Sample Paper Series- II

Simplify  = 

If. 2^a = 3^b = 12^c then  =

​The value of log ₆₄512 is 

The value of of  (log_b a log_c b log_a c)³ =

If α and β be the roots of the equation 2x²-4x-3=0 the value of α²+β² is

If one root of the equation x²+ 7x+ p = 0 be reciprocal of the other then the value of p is________. 

Let A =  ; B=  then the value 3A-B

Mr. A plans to invest up to Rs. 30,000 in two stocks X and Y. Stock X(x) is priced at Rs.175 and Stock Y(y) at Rs.95 per share. This can be shown by

A sum of money doubles itself at compounded interest in 10 years in how many years will it becomes eight times?

A machine costs Rs .1,00, 000. The depreciation rate is 10% per annum . The scrap value of the machine at the end of 5 years is

Rs. 10,000 is invested at annual rate of interest of 10% p.a. The amount after two years at annual compounding is

The annual birth rate and death rate per 1000 are 39.4 and 19.4 respectively. The number of years in which population will be doubled assuming that there is no immigration or emigration is approximately

If the effective rate of interest is 12% per annum and the interest is compounded quarterly, the nominal rate of interest per annum

A machine can be purchased for Rs. 50, 000. Machine will be contributing Rs. 12, 000 per year for the next five years. Assuming borrowing cost is 10% per annum. Determine whether machine should be purchased or not

X bought a TV costing 25,000 making down payment of Rs. 5000 and agreeing to make equal annual payment for four years. How much would be each payment if the interest on unpaid amount be 14% compounded annually? [P(4, 0.14) = 2.91371]

The future value of annuity on Rs. 5000 a year for 7 years at 14% per annum compound interest is given (1.14)⁷= 2.5023

Rs.5000 paid for ten years to off a loan. What is the loan amount if interest rate be 14% per annum com pounded annually? (Given P (10, 0.14) = 5.21611

Suppose your friend decided gift to you R s. 10000 every year starting from today for the next five years. Your deposit this amount in a bank as and when you receive and get 10% per annum interest compounded annually. What is the present value of this annuity?

Rs.1000 is invested at the end of each month in an account paying interest 6% per year compounded monthly. What is the future value of annuity after 10 th payment? (Given that (1.005) 10 = 1.0511)

The differenc e between CI and SI on a certain money invested for three years at 6% per annum is Rs. 110.16. The sum is

Simple interest on Rs.3500 for 3 years at 12% per annum is

A function f(x) is an even function, if

If A = {1, 2, 3, 4} and B = {5, 6, 7,6}, then c ardinal num ber of the set A×B is _____ 

Find the f o g for the func tions f (x) =x^3, g (x) = x+ 1

if nP₄ = 12nP₂ then n=

The number of sub sets of function {2, 3, 5, 6}

A m an has 5 friends’. In how m any ways can be invite one or more of his friends to dinner?

The sum of the first two term s of a GP is 5/3 and the sum of infinity of the series is 3. The common ratio is

The sum of the infinite series 1+2/3+4/9+………is

Which term of the AP 64,60,56,52….is Zero

​if x=at², y=2at then  is equal to

​The gradient of the c urve y = 4x² – 2x at x =1 is 

​If x = at³, y = a/t³,dy/dx at t = 1 is 

Find odd one out of the series  7, 9, 11, 12, 14, 15

Find odd one out of the series   37, 45, 49, 65, 79

Find the missing number of the series  22, 24, 28, ?  , 52, 84

Find the missing number of series  1, 5, 13, 25, 41,  ?

If SUMMER is coded as RUNNER the code for WINTER will be

In a certain code KAVERI is written as VAKIRE. How is MYSORE written in that code?

A man is facing East, then he turns left and goes 10m then turns right and goes 5 m then goes 5 m to the South and from there 5 m to West. In which direction is be from his original place?

From her hom e Prerna wishes to go to sc hool.  From hom e she goes towards North and then turns left and then turns right, and finally she turns left and reaches school.  In which direction her school is situated with respect to her home?

A child walks 25 feet towards North, turns right and walks 40 feet, turns right again and walks 45 feet .  He then turns left and walks 20 feet.  He turns left again walks 20 feet. Finally, he turns to his left to walks another 20 feet.  In which direction is the child from his starting point?

In a college party, 5 girls are sitting in a row. F is to the left of M and to the right of O. R is sitting to the right of N but to the left of O. Who is sitting in the middle?

Five friends P, Q, R, S and T are sitting in a row fac ing North. Here, S is between T and Q and Q is to the immediate left of R. P is to the immediate left of T. Who is in the middle?

Study the following information carefully to answer the given questions. Eight person’s P to W are sitting in front of one another in two rows. Each row has four persons. P is between U and V and facing North. Q, who is to the immediate left of M is facing W. R is between T and M and W is to the immediate right of V.
Q. Who is sitting in front of R?

