There are 4 bus routes between A and B and 3 bus routes between B and C. A man can travel round trip in number of ways by bus from A to C via B. If he does not want to use a bus route more than once, in how many ways can he make the round trip?

For the post of 5 teachers, there are 23 applicants. 2 posts are reserved for SC candidates and there are 7 SC candidates among the applicants. In how many ways can the selection be made?

At what time between 2 and 3 O'Clock will the hands of a clock coincide?

Find the union set of A = {x :x is a natural number and 1 < x ≤ 5} and B = {x : x is a natural number and 5 < x ≤ 10}.

A and B can do a work in 8 days; B and C can do the same work in 12 days; A, B and C together can finish it in 6 days. In how many days A and C together will do the same work?

Differentiate the function with respect to x:

Convert the decimal number to the binary number: 517

Given a G.P. with a = 729 and 7th term = 64, determine S7.

Find the equation of the line passing through the point (-1, 3) and perpendicular to the line 3x - 4y - 16 = 0

Find the domain and the range of the given function: f(x) = 1/(1−x^2)

Find the present value of ₹25,000 due 10 years hence when the interest of 8% is compounded: i. annually

4y - 16 = 0

Find the domain and the range of the given function: f(x) = 1/(1−x)

Find the present value of ₹25,000 due 10 years hence when the interest of 8% is compounded: i. annually ii. semi-annually iii. quarterly iv. continuously

Simplify: 1/(1+a)^(m−n) a^(m−p) 1/(1+a)^(n−m) a^(n−p) 1/(1+a)^(p−m) a^(p−n)

Let A = {1, 2, 4, 5}, B = {2, 3, 5, 6}, C = {4, 5, 6, 7} verify the following identity: A ∪ (B ∩ C) = [(A ∩ B) ∪ (A ∩ C)]

In a factory which manufactures bolts, machines A, B and C manufacture respectively 30%, 50% and 20% of the bolts. Of their outputs 3, 4 and 1 per cent respectively are defective bolts. A bolt is drawn at random from the product and is found to be defective. Find the probability that this is not manufactured by machine B.

A die has two faces with number 1, three faces each with number 2 and one face with number 3. If die is ruled once, find (i) P (3) (ii) P (1 or 2) (iii) P (2)

Suppose f(x) = a+bx, if f(1) = 4, then what are the possible values of a and b?

Compute the moment coefficient of skewness for the following distribution: Marks obtained 0-10 10-20 20-30 30-40 40-50 50-60 60-70 Frequency 6 1 2 2 2 4 1 2 8

Calculate the mean deviation about the mean for the following data: Income per day 0 - 100 100 - 200 200 - 300 300 - 400 400 - 500 500 - 600 600 - 700 700 - 800 Number of persons 4 8 9 10 7 5 4 3

Find the equation of a circle whose centre is a point (1, -2) and which passes through the centre of the circle 2x^2 + 2y^2 + 4y = 5.

Read the text carefully and answer the questions: Population vs Year graph given below. In which year the population becomes 110 crores? Find the equation of line perpendicular to line AB and passing through (1995, 97). Write the equation of line AB? Find the slope of line AB.

Read the text carefully and answer the questions: In class of Statistics, teacher was discussing the concept of Measures of Correlation, in which he was discussing about Karl Pearson's Coefficient of Correlation. Find Karl Pearson’s coefficient of correlation between X and Y for the following: Cov(x,y) / (√Varx * √Vary)

What is the value in this data? (a) Σxy What is the value? (b) Σx^2 What is the value of? (c) Σy^2 What is the value of Karl Pearson's Coefficient of Correlation between x and y?

Read the text carefully and answer the questions: A mobile number is having 10 digits. It is not just a group of numbers strung out at random. All mobile numbers have 3 things in common, a 2-digit Access code (AC), a 3-digit provider code (PC), and a 5 digit subscriber code (SC).

How many mobile number are possible if number start with 98073 and no other digit can repeat? How many AC code are possible if both digit in AC code are different and must be greater than 6? How may mobile number are possible if AC and PC code are fixed and digits can repeat? How many mobile numbers are possible with AC code 98 and PC code 123 and digit used in AC and PC code will not be used in SC code? In how many ways these five students can sit in a row? Total number of sitting arrangements if Mohit and Sachin sit together? What are the possible arrangements if Rohit and Mohan sits at the extreme positions? What are the possible orders if Kapil is sitting in the middle?

Therefore, the Domain of R is the values of x or the first element of the ordered pair. So, Domain = {2, 3, 4, 5}

Given that the equation of two diameters of a circle are x - y = 5 and 2x + y = 4 and the radius is 5. We know that the intersection point of the diameters be a centre. So, solving equation x - y = 5 and 2x + y = 4 for x and y. We get x = 3, y = -2. Centre = (h, k) = (3, -2) radius = r = 5. The required equation of the circle is (x - h)^2 + (y - k)^2 = r^2.

Son's 1 day's work = The son alone can do the work in = 7 days

Given x1, x2, ..., xn be n observations and Mean of these n observations, = 48 and their standard deviation, SDx = 12. Another series of n observations is given such that wi = lxi + k for i = 1, 2, ..., n, where l and k are constants and mean of these n observations, = 55 and their standard deviation, SDw = 15.

