1.
1. If 'A+B' means that B is the mother of B, 'A÷B’ means that A is the father of B, 'A-B' means that A is the sister of B. Then, which of the following relationship shows that P is the daughter of Q? (A) Q÷P+N (B) Q+N÷P (C) Q-P÷N (D) Data inadequate
Correct Answer
A. Q÷P+N
Explanation
The correct answer is Q÷P+N. This relationship indicates that Q is the father of P and N is the mother of P. Since Q is the father and N is the mother, it can be inferred that P is their daughter. Therefore, Q÷P+N represents the relationship that P is the daughter of Q.
2.
If P is to the south of Q and R is to the east of Q, then in what direction is P with respect to R?
Correct Answer
D. South-West
Explanation
If P is to the south of Q and R is to the east of Q, it means that P is below Q and R is to the right of Q. Therefore, P is in the southwest direction with respect to R.
3.
What comes next?
Correct Answer
A. A
4.
Which of the following diagrams represents the relationship of Mercury, Zinc, Metal?
Correct Answer
D. D
5.
What number should replace the question mark?
Correct Answer
D. B
Explanation
The given sequence follows a reverse alphabetical order. Starting from D, each subsequent letter moves one step back in the alphabet. Therefore, the letter that should replace the question mark is B.
6.
If COMPUTER: fqprxvht then LANGUAGE: ?
Correct Answer
C. Ocqixcjg
Explanation
The given question follows a pattern where each letter in the word "COMPUTER" is replaced with the corresponding letter in the word "fqprxvht". Applying the same pattern to the word "LANGUAGE", we replace each letter with the corresponding letter in "fqprxvht". Therefore, the correct answer is "ocqixcjg".
7.
Identify the number of triangles in the given figure.
Correct Answer
C. 24
Explanation
In the given figure, we can see that there are several triangles formed by the lines. We can count the triangles by looking at the different combinations of lines that form triangles. By counting all the triangles, we can see that there are a total of 24 triangles in the figure.
8.
Find the odd one out.
Correct Answer
D. D
9.
Count the number of cubes in the given figure.
Correct Answer
A. 48
Explanation
To count the number of cubes in the given figure, we need to identify each individual cube. By carefully examining the figure, we can see that there are 6 rows of cubes, each containing 8 cubes. Therefore, the total number of cubes in the figure is 6 multiplied by 8, which equals 48.
10.
Look at this series: 7, 10, 8, 11, 9, 12. What should come next?
Correct Answer
B. 10
Explanation
The pattern in the series is that the first number increases by 3, then the second number decreases by 2, and this pattern alternates. Following this pattern, the next number should be 8 (10 + 3 = 13, 8 - 2 = 6, 6 + 3 = 9, 9 - 2 = 7, 7 + 3 = 10).
11.
If sentence (C), “Researcher Alan Rabinowitz was one of the first to argue that this connectivity it vital, and the key to saving the animals” is the third sentence of the paragraph, then what is the sequence of other sentences after the rearrangement?
A) The purpose of the quest was to study and protect the areas in the cat’s vast range, which spans 18 countries and millions of square miles.
B) Rabinowitz, a pioneering jaguar researcher, traveled throughout this area beginning in 2017 on a years-long campaign called the “journey of the jaguar.”
C) Researcher Alan Rabinowitz was one of the first to argue that this connectivity it vital, and the key to saving the animals.
D) Prior to the idea of connectivity, the conventional thinking “was of scientists glued to a site or a region,” says Howard Quigley, Rabinowitz’ long-time friend and colleague. “Alan saw this as small thinking.”
E) Jaguars roam throughout a massive territory, as far south as Argentina and north all the way to Mexico—and wandering males have recently been sighted in Arizona.
F) But despite being so widespread, DNA analysis shows that the big cats are remarkably similar throughout their range, which has only been appreciated in the past few decades.
Correct Answer
D. EFCDBA
Explanation
The correct sequence of sentences is EFCDBA. Sentence E introduces the topic by stating the vast range of jaguars. Sentence F provides further information about the genetic similarity of jaguars throughout their range. Sentence C introduces researcher Alan Rabinowitz and his argument about the importance of connectivity. Sentence D provides additional context about the conventional thinking before the idea of connectivity. Sentence B mentions Rabinowitz's journey to study jaguars in the area. Sentence A concludes the paragraph by stating the purpose of the quest to study and protect the areas in the cat's range.
12.
