nikunjwadgeri60/mydataset · Datasets at Hugging Face

entry stringlengths 86 1.26k	text stringclasses 1 value
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question The solution area of the line would not include the origin, as 0 ≥ 1 is not true. , think step by step [/INST] , The answer is N/A
[INST] help me answer this question (1 – i)4, think step by step [/INST] (1 – i)4 = [(1 – i)2]2 = [1 + i2 – 2i]2 = [1 – 1 – 2i]2 = (-2i)2 = 4(-1) = -4 + 0i , The answer is -4 + 0i
[INST] help me answer this question Is it a statement?, think step by step [/INST] The day that is being referred to is not evident from the sentence. , The answer is No, it is not a statement.
[INST] help me answer this question What is the probability of getting 3 heads?, think step by step [/INST] , The answer is The probability of getting 3 heads is 1/8.
[INST] help me answer this question Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6., think step by step [/INST] , The answer is The coefficient of x2 in the expansion (1 + x)m is mC2 when m >= 2. So, m should be 2 or any positive value greater than or equal to 2.
[INST] help me answer this question 3x – 2 < 2x + 1, think step by step [/INST] (Blank) , The answer is x < 3
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question Given x – 2y ≤ 3 , think step by step [/INST] , The answer is N/A
[INST] help me answer this question What is the length of the major axis?, think step by step [/INST] , The answer is Length of major axis = 2a = 2 (5) = 10
[INST] help me answer this question Write the fraction 5/6 as a decimal., think step by step [/INST] To convert a fraction to a decimal, we divide the numerator by the denominator. In this case, 5 divided by 6 equals 0.833333333333 when expressed as a repeating decimal. , The answer is The fraction 5/6 as a decimal is 0.833333333333.
[INST] help me answer this question Factorize the given expression: 12x² + 16x, think step by step [/INST] , The answer is The factorized form of the given expression is 4x(3x + 4).
[INST] help me answer this question (iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}, think step by step [/INST] Not every circle in the plane is a circle with radius 1 unit in the same plane. , The answer is {x: x is a circle in the plane} ⊄ {x: x is a circle in the same plane with radius 1 unit}
[INST] help me answer this question If you do not have winter clothes, then you do not live in Delhi., think step by step [/INST] This is the contrapositive of the statement in (a). , The answer is
[INST] help me answer this question (Explore – NCERT Class 11 Solutions), think step by step [/INST] The data contains a link to explore NCERT Class 11 Solutions, but does not include the solutions directly. , The answer is Not provided in the data.
[INST] help me answer this question Find the derivative of (iii) x-3 (5 + 3x), think step by step [/INST] , The answer is The derivative of x-3 (5 + 3x) is not provided.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question (iii) Subsets of {1, 2, 3} are, think step by step [/INST] , The answer is Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question Find the discriminant of the quadratic equation x^2 + x/√2 + 1 = 0, think step by step [/INST] , The answer is The discriminant (D) of the quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac. For the given equation, a = 1, b = 1/√2, and c = 1.
[INST] help me answer this question Determine which number is larger, (1.1)10000 or 1000, using the binomial theorem., think step by step [/INST] The binomial theorem is applied to (1.1)10000 to compare. , The answer is (1.1)10000 > 1000
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question What is the value of the expression ((5!)/(3!)) * (1/2!) when simplified?, think step by step [/INST] The value of the expression can be simplified by cancelling out the common factors in the numerator and denominator. The expression reduces to (5!/(3!2!)) = (54)/(2*1) = 10. , The answer is The value of the expression is 10.
[INST] help me answer this question 10. sin x = 1/4, x in quadrant II, think step by step [/INST] N/A , The answer is tan x/2 = sin x/2 / cos x/2
[INST] help me answer this question (-2 – 1/3i)3, think step by step [/INST] Not available in the text , The answer is -22/3 – 107/27i
[INST] help me answer this question What is the probability of getting no head?, think step by step [/INST] , The answer is The probability of getting no head is 1/8.
[INST] help me answer this question What is the standard deviation for the given data?, think step by step [/INST] , The answer is Standard Deviation = 5.553