Assertion: Mean of the given series = 50. Mean deviation about mean = 8.4. Hence, Assertion is true and Reason is false.

Let A be the event that Mr. A hit the target and B be the event that Mr. B hit the target. Now, P (exactly one of them hits the target) = P(A or B) = P(A) + P(B) = P(A) P + P P(B).

Total number of ways = 10! Total number of ways in which 5 boys and 5 girls are sitting in a row = 2 5! 5! Required probability =

For C.I.: C.I. = 15000 - 15000 = 15000 = ₹ 1224. S.I. = ₹ 1200. Difference between C.I. and S.I. = ₹ 1224 - ₹ 1200 = ₹24.

We have to select 2 posts out of 7 SC and 3 posts out of 16. Required number of ways = 11760.

Assertion: A is true but R is false. Explanation: Assertion Mean of the given series.

At 2 O' clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 minute spaces apart. To be coincident, the minute hand must gain 10 minute spaces.

Suppose A, B and C alone can do the work in nA, nB and nC days respectively. A and B together can do the work in 8 days. B and C together can do the work in 12 days. A, B and C together can do the work in 6 days. Subtracting (i) and (ii) successively from (iii), we get and Hence, A and C together can do the work in 8 days.

Let, y = Differentiate with respect to x we get, [Using quotient rule] = [Using product rule] = = = = = e^x x^{-2} [ + log x - log x]

Given decimal number is 517. The required binary number is 1000000101.

Let r be the common ratio of G.P. Then a7 = 64 ar^{7-1} = 64 729 r^{6} = 64 When r = = 2187 - 128 = 2059 When r = = (2187 + 128) = = 463.

The given equation is 3x - 4y - 16 = 0. Slope of the line, m1 = Slope of the perpendicular line, m2 = -.

Since the line passes through (-1, 3), so the equation of the line is y - y0 = m(x - x0) y - 3 = m2(x + 1) y - 3 = -(x + 1) 3y - 9 = -4x - 4 4x + 3y - 5 = 0.

Let P be the present value of S = 25000. i. We have, S = 25000, i = 0.08 and n = 10. P = S(1 + i)^{-n} P = 25000(1 + 0.08)^{-10} = 25000(1.08)^{-10} = 25000 0.46319349 = 11579.83 Hence, the present value is ₹11,579.83.

We have, S = 25000, i = 0.04 and n = 10 2 = 20 P = S(1 + i)^{-n} P = 25000(1 + 0.04)^{-20} = 25000(1.04)^{-20} = 25000 0.45638695 = 11409.67 Hence, the present value is ₹11,409.67.

We have, S = 25000, i = 0.02 and n = 10 4 = 40 P = S(1 + i)^{-n} P = 25000(1 + 0.02)^{-40} = 25000(1.02)^{-40} = 25000 0.45289042 = 11322.26 Hence, the present value is ₹11,322.26.

We have, S = 25000, r = 0.08 and n = 10 P = Se^{-r n} P = 25000 e^{-0.8} = 25000 0.44933 = 11233.25 Hence, the present value is ₹11,233.25.

We construct the following table: 1 1++a m−n a m−p 1 1++a n−m a n−p 1 1++a p−m a p−n a n+p ++a n+p a m+p a m+n a m+p ++a m+p a m+n a n+p + a m+n +a m+n a m+p a n+p ++a n+p a m+p a m+n ++a n+p a m+p a m+n.

Given circle is 2x^2 + 2y^2 + 4y = 5. Centre is (0, -1). radius =

In class of Statistics, teacher was discussing the concept of Measures of Correlation, in which he was discussing about Karl Pearson's Coefficient of Correlation. This is the best method for finding correlation between two variables provided the relationship between the two variables is linear. This method is also known as product moment correlation coefficient. Pearson's correlation coefficient may be defined as the ratio of covariance between the two variables to the product of the standard deviations of the two variables. If the two variables are denoted by x and y and of the corresponding bivariates data are (x_i, y_i) for i = 1, 2, 3, ..., n, then the coefficent of correlation between x and y due to Karl Pearson, is given by: r = r_xy or, r_xy = where, cov(x, y) = If x - are small fractions, we use r = If x, y are small numbers, we use

Find Karl Pearson’s coefficient of correlation between X and Y for the following: x54321 y421086

A mobile number is having 10 digits. It is not just a group of numbers strung out at random. All mobile numbers have 3 things in common, a 2-digit Access code (AC), a 3-digit provider code (PC), and a 5 digit subscriber code (SC). AC code and PC code are fixed, then

Five friends Mohit, Sachin, Rohit, Mohan and kapil were playing in a ground, where they sit in a row in a straight line. The digits which can be used are, 6, 5, 4, 2, 1. Number of ways to fill the 5 places = 5! = 120. Digits which can be used in AC code are 7, 8, 9. Total AC code = 3P2 = 3! = 6. If AC and PC are fixed then only 5 digits is to be filled if digits can repeat then total ways = 100000 = 10^5. Total ways = 5^5 = 3125. Total number of ways = 5! = 120. Two position are fixed for Mohit and Sachin therefore considering it as one unit, total students left = 3 + 1 = 4. Total possible arrangement = 4! * 2! = 48.