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1. a

2. b

3. c

4. d

What is the number of 6-digit numbers that can be  fonned  only  by  using  0, 1, 2, 3, 4 and 5 (each once); and divisible by 6 ?

1. 96

2. 120

3. 192

4. 312

What is the binary number equivalent to decimal number 1011 ?

1. 1011

2. 111011

3. 11111001

4. 111110011

Let A be a  matrix  of  order  3x3  and IAI = 4. If |2 adj(3A)| = 2^a3^β, then what is the value of (a + β) ?

1. 12

2. 13

3. 17

4. 24

1. a

2. b

3. c

4. d

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor 2

Consider the following statements in respect of square matrices A,B, C each of same order n :

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither I nor 2

1. a

2. b

3. c

4. d

Let AX= B be a system of 3 linear equations with 3-unknowns. Let X1 and X₂ be its two distinct solutions. If thecombination aX₁ + bX₂ is a solution of AX= B; where a, b are real numbers, then which  one  of the following is correct ?

1. a= b

2. a+ b = 1

3. a+ b = 0

4. a -  b  = 1

What is the sum of the roots of the 
equation | 0        x-a     x-b |
               | 0          o      x-c |  =  0
               |  x+b       x+c   1 |  

1. a + b + c

2. a - b + c

3. a + b - c

4. a - b - c

If 2 - i √3  where i = √-1  is  a  root of the equation x² + ax+ b = 0, then what is the value of(a+ b)?

1. -11

2. -3

3. 0

4. 3

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. 5

2. 6

3. 7

4. n cannot be determined

For how many integral values of k, the equation x²- 4x + k = 0, where k is an integer has real roots and both of them lie in the interval (0, 5) ?

1. 3

2. 4

3. 5

4. 6

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. A = R\{-j} and B = R\{-f}

2. A= Rand B = R\{-j}

3. A=R\{-f} and B == R\{0}

4. A=R\{-5/3} and B = R\{2/3}

a  and  β are  distinct  real  roots  of  the quadratic equation x²+ ax+ b = 0.
Which of the following statements is/are sufficient to find a?

1. a+β= 0, a² +β² = 2
2. aβ² = -1, a = 0
Select the correct answer using the code given below :

1. I only

2. 2 only

3. Both I and 2

4. Neither I nor 2

1. 6

2. 8

3. 9

4. 10

How many terms are there in the expansion of (3x- y )⁴(x + 3y )⁴  ?

1. 9

2. 12

3. 15

4. 17

p,  q,  r and  s  are  in  AP  such   that p + s = 8 and qr= 15. What is the difference between largest and smallest numbers?

1. 6

2. 5

3. 4

4. 3

Consider the following statements for a fixed natural number n :

1. C (n,r) is greatest if n = 2r

2. C (n,r) is greatest if n = 2r - 1 and n = 2r + 1.

Which of the statements given above is/are correct?

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor 2

m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m + n)?

1. 6

2. 7

3. 8

4. 9

Let x be the number of permutations of the word ' PERMUTATIONS' andy be the number of permutations of the word ' COMBINATIONS.' Which one of the following is correct ?

1. x  = y

2. y  = 2x

3. x  = 4y

4. y  = 4x

5-digit numbers are formed using the digits 0, 1, 2, 4, 5 without repetition. What is the percentage of numbers which are greater than 50,000?

1. 20%

2. 25%

3. 75%

4. 100%

What is cos2β equal to?

1. (cosa - sina)²

2. (cosa + sina)²

3. (cosa - sina)³

4. (cosa - + sina)³

Waht is value of sec2y?

Consider the following for the next two (02 items) that follow:

A flagstaff 20m  long standing on a pillar 10m high subtends an angles tan^-1(0.5) at a pointg P on the ground. Let θ be the angle by the pillar at this point P.

Question:

If x is the distance of P from bottom of the pillar, then consider the following statem nts :

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither 1 nor 2

Consider the following for the next two (02 items) that follow:

A flagstaff 20m  long standing on a pillar 10m high subtends an angles tan^-1(0.5) at a pointg P on the ground. Let θ be the angle by the pillar at this point P.

Question:

What is a possible value of tan θ ?

Consider the following for the next two (02) items that follow:

The perimeter of a triangle  ABC is 6 times the AM of sine of angles the triangle.

Further BC = √3 and CA = 1.

Question:

What is the perimeter of the triangle ?

1. √3 + l

2. √3 +2

3. √3 + 3

4. 2√ 3 + 1

Consider the following for the next two (02) items that follow:

The perimeter of a triangle  ABC is 6 times the AM of sine of angles the triangle.

Further BC = √3 and CA = 1.

Question:

1. 1 only

2. 2 only

3. Both 1 and 2

4. Neither I nor 2

Consider the following for the nextg two (02) items that follow:

Let x = sin²A+sinA+1 where 0 < A ≤ π/2
            sin A

Question:

What is the minimum value of x ?

1. 1

2. 2

3. 3

4. 4

Consider the following for the nextg two (02) items that follow:

Let x = sin²A+sinA+1 where 0 < A ≤ π/2
            sin A

Question:

At what value of A does x attain the minimum value ?

