Sample Paper Series- I

​The value of 

​If a = log₁₂ 24, b = log₃₆ 24 ,b = log₄₈ 36 then prove that 1 + abc =

If x = 5^1/3 + 5^-1/3, 5x³ - 15x  is given by 

Ten years ago the age of a father was four times his son. Ten years hence the age of the father will be twice that of his son. The present age of the father and the son are

When two roots of quadratic equations are α and 1/α then what will be quadratic equation.

Let α and β be the roots of equation x²+7 x + 12 = 0. Then the value of  will be 

If A = then Adjoint of Matrix A 

If A =  and A = A^T, then 

If A =  (here i² = -1) then IAI = 

​On solving the inequalities 5x + y ≤100, x + y ≤ 60, x ≥ 0 and y ≥ 0, we get the following situation.

A certain m oney doubles itself in 10 years when deposited on sim ple interest. It would triple itself in

A man deposited Rs. 8, 000 in a bank for 3 years at 5% per annum compound interest, after 3 years he will get

The effective rate of interest for one year corresponding to a nominal at 7% rate of interest per annum convertible quarterly is

The value of furniture deprec iates by 10% a year, if the present valu e of the furniture in an offic e is Rs. 21870, calculate the value of furniture 3 years ago.

The population of a town increases every year by 2 % of the population beginning of that year. The number of years by which the total increase of population be 40% is

Find the future value of an annuity of Rs. 500 m ade annually for 7 years at interest rate of 14 % per annum [Given that (1.14)7 = 2.5023]

Rs. 200 invested at the end of each month in an account paying interest 6% per year compounded monthly. What is the future value of this annuity after 10 th paym ent? [Given that (1.005) 10 = 1.0511]

Suppose your father decides to gift you Rs. 10,000 every year starting from today for the next five years, you deposit this amount in a bank as and when you receive and get 10% per annum interest rate compounded annually. What is the present value of this annuity? ( P(4, 0.10) = 3.16987)

Nominal Rate of Return =

Net Present Value (NPV) 

The annual birth rates per 1,000 are 39.4 and 19.4 respectively. The number of years which the population will be doubled assuming there is no immigration or emigration is

Y bought Motor Bike Costing 80,000 by making down payment of Rs. 30000 and agreeing to make annual payment for four years. How much would be each payment if the interest on unpaid amount be 14% compounded annually. [Given P (4, 0.14) = 2.91371]

The value of K, for which the terms 7K +3, 4K-5, 2K+10 are in A.P., is

If A = {1,2,3,4} and B = {1,4,9,16,25} is a function of f is defined set A to B where f(x) = x2 then the range of f is

If ⁿP_r = 336 and ⁿC_r = 56, then n and r will be

If A = {1,2,3,4,5,6,7} and B = {2,4,6} Cardinal number of AUB

In how many ways the letters of the word ‘ARRANGE’ be arranged?

The num ber of ways in whic h 8 exam ination papers be arranged so that the best and worst papers never come together.

ⁿP_r = 720 and ⁿC_r = 120 then value of r is

Find the three numbers in G.P, whose sum is 19 and produc t is 216.

The nth term of the sequenc e -1,2, -4, 8,.is

If f(x) = x+3 and g(x) = x², then fog(x)

​Given x = 2t + 5, y = t² -2; dy/dx is c alc ulated 

The slope of the tangent to the curve y = x²-x at the point, where the line y= 2 cuts the curve in the first quadrant, is

For the curve x²+y²+2gx+2hy = 0, the value of dy/dx at (0,0) is

Find the missing term of the number series 24, 60, 120, 210,? 

GO = 32, SHE = 49, then SOME will be equal to

in a c ertain Code DECEM BER is written as ERM BCEDE. Whic h word will be written as ERM BVENO in that code?

Find the missing term of the number series 48, 24, 96,48,192,?

Ramu walks 5 Kms starting from his house towards west then turns right and walks 3 km. Thereafter he takes left turn and walks 2 km. Further, he turn left and walks 3 km. Finally, he turns right and walks 3 kms. In what direction he is now from his house.

Six children A, B, C, D, E and F are sitting in a row. B is between F and D. E is between A and C. However, A does not stand next to F or D. C does not stand next to D. F is between which of the following pairs of children?