[INST] help me answer this question What is the role of the ribosome?, think step by step [/INST] Ribosomes are crucial for protein synthesis, facilitating the translation of genetic information into functional proteins that are necessary for various cellular processes and functions. , The answer is The ribosome is a complex cellular structure composed of proteins and rRNA. Its primary role is to serve as the site of protein synthesis within a cell. Ribosomes read the genetic information encoded in mRNA and catalyze the formation of peptide bonds between amino acids, leading to the production of new proteins.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question Is it a statement?, think step by step [/INST] It is not evident to whom 'he' is referred. , The answer is No, it is not a statement.
[INST] help me answer this question 5 men can occupy 5 seats and ways they can be seated = 5P5, think step by step [/INST] We have 5 men to be seated in 5 odd places. The number of permutations of n objects is nPn = n!. So, the number of ways to seat 5 men in 5 odd places is 5P5 = 5! = 5 * 4 * 3 * 2 * 1 = 120. , The answer is Ways men can be seated = 120
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question Question : 2x + y >= 6, think step by step [/INST] N/A , The answer is The solution region of the given inequality is above the line 2x + y = 6. (Away from the origin).
[INST] help me answer this question Does the equation of the circle becomes when h = -2?, think step by step [/INST] , The answer is (x + 2)2 + y2 = 25
[INST] help me answer this question How many sets are there in this exercise?, think step by step [/INST] There are 9 questions in the exercise, and each question (and its corresponding subparts) represents a set. , The answer is There are 9 sets in this exercise.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question N/A, think step by step [/INST] Class 11 Maths NCERT supplementary or miscellaneous exercise solutions PDFs are provided here. , The answer is N/A
[INST] help me answer this question a^2 + b^2 = c^2, think step by step [/INST] , The answer is This equation represents one of the properties of a right-angled triangle, where a, b, and c are the lengths of the sides.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question y2 = 12x, think step by step [/INST] Since the coefficient of x is positive, the parabola opens towards the right. On comparing the given equation with y2 = 4ax, we get 4a = 12, which gives a = 3. Thus, the coordinates of the focus are (a, 0) = (3, 0), and the equation of directrix is x = -a, which gives x = -3. The length of the latus rectum is 4a = 12. , The answer is The coordinates of the focus are (3, 0), the axis of the parabola is the x-axis, the equation of the directrix is x = -3, and the length of the latus rectum is 12.
[INST] help me answer this question What is the value of x in the equation 3x + 4 = 20?, think step by step [/INST] To find the value of x, you need to isolate x. To do this, subtract 4 from both sides of the equation to get 3x = 16, and then divide both sides by 3 to get x = 16/3 = 6. , The answer is The value of x is 6.
[INST] help me answer this question 3(x – 2)/5 ≤ 5 (2 – x)/3, think step by step [/INST] The solutions of the given inequality are defined by all the real numbers less than or equal to 2. Hence, the required solution set is (-∞, 2]. , The answer is x ≤ 2
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question 9. cos x = -1/3, x in quadrant III, think step by step [/INST] N/A , The answer is tan x/2 = sin x/2 / cos x/2
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question How many terms of G.P. 3, 3^2, 3^3, … are needed to give the sum 120?, think step by step [/INST] , The answer is The number of terms.
[INST] help me answer this question Which firm, A or B, shows greater variability in individual wages?, think step by step [/INST] , The answer is Firm B shows greater variability in individual wages with a variance of 121 compared to firm A's variance of 100.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question Given x2/16 + y2/9 = 1, what is the length of the major axis?, think step by step [/INST] , The answer is Length of major axis = 2a = 2 (4) = 8
[INST] help me answer this question Find the value of sin 765°., think step by step [/INST] We know that the values of sin x repeat after an interval of 2π or 360°. Therefore, sin 765° = sin (45° + 720°) = sin 45°. Hence, sin 765° = 1/√2. , The answer is The value of sin 765° is 1/√2.