​Study the following information carefully to answer the given questions. Eight person’s P to W are sitting in front of one another in two rows. Each row has four persons. P is between U and V and facing North. Q, who is to the immediate left of M is facing W. R is between T and M and W is to the immediate right of V.
Q. Who is to the immediate right of R?

​​Study the following information carefully to answer the given questions. Eight person’s P to W are sitting in front of one another in two rows. Each row has four persons. P is between U and V and facing North. Q, who is to the immediate left of M is facing W. R is between T and M and W is to the immediate right of V.
Q. In which of the following pairs, persons are sitting in front of each other?

​​Study the following information carefully to answer the given questions. Eight person’s P to W are sitting in front of one another in two rows. Each row has four persons. P is between U and V and facing North. Q, who is to the immediate left of M is facing W. R is between T and M and W is to the immediate right of V.
Q. X is the husband of Y. W is the daughter of X. Z is husband of W. N is the daughter of Z. What is the relationship of N to Y?

A’ reads a book and find the nam e of the author fam iliar. T he author ‘B’ is the paternal un c le of ‘C’. ‘C’ is the daughter of ‘A’. How is ‘B’ related to ‘A’?

‘A’ s m other is sister of B and she has a daughter C who is 21 years old. How is B related to D?

Each of the following questions contains two statem ents followed by two conclusions num bered I and II. You have to consider the two statements to be true, even if they seen to be at variance at the commonly known facts. You have to decide whic h of the given conclusions definitely follows from the given statements
Q. Statements: I. All pots are cups.
II. All cups are bowls.
Conclusions: I. All pots are bowls. II. All cups are pots.

Each of the following questions contains two statem ents followed by two conclusions num bered I and II. You have to consider the two statements to be true, even if they seen to be at variance at the commonly known facts. You have to decide whic h of the given conclusions definitely follows from the given statements
Q. Statements: I. All roads are poles
II. No poles are bungalows
Conclusions: I. Some roads are bungalows
II. Some bungalows are poles

Each of the following questions contains two statem ents followed by two conclusions num bered I and II. You have to consider the two statements to be true, even if they seen to be at variance at the commonly known facts. You have to decide whic h of the given conclusions definitely follows from the given statements
Q. Statements: I. Som e c ats are kittens.
II. All goats are kittens.
Conclusions: I. Some cats are goats
II. Some goats are cats.

The best method to collect data, in case of a natural calamity, is

The entire upper part of a table is known as

A frequency distribution

Mode of a distribution can be obtained from

The presence of extreme observations does not affect

For a moderately skewed distribution, which of the following relationship holds?

Quartiles can be determined graphically using

If there are 3 observations 15, 20, 25 then the sum of deviation of the observations from their AM is 

The third decile for the numbers 15, 10, 20, 25, 18, 11, 9, 12 is

Which measures of dispersions is not affected by the presence of extreme observations?

Which measure is based on only the central fifty percent of the observations?

If the profits of a com pany rem ain the sam e for the last ten m onths, then the standard deviation of profits for these ten months would be?

The range of 15, 12, 10, 9, 17, 30 is

If the range of x is 2, what would be the range of –3x +50 ?

If x and y are related by 2x+3y+4 = 0 and SD of x is 6, then SD of y is

If x and y are related by y = 2x+ 5 and the SD and AM of x are known to be 5 and 10 respectively, then the coefficient of variation is

​If for two events A and B, P(A ∩ B)  = P(A) x P(B), then the two events A and B are

Addition Theorem of Probability states that for any two events A and B,

If a random variable x assum es the values x₁, x₂, x₃, x₄ with c orresponding probabilities p₁, p₂ , p₃, p₄ then the expec ted value of x is

If an unbiased die is rolled once, the odds in favour of getting a point which is a multiple of 3 is

A, B, C are three mutually independent with probabilities 0.3, 0.2 and 0.4 respec tively. What is P (ABC)?

What is the chance of throwing at least 7 in a single cast with 2 dice?

A binomial distribution is

The maximum value of the variance of a binomial distribution with parameters n and p is

Which one is uniparametric distribution?

The mean deviation about median of a standard normal variate is

If the points of inflexion of a normal curve are 40 and 60 respectively, then its mean deviation is 

​What is the first quartile of X having the following probability density function?
 

Correlation analysis aims at

The two lines of regression become identical when

If the coefficient of correlation between two variables is 0.7 then the percentage of variation unaccounted for is

If the regression coefficient of y on x is 2.5, the correlation coefficient 0.6 and the SD is y of is 4, the SD of x is

If the regression coefficient of y on x is 1.5 and the variances of x and y is 4/9 then the correlation coefficient is

If the coefficient of determination is 0.64 and the regression coefficient of x on y is 4 then then the regression coefficient of y on x is

Chain index is equal to

The formula should be independent of the unit in which or for which price and quantities are quoted in

The formula for conversion to current value

Damages due to floods, droughts, strikes fires and political disturbances are:

The rise and fall of a time series over periods longer than one year is called:

A time series has: