The problem presents an alphabetical series where each term consists of two letters. We need to identify the pattern in both the first and second letters of each term to find the missing term.
C) EV is the correct option because the first letters follow a forward alphabetical sequence (A, B, C, D, E) and the second letters follow a reverse alphabetical sequence (Z, Y, X, W, V).
The question asks to identify the term for saturated hydrocarbons. This requires knowledge of basic organic chemistry classifications, specifically the distinction between saturated and unsaturated hydrocarbons.
Correct Option: B) alkanes are saturated hydrocarbons, characterized by having only carbon-carbon single bonds and the maximum number of hydrogen atoms possible.
The question asks to identify the Scientific Adviser to the Defence Minister and DRDO's DG (Missiles & Strategic Systems) who received the first IEI-IEEE Award for Engineering Excellence-2015 for contributions to missiles and aerospace technologies. This requires knowledge of prominent scientists and their roles/awards in India's defence sector around 2015.
B) Dr. G. Satheesh Reddy was the Scientific Adviser to the Defence Minister and DG (Missiles & Strategic Systems) of DRDO. He received the first IEI-IEEE Award for Engineering Excellence-2015 for his contributions to missiles and aerospace technologies.
If 12x2 - ax + 7 = ax2 + 9x + 3 has only one (repeated) solution, then the positive integral solution of a is:
The given equation is a quadratic equation. For a quadratic equation to have only one (repeated) solution, its discriminant must be equal to zero. We will first rearrange the given equation into the standard quadratic form \(Ax^2 + Bx + C = 0\), then set its discriminant \((B^2 - 4AC)\) to zero and solve for the positive integral value of \(a\).
Rearrange the equation: The given equation is: \[ 12x^2 - ax + 7 = ax^2 + 9x + 3 \] To bring it to the standard quadratic form \(Ax^2 + Bx + C = 0\), move all terms to one side:
\[ 12x^2 - ax^2 - ax - 9x + 7 - 3 = 0 \] \[ (12 - a)x^2 + (-a - 9)x + (7 - 3) = 0 \] \[ (12 - a)x^2 - (a + 9)x + 4 = 0 \]Identify coefficients: Comparing this with the standard form \(Ax^2 + Bx + C = 0\), we have: \(A = 12 - a\) \(B = -(a + 9)\) \(C = 4\)
Apply the discriminant condition: For a quadratic equation to have only one (repeated) solution, its discriminant must be zero. The discriminant is given by \(D = B^2 - 4AC\). Set \(B^2 - 4AC = 0\): \[ (-(a + 9))^2 - 4(12 - a)(4) = 0 \] \[ (a + 9)^2 - 16(12 - a) = 0 \]
Solve for \(a\): Expand and simplify the equation: \[ a^2 + 18a + 81 - (192 - 16a) = 0 \] \[ a^2 + 18a + 81 - 192 + 16a = 0 \] \[ a^2 + 34a - 111 = 0 \] This is another quadratic equation in terms of \(a\). We can solve it using factorization or the quadratic formula. Let's try factorization. We need two numbers that multiply to -111 and add to 34. These numbers are 37 and -3. \[ a^2 + 37a - 3a - 111 = 0 \] \[ a(a + 37) - 3(a + 37) = 0 \] \[ (a - 3)(a + 37) = 0 \] This gives two possible values for \(a\): \(a - 3 = 0 \implies a = 3\) \(a + 37 = 0 \implies a = -37\)
Choose the positive integral solution: The question asks for the positive integral solution of \(a\). Between \(3\) and \(-37\), the positive integral solution is \(a = 3\).
Correct Option: D) 3
Raj takes 2\( \frac{1}{3} \) hours to complete a certain distance at a speed of 51 km/hr. What time would Kiran take to complete the same distance at a speed of 68 km/hr?
2 hours
1\( \frac{3}{4} \) hours
1\( \frac{1}{2} \) hours
1\( \frac{2}{3} \) hours
The problem involves calculating the time taken to cover a certain distance, given speed and time for one person, and then finding the time taken by another person to cover the same distance at a different speed. We will use the fundamental formula: \(\text{Distance} = \text{Speed} \times \text{Time}\).