[INST] help me answer this question Find the variance for the data 4, 7., think step by step [/INST] The variance is calculated as the sum of (xi - x_mean)^2 divided by the number of observations, which comes out to be 2.25. , The answer is The variance of the data is 2.25.
[INST] help me answer this question What is the negation of the statement `in India, there exists a state which does not have a capital`?, think step by step [/INST] , The answer is The negation of this statement is: `For every state in India, it has a capital.`
[INST] help me answer this question Find the value of y in the following equation: 2(3y - 4) = 16, think step by step [/INST] To find the value of y, we first distribute the 2 to both terms inside the parentheses, which gives us 6y - 8 = 16. Then, we add 8 to both sides to get 6y = 24. Finally, we divide both sides by 6 to get y = 4. , The answer is The value of y is 2.
[INST] help me answer this question Hence, the shaded area in the graph is the required solution area for the given inequalities. , think step by step [/INST] , The answer is N/A
[INST] help me answer this question Does the origin (0, 0) lie in the line graph of y > x?, think step by step [/INST] Solving for y = x, we get x= 0, y = 0, which are the coordinates of the origin. , The answer is Yes, the origin lies on the line graph.
[INST] help me answer this question (ii) (–3, 7, 2) and (2, 4, –1), think step by step [/INST] , The answer is √43 units
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question What is the first inequality given in the problem?, think step by step [/INST] , The answer is x + 2y ≤ 10
[INST] help me answer this question Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b^2}. Are the following true? (i) (a, a) ∈ R, for all a ∈ N, think step by step [/INST] , The answer is No, it is not true that (a, a) ∈ R, for all a ∈ N.
[INST] help me answer this question Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0., think step by step [/INST] This is the solution for finding the coordinates of the foot of perpendicular from a given point to a given line. , The answer is The coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0 are (68/25, -49/25)
[INST] help me answer this question Is it a statement?, think step by step [/INST] The product of (-1) and 8 is -8, but the sentence states the product to be -1. , The answer is No, it is not a statement.
[INST] help me answer this question (subpart) Is BC = AD?, think step by step [/INST] BC ≠ AD; BC = √43, and AD = √30 , The answer is No
[INST] help me answer this question In which direction is the solution area for the second inequality?, think step by step [/INST] , The answer is The solution area for the second inequality is towards the right of the line graph.
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r., think step by step [/INST] , The answer is By using the general term Tr+1 = nCr an-r br, we can find that n = 7 and r = 3.
[INST] help me answer this question Find the distance between parallel lines 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0, think step by step [/INST] N/A , The answer is The distance between parallel lines is 65/17.
[INST] help me answer this question According to the question, the entire students should have an average of at least 60 marks, think step by step [/INST] To find the minimum number of marks, we need to first find the total marks of all students and then divide it by the number of students. After simplification, we get x ≥ 35. , The answer is The minimum number of marks that each student should obtain is 35.
[INST] help me answer this question What is the mean for Y?, think step by step [/INST] , The answer is The mean (ȳ) for Y is 105.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question Find the slope of the line BC., think step by step [/INST] , The answer is The slope of the line BC (m2) = (-1-5)/(-1-3) = -6/-4 = 3/2
[INST] help me answer this question Find the domain and range of the following real function., think step by step [/INST] , The answer is Given, f(x) = –\|x\|, x ∈ R The domain of f is R because f(x) is defined for x ∈ R. The range of f(x) = –\|x\| is all real numbers except positive real numbers. Therefore, the range of f is given by (–∞, 0].
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question Find the equation of the line passing through the point (2, 2√3) and inclined with the x-axis at an angle of 75o., think step by step [/INST] , The answer is The equation of the line is (2 + √3) x – y – 4 = 0.
