radius). If the curved surface areas of the two parts are equal, then the ratio of its radius
The ratio of its radius and the height of the conical part is 1:√3.
- The median of the first nine prime numbers is:
11
- Two dice are thrown together. The probability of getting the same number on both dice, is:
The probability of getting the same number on both dice is (1)/(6).
- In a family of two children, the probability of having at most one boy, is:
The probability of having at most one boy is (3)/(4).
- If cosec B = (√3)/(2) and A + B = 90^°, then the value of sec A is:
The problem statement contains an invalid value for cosec B, as (√3)/(2) ≈ 0.866, which is less than 1. The cosecant of a real angle must be greater than or equ
- The maximum value of (1)/(cosec θ), (0 ≤ θ ≤ 90^°) is:
1
- From a point P which is at a distance of 17 cm from the centre O of a circle of radius 8 cm, the pair of tangents PQ and PR to the circle are drawn. The area of
The area of triangle OPQ is 60 cm².
- A circle of radius 7 cm is inscribed in a square. Find the area of the shaded region. Use π = (22)/(7). (circle, square, radius, area, inscribed)
The area of the shaded region is 42 cm².
- Two angles of a triangle are 50 and 30. What is the third?
The third angle of the triangle is 100^°.
- [25] Jessica the jackrabbit wants to climb down a wall. The wall consists of 2026 horizontal layers stacked vertically. The n -th layer from the top is partitio
2^(2025)
- 29. (a) Find the general solution of the differential equation 2x² (dy)/(dx) = y² + 2xy. (differential equation, general solution, calculus, homogeneous equatio
The general solution of the differential equation is y = (2x)/(C - ln|x|).
- If a triangle has sides a = 5 cm, b = 12 cm and c = 13 cmCalculate the semi-perimeter (s)
The semi-perimeter (s) of the triangle is 15 cm.
- Two angles of a triangle are 50 and 130. What is the third?
A triangle with angles 50^° and 130^° cannot exist, as the sum of these two angles is already 180^°, implying the third angle would be 0^°.
- Find the equation of the circle with centre (-3,2) and radius 10.
The equation of the circle is (x+3)² + (y-2)² = 100.
- Find the equation of the circle with centre (-3,2) and radius 9.
(x+3)² + (y-2)² = 81
- The HCF and LCM of two numbers are 99 and 765, respectively. If one of the numbers is 45, what is the other number?
The other number is 1683.
- The HCF and LCM of two numbers are 11 and 770, respectively. If one of the numbers is 45, what is the other number?
The other number is approximately 188.22. However, since HCF and LCM are defined for integers, and the result is not an integer, there might be an error in the
- The HCF and LCM of two numbers are 9 and 360, respectively. If one of the numbers is 45, what is the other number?
The other number is 72.
- what is x square - 3 x + Y = 0
The equation x² - 3x + y = 0 represents a parabola opening downwards with x-intercepts at (0, 0) and (3, 0), and its vertex at ((3)/(2), (9)/(4)).
- What What is What is What is x What is x square What is x square What is x square minus What is x square minus What is x square minus What is x square minus Wha
The equation x² - 3x - y = 0 represents a parabola.
- In a △ ABC, AD is a median and AE BC. Prove that: AC²=AD²+BC· DE+((BC)/(2))²
AC²=AD²+BC· DE+((BC)/(2))²
- 5x + 3y = 9 (I) 2x - 3y = 12 (II) (linear equations, system of equations, variables, coefficients)
The solution to the system of equations is x=3 and y=-2.
- Question: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Find their present ages.
The present age of the father is 36 years and the present age of the son is 9 years.
- X square + 2 X + 3 is equal to zero
The equation has no real roots.
- Find the roots of the equation (1)/(2x-3) + (1)/(x-5) = 1 x ≠ (3)/(2), 5 (rational equation, roots, domain, excluded values)
The roots of the equation are x = (8 + 3√2)/(2) and x = (8 - 3√2)/(2).
- If two angles of a triangle are 50 and 30. What is the 3rd angle?
The third angle is 100^°.
- One angle of a triangle is 50. The other is 30. What is the third?
The third angle of the triangle is 100^°.
- Find the roots of the equation (1)/(2x-3) + (1)/(x-5) = 1 x ≠ (3)/(2), 5 (roots, equation, fractions, domain, quadratic)
The roots of the equation are x = (8 + 3√2)/(2) and x = (8 - 3√2)/(2).