Refer to the following letter series and answer the question.
(Left) J B I S O E Z I L U B O P A R D I H O M A K O (Right)
How many such consonants are there, each of which is immediately preceded by a vowel and also immediately followed by a vowel?
The question asks about the trend of the atomic number when moving across a period in the modern periodic table. We need to recall the definition of atomic number and how elements are arranged in the periodic table.
For example, in Period 2, the elements are Lithium (Li, \(Z=3\)), Beryllium (Be, \(Z=4\)), Boron (B, \(Z=5\)), Carbon (C, \(Z=6\)), Nitrogen (N, \(Z=7\)), Oxygen (O, \(Z=8\)), Fluorine (F, \(Z=9\)), and Neon (Ne, \(Z=10\)). As you can see, the atomic number increases by one unit from left to right.
Correct Option: D) The atomic number increases by one unit. This statement accurately describes the trend of atomic number across a period in the modern periodic table.
Study the given table and answer the question that follows.
The table shows percentage of marks obtained by a candidate in five subjects and the weightage given to the subjects in an examination.
| Subject | English | Hindi | Maths | Social Studies | Science |
| Marks Percentage | 90 | 92 | 93 | 78 | 86 |
| Weightage to subjects | 2 | 2 | 3 | 1 | 2 |
Find the difference between the weighted average and the average if all subjects had equal weightage.
To solve this problem, we need to calculate two types of averages: the weighted average and the simple average (average with equal weightage). Then, we will find the difference between these two values.
From the table, we have:
Sum of (Marks Percentage \(\times\) Weightage):
\[ 180 + 184 + 279 + 78 + 172 = 893 \]Sum of Weightage:
\[ 2 + 2 + 3 + 1 + 2 = 10 \]Weighted Average:
\[ \text{Weighted Average} = \frac{893}{10} = 89.3\% \]Sum of Marks Percentages:
\[ 90 + 92 + 93 + 78 + 86 = 439 \]Number of subjects = \(5\)
Simple Average:
\[ \text{Simple Average} = \frac{439}{5} = 87.8\% \]A) 1.5 % is the correct difference between the weighted average and the average if all subjects had equal weightage.
If \(\sqrt{21}\) = 4.58, then the value of \(\sqrt{\frac{7}{3}}\), correct to 3 decimal places, is:
The problem asks us to find the value of \(\sqrt{\frac{7}{3}}\) given that \(\sqrt{21} = 4.58\). We can simplify the expression \(\sqrt{\frac{7}{3}}\) by rationalizing the denominator or by manipulating it to involve \(\sqrt{21}\).
Thus, the value of \(\sqrt{\frac{7}{3}}\) correct to 3 decimal places is 1.527.
Correct Option: D) 1.527
The question asks to identify the correct statement regarding the biodegradability and recyclability of common materials like plastics and paper. We need to evaluate each option based on scientific understanding of these materials.
Correct Option: D) Paper is biodegradable.
Select the option that represents the letters that, when placed from left to right in the same sequence in the blanks below, will complete the letter series.
D _ B _ A _ C _ _ G F _ E _ _ H
The problem asks us to identify the sequence of letters that, when inserted into the blanks, completes a logical letter series. We need to look for a pattern in the given letters and the blanks.
Let's insert these letters into the blanks:
Original: D _ B _ A _ C _ _ G F _ E _ _ H
Insert C: D C B _ A _ C _ _ G F _ E _ _ H
Insert A: D C B A A _ C _ _ G F _ E _ _ H
Insert B: D C B A A B C _ _ G F _ E _ _ H
Insert D: D C B A A B C D _ G F _ E _ _ H
Insert H: D C B A A B C D H G F _ E _ _ H
Insert E: D C B A A B C D H G F E E _ _ H
Insert F: D C B A A B C D H G F E E F _ H
Insert G: D C B A A B C D H G F E E F G H
The completed series is: D C B A A B C D H G F E E F G H
This series can be broken into four groups of four letters:
This shows a clear and consistent pattern of reversed alphabetical order followed by forward alphabetical order, using two sets of four consecutive letters (A-D and E-H).