[INST] help me answer this question 1.(b) Passing through (0, 0) with slope m., think step by step [/INST] , The answer is Given: Point (0, 0) and slope, m = m We know that the point (x, y) lies on the line with slope m through the fixed point (x0, y0), if and only if, its coordinates satisfy the equation y – y0 = m (x – x0) So, y – 0 = m (x – 0) y = mx y – mx = 0 ∴ The equation of the line is y – mx = 0.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question (subpart) Is AB = CD?, think step by step [/INST] AB = CD = 6 , The answer is Yes
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question Are the following pair of statements a negation of each other, give reasons for the answer. (i) x + y = y + x is true for every real number x and y. (ii) There exists real numbers x and y for which x + y = y + x., think step by step [/INST] , The answer is The negation of the (i) statement is: `There exists real numbers x and y for which x + y ≠ y + x.` This statement is not the same as the (ii) statement, hence the given statements are not a negation of each other.
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question If `f(x) = x^2 - 3x + 2`, find `f'(x)`., think step by step [/INST] , The answer is `f'(x) = 2x - 3`.
[INST] help me answer this question How many terms of the A.P. -6, -11/2, -5, … are needed to give the sum –25?, think step by step [/INST] We used the sum formula for an A.P. and solved for the number of terms to determine the number of terms needed. , The answer is We need 8 terms to get the sum of -25.
[INST] help me answer this question For the given data, find the mean and standard deviation using the short-cut method., think step by step [/INST] Refer to the calculations in the answer. , The answer is The mean is 64 and the standard deviation is 1.691.
[INST] help me answer this question Find the value of z in the following equation: 5(2z + 3) - 10 = 35, think step by step [/INST] To find the value of z, we first distribute the 5 to both terms inside the parentheses, which gives us 10z + 15 - 10 = 35. Then, we simplify the expression on the left side of the equation to get 10z + 5 = 35. Next, we subtract 5 from both sides to get 10z = 30. Finally, we divide both sides by 10 to get z = 3. , The answer is The value of z is 3.
[INST] help me answer this question Find the equation of the circle with Centre (-2, 3) and radius 4., think step by step [/INST] , The answer is x2 + y2 + 4x – 6y – 3 = 0
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question Calculate the mean deviation about the median for the data: 36, 42, 45, 46, 46, 49, 51, 53, 60, 72., think step by step [/INST] First, we find the median (which is 47.5), then we calculate the absolute deviations from the median, and finally, we find the mean of these deviations. , The answer is The mean deviation about the median for the given data is 7.
[INST] help me answer this question Find R – Q, think step by step [/INST] R – Q represents the set of elements that are present in R but not in Q. Here, R is the set of real numbers and Q is the set of rational numbers. Therefore, R – Q is the set of irrational numbers. , The answer is Set of irrational numbers
[INST] help me answer this question Write the balanced chemical equation for the complete combustion of methane., think step by step [/INST] , The answer is The balanced chemical equation is as follows: CH4 + 2O2 -> CO2 + 2H2O
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.
[INST] help me answer this question Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?, think step by step [/INST] When we substitute x = -2.5 and y = 3.5 in the equation x2 + y2 = 25, we get x2 + y2 > 25, which implies that the point lies outside the circle. , The answer is The point (-2.5, 3.5) lies outside the circle x2 + y2 = 25.
[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.
[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.
[INST] help me answer this question Question: 7 ≤ (3x + 11)/2 ≤ 11, think step by step [/INST] The given inequality is 7 ≤ (3x + 11)/2 ≤ 11. After solving this inequality, we get x ∈ [1, 11/3]. , The answer is The solutions of the given inequality are all real numbers x greater than or equal to 1 but less than or equal to 11/3.
[INST] help me answer this question Find the derivative of the following functions. (vii) 2 tan x – 7 sec x, think step by step [/INST] , The answer is The derivative of 2 tan x – 7 sec x is not provided.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question The solution area of the line would not include the origin, as 0 ≥ 1 is not true. , think step by step [/INST] , The answer is N/A