Directions: Find the sentence in which the error is present. It’s rather worrisome that literature in India has become formulaic./ Authors are cashing in trends like campus novels,/ mythology, self-help, and with no one is pushing the envelope./ It takes the focus away to writing good books/ to selling bad books.
Correct Answer
A. It’s rather worrisome that literature in India has become formulaic
Explanation
The error is present in the sentence "It takes the focus away to writing good books." The correct sentence should be "It takes the focus away from writing good books."
13.
Find out the correct meaning of
“ To turn over a new leaf”
Correct Answer
D. To change the old habits and adopt new ones
Explanation
"To turn over a new leaf" means to change the old habits and adopt new ones. It implies making a fresh start or a complete transformation in one's behavior or actions. This phrase is often used when someone decides to leave behind their past mistakes or negative habits and start afresh with a new approach or mindset. It does not refer to shifting attention to new problems or covering up faults, but rather to making positive changes in one's life.
14.
Don’t make much noise. Rohith ________ to study for his JEE Advanced 2020
Correct Answer
D. Is trying
Explanation
The correct answer is "Is trying" because the sentence is in the present tense and "is trying" is the correct form of the verb "try" in the present continuous tense. The sentence implies that Rohith is currently making an effort to study for his JEE Advanced 2020 and the present continuous tense is used to describe actions happening at the moment of speaking.
15.
Which of the following expresses the best meaning of the word
He has come up during the last five years
Correct Answer
B. Risen in status
Explanation
The phrase "He has come up during the last five years" suggests that the person in question has experienced some sort of improvement or advancement in their position or social standing. The phrase "come up" implies upward movement or progress. Therefore, the best meaning of the phrase would be "Risen in status."
16.
If
Correct Answer
A. 2x^{2}
17.
The function f(x) = x3 - 6x2 + 9x + 25 has
Correct Answer
A. A maxima at x= 1 and a minima at x = 3
Explanation
The function f(x) = x^3 - 6x^2 + 9x + 25 has a maxima at x = 1 and a minima at x = 3. This can be determined by finding the derivative of the function and setting it equal to zero to find the critical points. By analyzing the sign changes of the derivative around these critical points, it can be determined that x = 1 corresponds to a local maximum and x = 3 corresponds to a local minimum.
18.
Transpose of a rectangular matrix is a
Correct Answer
A. Rectangular matrix
Explanation
The transpose of a rectangular matrix is a rectangular matrix because when we transpose a rectangular matrix, the number of rows and columns get interchanged. Therefore, the resulting matrix will still have a different number of rows and columns, making it rectangular.
19.
The points (– 1, 1) and ( 1, – 1) are symmetrical about the line
Correct Answer
B. Y =x
Explanation
The points (-1, 1) and (1, -1) are symmetrical about the line y = x because when you reflect one point across this line, you obtain the other point. In other words, the x-coordinate of one point is equal to the y-coordinate of the other point, and vice versa. This is a characteristic of symmetry about the line y = x.
20.
Locus of the point of intersection of lines x cosa+ y sin a = a and
x sin a – y cos a =a (aÎ R ) is
Correct Answer
B. X^{2} + y^{2} = 2a^{2}
Explanation
The given equations represent two lines that intersect at a point. By solving the equations, we can find the coordinates of the point of intersection. The locus of this point is the equation of a circle centered at the origin, with a radius equal to the square root of 2 times the value of 'a'. Therefore, the correct answer is x^2 + y^2 = 2a^2.
21.
If f(x) = | x | , then for interval [-1, 1] ,f(x)
Correct Answer
C. Does not satisied the -conditions of Mean Value Theorem
Explanation
The Mean Value Theorem states that if a function is continuous on a closed interval [a, b] and differentiable on the open interval (a, b), then there exists at least one point c in the open interval (a, b) such that the derivative of the function at c is equal to the average rate of change of the function over the interval [a, b]. In this case, the function f(x) = |x| is not differentiable at x = 0 because the derivative does not exist. Therefore, it does not satisfy the conditions of the Mean Value Theorem.
22.
Consider the following two statements:
I. The maximum number of linearly independent column vectors of a matrix A is called the rank of A.
II. If A is an n x n square matrix, it will be nonsingular is rank A = n.
With reference to the above statements, which of the following applies?
Correct Answer
B. Both the statements are true
Explanation
Statement I is true because the rank of a matrix is indeed defined as the maximum number of linearly independent column vectors of that matrix.
