This problem involves understanding directions and relative positioning. We need to determine the waiter's facing direction based on Latika's facing direction and the angle at which the waiter stands relative to Latika's right.
A) South
As explained in the step-by-step analysis, if Latika is facing West, her right is North. If the waiter stands 90° to her right (i.e., to her North) and is facing her to take the order, the waiter must be facing South.
If + means ÷, ÷ means -, - means ×, × means +, then find the value of the following expression:
84 + 3 ÷ 4 - 6 × 12 =?
This problem involves substituting given symbol meanings into an expression and then evaluating it using the order of operations (BODMAS/PEMDAS).
+ means ÷÷ means -- means ×× means +A) 16 is the correct value of the expression after substituting the new meanings of the symbols and applying the order of operations.
The question asks to identify the Indian gymnast who won a gold medal at the 2018 FIG Artistic Gymnastics World Challenge Cup. This requires knowledge of significant achievements of Indian gymnasts in international competitions.
Correct Option: B) Dipa Karmakar won the gold medal in the vault event at the 2018 FIG Artistic Gymnastics World Challenge Cup held in Mersin, Turkey. This was a significant milestone for Indian gymnastics.
To find the total distance, we need to use the relationship between distance, speed, and time. The journey is divided into two equal halves of distance, each covered at a different speed. We will calculate the time taken for each half and sum them up to match the given total time. Then, we can solve for the total distance.
Let the total distance of the journey be \(D\) km.
The car covers half the distance at 40 km/hr. So, the first half distance is \(\frac{D}{2}\) km.
Time taken for the first half (\(t_1\)) is given by:
\[ t_1 = \frac{\text{Distance}}{\text{Speed}} = \frac{D/2}{40} = \frac{D}{80} \text{ hours} \]The car covers the other half distance at 60 km/hr. So, the second half distance is also \(\frac{D}{2}\) km.
Time taken for the second half (\(t_2\)) is given by:
\[ t_2 = \frac{\text{Distance}}{\text{Speed}} = \frac{D/2}{60} = \frac{D}{120} \text{ hours} \]The total time taken for the entire journey is given as 8 hours.
So, \(t_1 + t_2 = 8\).
\[ \frac{D}{80} + \frac{D}{120} = 8 \]To solve for \(D\), find a common denominator for 80 and 120. The least common multiple (LCM) of 80 and 120 is 240.
\[ \frac{3D}{240} + \frac{2D}{240} = 8 \] \[ \frac{5D}{240} = 8 \]Now, isolate \(D\):
\[ 5D = 8 \times 240 \] \[ 5D = 1920 \] \[ D = \frac{1920}{5} \] \[ D = 384 \text{ km} \]A) The calculated total distance is 384 km, which matches option A.
The question asks to identify the state where Vansda National Park is located. This requires knowledge of the geographical distribution of National Parks in India.
Correct Option: D) Gujarat
Vansda National Park is located in the Navsari district of Gujarat, India. It is known for its dense moist deciduous forest and rich biodiversity, including leopards, hyenas, and various bird species.
The question asks to identify the scientist who provided the basic theory about the nature of matter. This refers to the atomic theory, which explains matter in terms of atoms and their properties.
Correct Option: C) John Dalton is renowned for his atomic theory, which laid the foundation for modern chemistry by explaining the nature of matter in terms of atoms. His postulates, though refined over time, were revolutionary in providing a scientific basis for understanding chemical reactions and the composition of substances.
The question asks to identify the acid predominantly present in tomatoes. This requires knowledge of common organic acids found in various fruits and vegetables.
Tomatoes are known to contain several organic acids, with oxalic acid being one of the prominent ones, especially in terms of its concentration and impact on flavor and nutrition.
Oxalic acid is naturally found in many plants, including leafy greens, vegetables, fruits, nuts, and seeds. Tomatoes contain oxalic acid, which contributes to their characteristic taste. While other acids like citric acid and malic acid are also present, oxalic acid is a significant component.
Who is the Director of the movie "Newton", released in 2017?
Saket Chaudhary
Anurag Kashyap
Amit V. Masurkar
K. Raghavender Rao
The question asks to identify the director of the critically acclaimed 2017 Indian film "Newton". This is a factual recall question related to Indian cinema, often tested in general knowledge sections of competitive exams.
The director of the movie "Newton" (2017) is Amit V. Masurkar.
C) Amit V. Masurkar is the director of the film "Newton", released in 2017. The film starred Rajkummar Rao in the lead role and was highly praised for its satirical take on the Indian electoral system.
The question asks to identify the metal commonly used for making electrical wires. This requires knowledge of the electrical conductivity and ductility of various metals.
Correct Option: A) Copper is an excellent conductor of electricity, second only to silver. It is also highly ductile, allowing it to be easily drawn into thin wires. Furthermore, it is relatively inexpensive compared to silver, making it the most practical and widely used metal for electrical wiring in homes, industries, and power transmission.
If 4x3 − 2x² + 5x − 8 is divided by (x−2), what will be the remainder?
To find the remainder when a polynomial \(P(x)\) is divided by a linear factor \((x-a)\), we can use the Remainder Theorem. The Remainder Theorem states that if a polynomial \(P(x)\) is divided by \((x-a)\), then the remainder is \(P(a)\).
The given polynomial is \(P(x) = 4x^3 - 2x^2 + 5x - 8\).
The divisor is \((x-2)\).
According to the Remainder Theorem, if \(P(x)\) is divided by \((x-a)\), the remainder is \(P(a)\).
In this case, comparing \((x-2)\) with \((x-a)\), we find that \(a = 2\).
Therefore, the remainder will be \(P(2)\).
Substitute \(x=2\) into the polynomial \(P(x)\):
\[ P(2) = 4(2)^3 - 2(2)^2 + 5(2) - 8 \]Perform the calculations:
\[ P(2) = 4(8) - 2(4) + 10 - 8 \]\[ P(2) = 32 - 8 + 10 - 8 \]\[ P(2) = 24 + 10 - 8 \]\[ P(2) = 34 - 8 \]\[ P(2) = 26 \]The remainder when \(4x^3 - 2x^2 + 5x - 8\) is divided by \((x-2)\) is 26.
B) 26 — This is the correct remainder obtained by applying the Remainder Theorem.