[INST] help me answer this question (1 – i)4, think step by step [/INST] (1 – i)4 = [(1 – i)2]2 = [1 + i2 – 2i]2 = [1 – 1 – 2i]2 = (-2i)2 = 4(-1) = -4 + 0i , The answer is -4 + 0i

[INST] help me answer this question Is it a statement?, think step by step [/INST] The day that is being referred to is not evident from the sentence. , The answer is No, it is not a statement.

[INST] help me answer this question What is the probability of getting 3 heads?, think step by step [/INST] , The answer is The probability of getting 3 heads is 1/8.

[INST] help me answer this question Find a positive value of m for which the coefficient of x2 in the expansion (1 + x)m is 6., think step by step [/INST] , The answer is The coefficient of x2 in the expansion (1 + x)m is mC2 when m >= 2. So, m should be 2 or any positive value greater than or equal to 2.

[INST] help me answer this question 3x – 2 < 2x + 1, think step by step [/INST] (Blank) , The answer is x < 3

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Given x – 2y ≤ 3 , think step by step [/INST] , The answer is N/A

[INST] help me answer this question What is the length of the major axis?, think step by step [/INST] , The answer is Length of major axis = 2a = 2 (5) = 10

[INST] help me answer this question Write the fraction 5/6 as a decimal., think step by step [/INST] To convert a fraction to a decimal, we divide the numerator by the denominator. In this case, 5 divided by 6 equals 0.833333333333 when expressed as a repeating decimal. , The answer is The fraction 5/6 as a decimal is 0.833333333333.

[INST] help me answer this question Factorize the given expression: 12x² + 16x, think step by step [/INST] , The answer is The factorized form of the given expression is 4x(3x + 4).

[INST] help me answer this question (iv) {x: x is a circle in the plane} … {x: x is a circle in the same plane with radius 1 unit}, think step by step [/INST] Not every circle in the plane is a circle with radius 1 unit in the same plane. , The answer is {x: x is a circle in the plane} ⊄ {x: x is a circle in the same plane with radius 1 unit}

[INST] help me answer this question If you do not have winter clothes, then you do not live in Delhi., think step by step [/INST] This is the contrapositive of the statement in (a). , The answer is

[INST] help me answer this question (Explore – NCERT Class 11 Solutions), think step by step [/INST] The data contains a link to explore NCERT Class 11 Solutions, but does not include the solutions directly. , The answer is Not provided in the data.

[INST] help me answer this question Find the derivative of (iii) x-3 (5 + 3x), think step by step [/INST] , The answer is The derivative of x-3 (5 + 3x) is not provided.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question (iii) Subsets of {1, 2, 3} are, think step by step [/INST] , The answer is Φ, {1}, {2}, {3}, {1, 2}, {2, 3}, {1, 3}, and {1, 2, 3}.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Find the discriminant of the quadratic equation x^2 + x/√2 + 1 = 0, think step by step [/INST] , The answer is The discriminant (D) of the quadratic equation ax^2 + bx + c = 0 is given by the formula D = b^2 - 4ac. For the given equation, a = 1, b = 1/√2, and c = 1.

[INST] help me answer this question Determine which number is larger, (1.1)10000 or 1000, using the binomial theorem., think step by step [/INST] The binomial theorem is applied to (1.1)10000 to compare. , The answer is (1.1)10000 > 1000

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question What is the value of the expression ((5!)/(3!)) * (1/2!) when simplified?, think step by step [/INST] The value of the expression can be simplified by cancelling out the common factors in the numerator and denominator. The expression reduces to (5!/(3!*2!)) = (5*4)/(2*1) = 10. , The answer is The value of the expression is 10.

[INST] help me answer this question 10. sin x = 1/4, x in quadrant II, think step by step [/INST] N/A , The answer is tan x/2 = sin x/2 / cos x/2

[INST] help me answer this question (-2 – 1/3i)3, think step by step [/INST] Not available in the text , The answer is -22/3 – 107/27i

[INST] help me answer this question What is the probability of getting no head?, think step by step [/INST] , The answer is The probability of getting no head is 1/8.