Raj's time \((T_R)\) is given as \(2\frac{1}{3}\) hours. Convert this mixed fraction to an improper fraction:
\[ T_R = 2\frac{1}{3} = \frac{(2 \times 3) + 1}{3} = \frac{7}{3} \text{ hours} \]Raj's speed \((S_R)\) is given as 51 km/hr.
Now, calculate the distance \((D)\) using the formula \(\text{Distance} = \text{Speed} \times \text{Time}\):
\[ D = S_R \times T_R = 51 \text{ km/hr} \times \frac{7}{3} \text{ hours} \]Simplify the expression:
\[ D = \frac{51 \times 7}{3} = 17 \times 7 = 119 \text{ km} \]Kiran needs to cover the same distance \(D = 119 \text{ km}\).
Kiran's speed \((S_K)\) is given as 68 km/hr.
Use the formula \(\text{Time} = \frac{\text{Distance}}{\text{Speed}}\) to find Kiran's time \((T_K)\):
\[ T_K = \frac{D}{S_K} = \frac{119 \text{ km}}{68 \text{ km/hr}} \]Simplify the fraction. Both 119 and 68 are divisible by 17:
\[ T_K = \frac{119 \div 17}{68 \div 17} = \frac{7}{4} \text{ hours} \]Convert the improper fraction to a mixed fraction:
\[ T_K = \frac{7}{4} = 1\frac{3}{4} \text{ hours} \]B) \(1\frac{3}{4}\) hours is the time Kiran would take to complete the same distance at a speed of 68 km/hr.
This question asks us to identify which of the given options can do the most work. The ability to do work is directly related to the energy possessed by an object. We need to compare the types and magnitudes of energy associated with each option.
Comparing the energies, the squared velocity term in kinetic energy (\(KE = \frac{1}{2}mv^2\)) means that velocity has a much greater impact on energy than mass or height. A bullet, despite its small mass, travels at extremely high velocities (e.g., hundreds of meters per second), leading to very high kinetic energy and thus a greater capacity to do work upon impact compared to the other options.
B) A moving bullet — A moving bullet possesses kinetic energy, which is directly proportional to the square of its velocity (\(KE = \frac{1}{2}mv^2\)). Bullets are designed to travel at extremely high speeds. Even with a relatively small mass, the squared velocity term results in a very large amount of kinetic energy, allowing it to do significant work (e.g., penetrate objects).
To find the least number that must be subtracted from 7577 to get a perfect square, we need to find the largest perfect square less than 7577. This can be done by finding the square root of 7577 and then considering the integer part of the square root.
Estimate the square root of 7577: We can estimate the square root by looking at perfect squares of numbers close to \(\sqrt{7577}\).
So, the square root of 7577 lies between 80 and 90.
Find the exact integer part of the square root: Let's try squaring numbers between 80 and 90.
From these calculations, we see that \(87^2 = 7569\) is the largest perfect square less than 7577. The next perfect square, \(88^2 = 7744\), is greater than 7577.
Calculate the number to be subtracted: To get a perfect square (which is \(7569\)), we need to subtract the difference between 7577 and 7569 from 7577.
\[ \text{Number to be subtracted} = 7577 - 7569 \] \[ \text{Number to be subtracted} = 8 \]Thus, if we subtract 8 from 7577, we get 7569, which is a perfect square (\(87^2\)).
C) 8. Subtracting 8 from 7577 gives 7569, which is \(87^2\), a perfect square.
The problem asks us to evaluate an expression involving an absolute value. We need to perform the operations inside the absolute value first, and then apply the absolute value function.
The expression inside the absolute value bars is \(3(1) - 6\).
\[ 3(1) - 6 = 3 - 6 \]\[ 3 - 6 = -3 \]The absolute value of a number is its distance from zero on the number line, always resulting in a non-negative value. If the number is positive or zero, its absolute value is the number itself. If the number is negative, its absolute value is the positive version of that number.
In this case, we have \(|-3|\).
\[ |-3| = 3 \]Therefore, the value of \(|3(1) - 6|\) is \(3\).
Correct Option: D) 3
This question tests knowledge of the Latin names of common chemical elements, which are often the basis for their chemical symbols. We need to verify the Latin names for Sodium and Silver.
Correct Option: B) Both statements A and B are true
The question asks for the SI unit of electric charge. This is a fundamental concept in physics and electricity. We need to recall the standard SI units for various physical quantities to identify the correct one.
Correct Option: B) Coulomb