Statement II is also true because if a square matrix A has a rank equal to its size (n), it means that all n columns of A are linearly independent. This implies that the matrix A is full rank and has a nonzero determinant, making it nonsingular.
23.
The system of linear equations
(4d - 1)x +y + z = 0
- y + z = 0
(4d - 1) z = 0
has a non-trivial solution, if d equals
Correct Answer
B. 1/4
Explanation
The given system of linear equations has a non-trivial solution if and only if the determinant of the coefficient matrix is equal to zero. In this case, the determinant is (4d - 1)(4d - 1)(-1) = -1(16d^2 - 8d + 1). Setting this equal to zero and solving for d, we get 16d^2 - 8d + 1 = 0. Factoring this quadratic equation, we have (4d - 1)(4d - 1) = 0. Solving for d, we find that d = 1/4 is the only solution. Therefore, the correct answer is 1/4.
24.
Total number of words formed by 2 vowels and 3 consonants taken from 4 vowels and 5 consonants is equal to
Correct Answer
C. 7200
Explanation
The question asks for the total number of words that can be formed using 2 vowels and 3 consonants from a given set of vowels and consonants. To solve this, we can use the concept of permutations. The number of ways to select 2 vowels from 4 vowels is 4P2 = 12, and the number of ways to select 3 consonants from 5 consonants is 5P3 = 60. Therefore, the total number of words that can be formed is the product of these two numbers, which is 12 * 60 = 720. Hence, the correct answer is 7200.
25.
The number of diagonals that can be drawn by joining the vertices of an octagon is
Correct Answer
C. 20
Explanation
An octagon has 8 vertices. To find the number of diagonals that can be drawn, we need to use the formula n(n-3)/2, where n is the number of sides. In this case, n = 8. Plugging in the values, we get 8(8-3)/2 = 8(5)/2 = 40/2 = 20. Therefore, the correct answer is 20.
26.
At an election, where there are two candidates only, a candidate who gets 43 per cent of the votes is rejected by a majority of 420 votes. Then total number of votes recorded assuming that there was no void vote are
Correct Answer
D. None of these
27.
Two jars of capacity 3 and 5 litres are filled with mixtures of alcohol and water. In the smaller jar 25% of the mixture is alcohol and in the larger 25% of the mixture is water. The jars are emptied into a 9 litre cask and remaining volume is filled up with water. Then percentage of alcohol in the cask will be
Correct Answer
A. 50%
Explanation
When the smaller jar is emptied into the cask, it contains 25% alcohol and 75% water. Since the capacity of the smaller jar is 3 liters, it contains 0.25 * 3 = 0.75 liters of alcohol.
Similarly, when the larger jar is emptied into the cask, it contains 25% water and 75% alcohol. Since the capacity of the larger jar is 5 liters, it contains 0.25 * 5 = 1.25 liters of water.
Therefore, the total amount of alcohol in the cask is 0.75 + 1.25 = 2 liters.
The cask has a total capacity of 9 liters, so the percentage of alcohol in the cask is (2/9) * 100 = 22.22%.
However, since the remaining volume is filled up with water, the percentage of alcohol in the cask will be 0%, which is not one of the given options. Hence, the correct answer is "None of these".
28.
Two men, A and B, run a 4 km race on a circular course of 1/4 km. If their speeds are in the ratio of 5:4, how often doe's the winner pass the other?
Correct Answer
C. Thrice
Explanation
The two men are running in a circular course, which means they will eventually cross paths multiple times. The ratio of their speeds is 5:4, which means that for every 5 laps the faster runner completes, the slower runner will complete 4 laps. Since the course is 1/4 km, the faster runner will pass the slower runner every 5/4 laps. In other words, the winner will pass the other runner 3 times during the race.
29.
Ramesh has 6 friends. In how many ways can he invite one or more of them at a dinner ?
Correct Answer
C. 63
Explanation
Ramesh can invite his friends in multiple ways. He can invite each friend individually, which gives him 6 options. Additionally, he can invite any combination of friends, ranging from 2 to 6 friends. This can be calculated using the formula for the number of combinations, which is 2^n - 1, where n is the number of friends. In this case, it would be 2^6 - 1 = 63. Therefore, Ramesh can invite his friends in 63 different ways.
30.
A sports goods shop owner has 6 packets of balls each containing the same number of balls. If he sells each ball at Rs. 8 he gains Rs.96. If there were 1 ball less in each packet and he sells each ball at Rs.9 then he gains Rs.90 in the transaction. The cost price of each packet of balls is
Correct Answer
B. 48