[INST] help me answer this question What is the standard deviation for the given data?, think step by step [/INST] , The answer is Standard Deviation = 5.553

[INST] help me answer this question What is the role of the ribosome?, think step by step [/INST] Ribosomes are crucial for protein synthesis, facilitating the translation of genetic information into functional proteins that are necessary for various cellular processes and functions. , The answer is The ribosome is a complex cellular structure composed of proteins and rRNA. Its primary role is to serve as the site of protein synthesis within a cell. Ribosomes read the genetic information encoded in mRNA and catalyze the formation of peptide bonds between amino acids, leading to the production of new proteins.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Is it a statement?, think step by step [/INST] It is not evident to whom 'he' is referred. , The answer is No, it is not a statement.

[INST] help me answer this question 5 men can occupy 5 seats and ways they can be seated = 5P5, think step by step [/INST] We have 5 men to be seated in 5 odd places. The number of permutations of n objects is nPn = n!. So, the number of ways to seat 5 men in 5 odd places is 5P5 = 5! = 5 * 4 * 3 * 2 * 1 = 120. , The answer is Ways men can be seated = 120

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Question : 2x + y >= 6, think step by step [/INST] N/A , The answer is The solution region of the given inequality is above the line 2x + y = 6. (Away from the origin).

[INST] help me answer this question Does the equation of the circle becomes when h = -2?, think step by step [/INST] , The answer is (x + 2)2 + y2 = 25

[INST] help me answer this question How many sets are there in this exercise?, think step by step [/INST] There are 9 questions in the exercise, and each question (and its corresponding subparts) represents a set. , The answer is There are 9 sets in this exercise.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question N/A, think step by step [/INST] Class 11 Maths NCERT supplementary or miscellaneous exercise solutions PDFs are provided here. , The answer is N/A

[INST] help me answer this question a^2 + b^2 = c^2, think step by step [/INST] , The answer is This equation represents one of the properties of a right-angled triangle, where a, b, and c are the lengths of the sides.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question y2 = 12x, think step by step [/INST] Since the coefficient of x is positive, the parabola opens towards the right. On comparing the given equation with y2 = 4ax, we get 4a = 12, which gives a = 3. Thus, the coordinates of the focus are (a, 0) = (3, 0), and the equation of directrix is x = -a, which gives x = -3. The length of the latus rectum is 4a = 12. , The answer is The coordinates of the focus are (3, 0), the axis of the parabola is the x-axis, the equation of the directrix is x = -3, and the length of the latus rectum is 12.

[INST] help me answer this question What is the value of x in the equation 3x + 4 = 20?, think step by step [/INST] To find the value of x, you need to isolate x. To do this, subtract 4 from both sides of the equation to get 3x = 16, and then divide both sides by 3 to get x = 16/3 = 6. , The answer is The value of x is 6.

[INST] help me answer this question 3(x – 2)/5 ≤ 5 (2 – x)/3, think step by step [/INST] The solutions of the given inequality are defined by all the real numbers less than or equal to 2. Hence, the required solution set is (-∞, 2]. , The answer is x ≤ 2

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question 9. cos x = -1/3, x in quadrant III, think step by step [/INST] N/A , The answer is tan x/2 = sin x/2 / cos x/2

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question How many terms of G.P. 3, 3^2, 3^3, … are needed to give the sum 120?, think step by step [/INST] , The answer is The number of terms.

[INST] help me answer this question Which firm, A or B, shows greater variability in individual wages?, think step by step [/INST] , The answer is Firm B shows greater variability in individual wages with a variance of 121 compared to firm A's variance of 100.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Given x2/16 + y2/9 = 1, what is the length of the major axis?, think step by step [/INST] , The answer is Length of major axis = 2a = 2 (4) = 8

[INST] help me answer this question Find the value of sin 765°., think step by step [/INST] We know that the values of sin x repeat after an interval of 2π or 360°. Therefore, sin 765° = sin (45° + 720°) = sin 45°. Hence, sin 765° = 1/√2. , The answer is The value of sin 765° is 1/√2.

[INST] help me answer this question Find the variance for the data 4, 7., think step by step [/INST] The variance is calculated as the sum of (xi - x_mean)^2 divided by the number of observations, which comes out to be 2.25. , The answer is The variance of the data is 2.25.