Five students are A,B,C,D and E are standing in arrow . D is on the right of E; B is on the left of E but on right of A. D is next to C on his left. The student in middle is

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 im m ediate 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?

In each of the of the following below are given two statements followed by two conclusion numbered I and II. You have to take the given two statements to be true even if they seem to be variance from commonly known facts. Read the conclusions logically follows from the two given statements. Disregarding commonly known facts.
Statements: I. Some rats are Cats II. All Cats are bats.
Conclusions: No rats are cats Some rats are bats.

In each of the of the following below are given two statements followed by two conclusion numbered I and II. You have to take the given two statements to be true even if they seem to be variance from commonly known facts. Read the conclusions logically follows from the two given statements. Disregarding commonly known facts.
Statements: I. No house is an apartment.
II. Some apartments are bungalows.
Conclusions: No house is a bungalow.
All bungalows being houses is a possibility.

In each of the of the following below are given two statements followed by two conclusion numbered I and II. You have to take the given two statements to be true even if they seem to be variance from commonly known facts. Read the conclusions logically follows from the two given statements. Disregarding commonly known facts.
Statements: I. All Pens are ink.
II. No ink is an eraser.
Conclusions: No pen is an eraser.
Some erasers are pens.

In each of the of the following below are given two statements followed by two conclusion numbered I and II. You have to take the given two statements to be true even if they seem to be variance from commonly known facts. Read the conclusions logically follows from the two given statements. Disregarding commonly known facts.
Statements: I. No toffee is Coffee
II. No Sweet is Toffee.
Conclusions: No coffee is sweet.
All sweets are coffee.

C is mother of A and B. If D is the husband of B, then what is C to D

A is B’s sister, C is B’s mother, D is C’s father of E is D’s mother, then how is A related D?

A, Q, Y and Z are different persons. Z is the father of Q. A is the daughter of Y and Y is the son of Z. If P is the son of Y and B is the brother of P, then

A is father of C and D is son of B. E is brother of A. If C is sister of D how is B related to E?

A Driver left his village and drove North for 20 Km , after whic h he stopped for breakfast.  T hen he turned left and drove another 30 km, when he stopped for lunch. After some rest, he again turned left and drove 20 kms before stopping for evening tea.  Once more he turned left and drove 30 kms to reach the town where he had supper.  After evening tea in which direction did he drive?

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?

Statistics is applied in

The primary data are collected by

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

‘Stub’ of a table is the 

Pie-diagram is used for

For open-end classification, which of the following is the best measure of central tendency?

The presence of extreme observations does not affect

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

Which of the following results hold for a set of distinct positive observations?

Quartiles are the values dividing a given set of observations into

If x and y are related by x–y–10 =0 and mode of x is known to be 23, then the mode of y is

What is the value of the first quartile for observations 15, 18, 10, 20, 23, 28, 12, 16?

If the relationship between two variables u and v are given by 2u + v + 7 = 0 and if the AM of u is 10, then the AM of v is  

​Which one is an absolute measure of dispersion?

The range of 15, 12, 10, 9, 17, 20 is

The standard deviation of, 10, 16, 10, 16, 10, 10, 16, 16 is

If all the observations are multiplied by 2, then

The quartiles of a variable are 45, 52 and 65 respectively. Its quartile deviation is

If P(A∩B) = 0, then the two events A and B are

If A, B and C are mutually exclusive and exhaustive events, then P(A) + P(B) + P(C) equals to

Variance of a random variable x is given by

If a card is drawn at random from a pack of 52 cards, what is the chance of getting a Spade or an ace?

Given that P (A) = 1/2, P (B) = 1/3, P (AB) = 1/4, what is P (A’/B’)

A binomial distribution is

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

The total area of the normal curve is

The interval (µ - 3σ, µ + 3σ) covers

If the mean deviation of a normal variable is 16, what is its quartile deviation?

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

For Poisson fitting to an observed frequency distribution

What is spurious correlation?

The covariance between two variables is

If r = 0.6 then the coefficient of non-determination is

If the sum of squares of difference of ranks, given by two judges A and B, of 8 students in 21, what is the value of rank correlation coefficient?

Weighted G.M. of relative formula satisfy ________test

Laspyre's method and Paasche’s method do not satisfy

Fisher’s index number is based on

Purchasing Power of Money is

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

The additive model of Time Series