If log₁₀(x - 2) = 2, what is the value of x?
Mathematics
Question · Easy
Two lines, one point: an emo ballad
Short
Which of the following is an irrational number?
Find the HCF of 96 and 404 using the prime factorization method.
Question · Medium
If A and B are two sets such that A ⊂ B, then what is A ∪ B?
Let A = {x : x is a letter in the word 'FOLLOW'} and B = {x : x is a letter in the word 'WOLF'}. Which of the following is correct?
If n(A) = 15, n(B) = 20, and n(A ∩ B) = 7, find n(A ∪ B).
If the sum of the zeroes of the quadratic polynomial kx² + 2x + 3k is equal to their product, find the value of k.
The number of zeroes of a cubic polynomial is at most:
If one zero of the quadratic polynomial x² + 3x + k is 2, then the value of k is:
For what value of k will the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 represent coincident lines?
If a pair of linear equations is consistent, then the lines representing them will be:
Solve the system of equations: x + y = 14 and x - y = 4.
What is the discriminant of the quadratic equation 2x² - 4x + 3 = 0?
If the roots of the quadratic equation ax² + bx + c = 0 are real and equal, then which of the following is true?
If one root of the quadratic equation 3x² + px - 2 = 0 is 2, find the value of p.
Find the 10th term of the Arithmetic Progression (AP): 2, 7, 12, ...
If the sum of first n terms of an AP is given by S_n = 3n² + 5n, find its common difference.
Question · Hard
In a Geometric Progression (GP), if the first term is 3 and the common ratio is 2, find the 6th term.
Find the distance between the points A(2, 3) and B(5, 7).
The coordinates of the midpoint of the line segment joining P(-2, 8) and Q(-6, -4) are:
If the slope of the line joining (3, y) and (2, 7) is -3, find the value of y.
In triangle ABC, D and E are points on AB and AC respectively such that DE || BC. If AD = 1.5 cm, DB = 3 cm, and AE = 1 cm, find EC.
If two triangles ABC and PQR are similar such that AB/PQ = 1/3, then find the ratio of their areas, Area(ABC)/Area(PQR).
The areas of two similar triangles are 81 cm² and 49 cm². If the altitude of the larger triangle is 4.5 cm, what is the corresponding altitude of the smaller triangle?
A tangent PQ at a point P of a circle of radius 5 cm meets a line through the center O at a point Q so that OQ = 12 cm. Find the length of PQ.
How many tangents can be drawn to a circle from a point inside the circle?
The angle between a tangent to a circle and the radius drawn through the point of contact is:
If the radius of a sphere is doubled, what is the ratio of the volume of the new sphere to that of the original sphere?
The total surface area of a solid hemisphere of radius r is:
Find the volume of a right circular cylinder whose radius is 7 cm and height is 10 cm. (Use π = 22/7)
If sin θ = 3/5, what is the value of tan θ?
Evaluate: (sec² A - tan² A).
If cos(A + B) = 0 and sin(A - B) = 1/2, where A, B are acute angles, find A and B.
A tower stands vertically on the ground. From a point on the ground, which is 15 m away from the foot of the tower, the angle of elevation of the top of the tower is found to be 60°. What is the height of the tower?
A kite is flying at a height of 60 m above the ground. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is 60°. Find the length of the string, assuming there is no slack.
The angle of depression of a car parked on the road from the top of a 150 m high tower is 30°. Find the distance of the car from the tower.
Which of the following cannot be the probability of an event?
Two dice are thrown together. What is the probability of getting a sum of 8?
If the probability of winning a game is 0.72, what is the probability of losing it?
Find the median of the following data: 24, 36, 40, 18, 25, 32, 28.
If the mean of five observations x, x + 2, x + 4, x + 6, and x + 8 is 11, find the value of x.
For a given distribution, the mode and mean are 28 and 31 respectively. Find the median using the empirical relation.
Which of the following represents the relation between Celsius scale (C) and Fahrenheit scale (F) of temperature?
Physics
At what temperature do the Celsius and Fahrenheit scales read the same value?
What is the SI unit of specific heat capacity?
The focal length of a spherical mirror of radius of curvature R is given by:
An object is placed at a distance of 10 cm in front of a concave mirror of focal length 15 cm. The nature of the image formed is:
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