[INST] help me answer this question What is the negation of the statement `in India, there exists a state which does not have a capital`?, think step by step [/INST] , The answer is The negation of this statement is: `For every state in India, it has a capital.`

[INST] help me answer this question Find the value of y in the following equation: 2(3y - 4) = 16, think step by step [/INST] To find the value of y, we first distribute the 2 to both terms inside the parentheses, which gives us 6y - 8 = 16. Then, we add 8 to both sides to get 6y = 24. Finally, we divide both sides by 6 to get y = 4. , The answer is The value of y is 2.

[INST] help me answer this question Hence, the shaded area in the graph is the required solution area for the given inequalities. , think step by step [/INST] , The answer is N/A

[INST] help me answer this question Does the origin (0, 0) lie in the line graph of y > x?, think step by step [/INST] Solving for y = x, we get x= 0, y = 0, which are the coordinates of the origin. , The answer is Yes, the origin lies on the line graph.

[INST] help me answer this question (ii) (–3, 7, 2) and (2, 4, –1), think step by step [/INST] , The answer is √43 units

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question What is the first inequality given in the problem?, think step by step [/INST] , The answer is x + 2y ≤ 10

[INST] help me answer this question Let R be a relation from N to N defined by R = {(a, b): a, b ∈ N and a = b^2}. Are the following true? (i) (a, a) ∈ R, for all a ∈ N, think step by step [/INST] , The answer is No, it is not true that (a, a) ∈ R, for all a ∈ N.

[INST] help me answer this question Find the coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0., think step by step [/INST] This is the solution for finding the coordinates of the foot of perpendicular from a given point to a given line. , The answer is The coordinates of the foot of perpendicular from the point (–1, 3) to the line 3x – 4y – 16 = 0 are (68/25, -49/25)

[INST] help me answer this question Is it a statement?, think step by step [/INST] The product of (-1) and 8 is -8, but the sentence states the product to be -1. , The answer is No, it is not a statement.

[INST] help me answer this question (subpart) Is BC = AD?, think step by step [/INST] BC ≠ AD; BC = √43, and AD = √30 , The answer is No

[INST] help me answer this question In which direction is the solution area for the second inequality?, think step by step [/INST] , The answer is The solution area for the second inequality is towards the right of the line graph.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question The coefficients of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r., think step by step [/INST] , The answer is By using the general term Tr+1 = nCr an-r br, we can find that n = 7 and r = 3.

[INST] help me answer this question Find the distance between parallel lines 15x + 8y – 34 = 0 and 15x + 8y + 31 = 0, think step by step [/INST] N/A , The answer is The distance between parallel lines is 65/17.

[INST] help me answer this question According to the question, the entire students should have an average of at least 60 marks, think step by step [/INST] To find the minimum number of marks, we need to first find the total marks of all students and then divide it by the number of students. After simplification, we get x ≥ 35. , The answer is The minimum number of marks that each student should obtain is 35.

[INST] help me answer this question What is the mean for Y?, think step by step [/INST] , The answer is The mean (ȳ) for Y is 105.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Find the slope of the line BC., think step by step [/INST] , The answer is The slope of the line BC (m2) = (-1-5)/(-1-3) = -6/-4 = 3/2

[INST] help me answer this question Find the domain and range of the following real function., think step by step [/INST] , The answer is Given, f(x) = –|x|, x ∈ R The domain of f is R because f(x) is defined for x ∈ R. The range of f(x) = –|x| is all real numbers except positive real numbers. Therefore, the range of f is given by (–∞, 0].

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Find the equation of the line passing through the point (2, 2√3) and inclined with the x-axis at an angle of 75o., think step by step [/INST] , The answer is The equation of the line is (2 + √3) x – y – 4 = 0.