C) CABDHEFG
When the letters CABDHEFG are placed in the blanks, the series becomes D C B A A B C D H G F E E F G H. This series follows a logical pattern of alternating reversed and forward alphabetical sequences of four letters each: (D C B A), (A B C D), (H G F E), (E F G H).
The question asks why Plaster of Paris (PoP) should be stored in sealed containers. This implies that PoP reacts with something in the air, leading to an undesirable change. We need to identify this reaction and its product.
A) It turns into a hard solid after reacting with moisture present in air. This is the correct explanation. Plaster of Paris (calcium sulfate hemihydrate) reacts with atmospheric moisture to form gypsum (calcium sulfate dihydrate), which is a hard, solid mass. This reaction causes the PoP to lose its utility, hence it must be stored in sealed, moisture-proof containers.
If one of the roots of a quadratic equation with rational coefficients is 2 + \(\sqrt{3}\), then the quadratic equation is given as ______.
x2 = 2 - \(\sqrt{3}\)
x2 - 4x + 1 = 0
x2 + 4x - 1 = 0
x2 - 2 = 0
When a quadratic equation has rational coefficients and one of its roots is irrational (involving a square root), the other root must be its conjugate. We can then use the relationships between roots and coefficients (sum of roots and product of roots) to form the quadratic equation.
Identify the given root: We are given that one root of the quadratic equation is \(x_1 = 2 + \sqrt{3}\).
Determine the second root: Since the coefficients of the quadratic equation are rational, if one root is \(a + \sqrt{b}\), the other root must be its conjugate, \(a - \sqrt{b}\). Therefore, the second root is \(x_2 = 2 - \sqrt{3}\).
Calculate the sum of the roots: \[ \text{Sum of roots} = x_1 + x_2 = (2 + \sqrt{3}) + (2 - \sqrt{3}) = 2 + 2 + \sqrt{3} - \sqrt{3} = 4 \]
Calculate the product of the roots: \[ \text{Product of roots} = x_1 \cdot x_2 = (2 + \sqrt{3})(2 - \sqrt{3}) \] This is in the form \((a+b)(a-b) = a^2 - b^2\). \[ = 2^2 - (\sqrt{3})^2 = 4 - 3 = 1 \]
Form the quadratic equation: A quadratic equation can be written in the form \(x^2 - (\text{Sum of roots})x + (\text{Product of roots}) = 0\). Substituting the calculated sum and product: \[ x^2 - (4)x + (1) = 0 \] \[ x^2 - 4x + 1 = 0 \]
Correct Option: B) x 2 - 4x + 1 = 0
The question describes a phenomenon where a beam of light becomes visible in a medium that is not perfectly transparent, such as dusty air. This visibility is due to the interaction of light with the particles present in the medium. We need to identify the optical phenomenon responsible for this effect.
A) scattering — Scattering is the process by which light or other radiation is deflected or diffused by encountering particles or other inhomogeneities in the medium. In the given scenario, the dust particles in the air scatter the light from the car's headlights, making the beam visible. This is a common observation and is also known as the Tyndall effect when observed in colloidal dispersions or suspensions like dusty air.
If x+y+z=0 and x2+y2+z2=36, then the value of xy+yz+zx is:
This problem involves algebraic identities. We are given two equations relating three variables \(x\), \(y\), and \(z\), and we need to find the value of an expression involving their products. The key is to use the algebraic identity for the square of the sum of three variables.
The square of the sum of three variables \(x\), \(y\), and \(z\) is given by the identity:
\[ (x+y+z)^2 = x^2 + y^2 + z^2 + 2(xy+yz+zx) \]We are given:
Substitute these values into the identity:
\[ (0)^2 = 36 + 2(xy+yz+zx) \]This simplifies to:
\[ 0 = 36 + 2(xy+yz+zx) \]Subtract 36 from both sides:
\[ -36 = 2(xy+yz+zx) \]Divide by 2:
\[ xy+yz+zx = \frac{-36}{2} \]\[ xy+yz+zx = -18 \]A) -18 is the correct value derived from the algebraic identity and the given conditions.