30 Questions
In the isosceles triangle ∆ABC with ∠C = 90° and AC = 5 cm, what is the length of side AB?
10 cm
In triangle ∆ABC, if AD is the bisector of ∠BAC and AB = 8 cm, BD = 6 cm, DC = 3 cm, what is the length of side AC?
4 cm
Which of the following probability statements is incorrect?
$P(A) > 1$
What is the shape of a shuttlecock used for playing badminton?
a hemisphere and a cone
If the equation of a straight line is x = 11, what can be said about this line?
parallel to X-axis
In a lucky draw where 135 tickets were sold and Kamalam's winning probability is 1/9, how many tickets did Kamalam buy?
15
What is the Highest Common Factor (HCF) of the quadratic expressions 𝒙² - 𝟐𝒙 - 𝟐𝟒 and 𝒙² - 𝒌𝒙 - 𝟔 if (𝒙 - 𝟔) is their HCF?
5
In a matrix, if the number of columns and rows are not equal, it is classified as a:
Rectangular matrix
Where is a tangent line to a circle perpendicular to the radius?
Point of contact
What is the variance of the first 20 natural numbers?
32.25
In Euclid’s division lemma for positive integers a and b, what condition must the remainder r satisfy in the equation a = bq + r?
$0 ≤ r < b$
What is the probability of drawing a Rs.500 or Rs.200 note from a purse containing notes of Rs.2000, Rs.500, and Rs.200 denominations?
$4/5$
In the given function f(x) = (x + 1)^3 - (x - 1)^3, what type of function does it represent?
Cubic
If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal, what is the value of (a, b)?
(2, -2)
For the identity function {(a, 8), (6, b)}, what are the values of a and b respectively?
(6, 6)
What is the sum of the exponents of the prime factors in the prime factorization of 1729?
3
If the first term of an arithmetic progression is 1 and the common difference is 4, which of the following will be a term of this A.P.?
10091
What is the point of intersection between 3x - y = 4 and x + y = 8?
(3, 5)
What is the correct formula for the function f(x) = √(1 + x^2)?
None of these
If the HCF of 65 and 117 can be expressed as 65m - 117, what is the value of m?
2
What is the value of (13 + 23 + 33 + ... + 153) - (1 + 2 + 3 + ... + 15)?
14280
What is the curved surface area of a right circular cone with a height of 15 cm and base diameter of 16 cm?
110π cm^2
What is the volume, in cm^3, of the largest sphere that can be cut off from a cylindrical log with a base radius of 1 cm and height of 5 cm?
(10/3)π
If the radius of the base of a right circular cylinder is halved while keeping the same height, what is the ratio of the volume of the new cylinder to the original cylinder?
1 : 4
In statistics, the sum of all deviations of the data from its mean is ____.
Zero
For the sets A = {1, 2}, B = {1, 2, 3, 4}, C = {5, 6}, and D = {5, 6, 7, 8}, which statement is true?
(𝑩 × 𝑫) ⊂ (𝑨 × 𝑪)
When selecting a page at random from a book, what is the probability that the digit at the unit place of the page number chosen is less than 7?
3/10
If the standard deviation of a data set is 3, what is the new variance if each value is multiplied by 5?
225
If the probability of getting a job for a person is x/3 and the probability of not getting the job is 2/3, what is the value of x?
1
In a scenario where two poles of heights 6 m and 11 m stand vertically on a plane ground with a distance of 12 m between their feet, what is the distance between their tops?
13 m
Test your knowledge on the sum of deviations from the mean of data and concepts in set theory. Questions include determining the sign of the sum of deviations and identifying relationships between sets based on Cartesian products.
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