[INST] help me answer this question 1.(b) Passing through (0, 0) with slope m., think step by step [/INST] , The answer is Given: Point (0, 0) and slope, m = m We know that the point (x, y) lies on the line with slope m through the fixed point (x0, y0), if and only if, its coordinates satisfy the equation y – y0 = m (x – x0) So, y – 0 = m (x – 0) y = mx y – mx = 0 ∴ The equation of the line is y – mx = 0.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question (subpart) Is AB = CD?, think step by step [/INST] AB = CD = 6 , The answer is Yes

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Are the following pair of statements a negation of each other, give reasons for the answer. (i) x + y = y + x is true for every real number x and y. (ii) There exists real numbers x and y for which x + y = y + x., think step by step [/INST] , The answer is The negation of the (i) statement is: `There exists real numbers x and y for which x + y ≠ y + x.` This statement is not the same as the (ii) statement, hence the given statements are not a negation of each other.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question If `f(x) = x^2 - 3x + 2`, find `f'(x)`., think step by step [/INST] , The answer is `f'(x) = 2x - 3`.

[INST] help me answer this question How many terms of the A.P. -6, -11/2, -5, … are needed to give the sum –25?, think step by step [/INST] We used the sum formula for an A.P. and solved for the number of terms to determine the number of terms needed. , The answer is We need 8 terms to get the sum of -25.

[INST] help me answer this question For the given data, find the mean and standard deviation using the short-cut method., think step by step [/INST] Refer to the calculations in the answer. , The answer is The mean is 64 and the standard deviation is 1.691.

[INST] help me answer this question Find the value of z in the following equation: 5(2z + 3) - 10 = 35, think step by step [/INST] To find the value of z, we first distribute the 5 to both terms inside the parentheses, which gives us 10z + 15 - 10 = 35. Then, we simplify the expression on the left side of the equation to get 10z + 5 = 35. Next, we subtract 5 from both sides to get 10z = 30. Finally, we divide both sides by 10 to get z = 3. , The answer is The value of z is 3.

[INST] help me answer this question Find the equation of the circle with Centre (-2, 3) and radius 4., think step by step [/INST] , The answer is x2 + y2 + 4x – 6y – 3 = 0

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question Calculate the mean deviation about the median for the data: 36, 42, 45, 46, 46, 49, 51, 53, 60, 72., think step by step [/INST] First, we find the median (which is 47.5), then we calculate the absolute deviations from the median, and finally, we find the mean of these deviations. , The answer is The mean deviation about the median for the given data is 7.

[INST] help me answer this question Find R – Q, think step by step [/INST] R – Q represents the set of elements that are present in R but not in Q. Here, R is the set of real numbers and Q is the set of rational numbers. Therefore, R – Q is the set of irrational numbers. , The answer is Set of irrational numbers

[INST] help me answer this question Write the balanced chemical equation for the complete combustion of methane., think step by step [/INST] , The answer is The balanced chemical equation is as follows: CH4 + 2O2 -> CO2 + 2H2O

[INST] help me answer this question `f(x) = sqrt(x - 1)`, think step by step [/INST] , The answer is The domain of the function is `x ≥ 1`.

[INST] help me answer this question Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?, think step by step [/INST] When we substitute x = -2.5 and y = 3.5 in the equation x2 + y2 = 25, we get x2 + y2 > 25, which implies that the point lies outside the circle. , The answer is The point (-2.5, 3.5) lies outside the circle x2 + y2 = 25.

[INST] help me answer this question `f(x) = (x + 3)/(x - 4)`, think step by step [/INST] , The answer is The domain of the function is all real numbers except `x = 4`.

[INST] help me answer this question `f(x) = 1/(x^2 + 1)`, think step by step [/INST] , The answer is The domain of the function is all real numbers.

[INST] help me answer this question Question: 7 ≤ (3x + 11)/2 ≤ 11, think step by step [/INST] The given inequality is 7 ≤ (3x + 11)/2 ≤ 11. After solving this inequality, we get x ∈ [1, 11/3]. , The answer is The solutions of the given inequality are all real numbers x greater than or equal to 1 but less than or equal to 11/3.

[INST] help me answer this question Find the derivative of the following functions. (vii) 2 tan x – 7 sec x, think step by step [/INST] , The answer is The derivative of 2 tan x – 7 sec x is not provided.