1. π/6

2. π/4

3. π/3

4. π/2

Consider the following for the next two (02) items that follow :
In the triangle ABC,
a²+b²+c² = ac+ √3 bc

Question:

What is the nature of the triangle ?

1. Equilateral

2. Isosceles

3. Right angled triangle

4. Scalene but not right angled

Consider the following for the next two (02) items that follow :
In the triangle ABC,
a²+b²+c² = ac+ √3 bc

Question:

If  c = 8, what is the area of the triangle?

1. 4√3

2. 6√3

3. 8√3

4. 12√3

Question:

At what value of x does the function attain minimum value ?

1. 2

2. 3

3. 4

4. 0

Question:

What is the minimum value of the function?

1. 2

2. 3

3. 4

4. 0

Question:

If the sum S is divided  by  8,  what is the remainder ?

1. 0

2. 1

3. 2

4. Cannot be determined

Question:

If the sum S is divided by 60, what is the remainder ?

1. 1

2. 3

3. 17

4. 34

Question:

What is the value of n ?

1. 4

2. 6

3. 8

4. 10

Question:

What is the length of the smallest side?

1. 12

2. 14

3. 16

4. 18

Consider the following for the (02) items that follow :
Given that next two
 
sin x+cos x+tan x+  cot x+sec x+cosec x  = 7

Question:

1. a

2. b

3. c

4. d

Consider the following for the (02) items that follow :
Given that next two
 
sin x+cos x+tan x+  cot x+sec x+cosec x  = 7

Question:

1. 0

2. 14

3. 21

4. 28

Question:

What is the HM of the roots of the equation?

1. 2

2. 4

3. 2√2

4. 2√3

Question:

1. a

2. b

3. c

4. d

Consider the following for the next two (02) items that follow:

Let ? (a,b,c,a) = | a         b         aα+b)
                          |  b         c         bα+c)
                          |aα+b  ba+c          0  )                                        

Question:

If ? (a, b, c, a)= 0 for every a > 0, then which one of the following is correct?

1. a, b, c are in AP

2. a, b, c are in GP

3. a, 2b, c are in AP

4. a, 2b, c are in GP

Consider the following for the next two (02) items that follow:

Let ? (a,b,c,a) = | a         b         aα+b)
                          |  b         c         bα+c)
                          |aα+b  ba+c          0  )                                        

Question:

1. a

2. b

3. c

4. d

Question:

What is the least value of m(θ) ?

1. n

2. 2n

3. 3n

4. 4n

Question:

1. n = tan²θ

2. n = cot²θ

3. n = sin ²θ

4. n = cos²θ

Consider the following for the next two (02) items that follow :
A quadrilateral is formed by the lines
x=0,y=O, x+y= 1 and 6x+y=3.

Question:

What is the equation of diagonal through origin ?

1. 3x + y = 0

2. 2x  + 3y  = 0

3. 3x - 2y = 0

4. 3x + 2y = 0

Consider the following for the next two (02) items that follow :
A quadrilateral is formed by the lines
x=0,y=O, x+y= 1 and 6x+y=3.

Question:

hat is the equation of other diago­ nal?

1. x  + 2y -  1 = 0

2. x  -    2y - 1  = 0

3. 2x + y + 1 = 0

4. 2x + y - 1 = 0

Question:

What is PE+ PF equal to?

1. 1

2. 2

3. 3

4. 4

Question:

1. a

2. b

3. c

4. d

Consider the following for the next two (02) items that follow :
The line y = x partitions the circle
( x- a)² + y² = a² in two segments.

Question:

1. a

2. b

3. c

4. d

Consider the following for the next two (02) items that follow :
The line y = x partitions the circle
( x- a)² + y² = a² in two segments.

Question:

1. a

2. b

3. c

4. d

Question:

What is u + v + w equal to ?

1. -2

2. -1

3. 1

4. 2

Question:

If P(x, y, z) is any point on the sphere, then what is PA2+ PB2 equal to ?

1. 15

2. 14

3. 13

4. 6.5

Question:

What is the value of k ?

1. 4

2. 2

3. 1

4. -1

Question:

What are the direction ratios of a line which is perpendicular to both the lines?

1. (1, 2, 10)

2. (-1, -2, 10)

3. (11, 12, -10)

4. (11, 2, - 10)

Question:

1. a

2. b

3. c

4. d

Question:

                                              → →     →

What is the angle between  (a+b) and c

1. π/2

2. π/3

3. π/4

4. π/6

Consider the following for the next two (02 items) that follow:

Let a vector a = 4î - 8 j + k make angles a, β, y with the positive directons of x,y,z axes respectively.

Question:

What is cosa equal to ?

Consider the following for the next two (02 items) that follow:

Let a vector a = 4î - 8 j + k make angles a, β, y with the positive directons of x,y,z axes respectively.

Question:

What is cos2β + cos2y equal to ? 

Consider the following for the next two (02) items that follow:

The position vectors of two points A and B are î -î and î + k respectively.

Question:

Consider the following points :

1. (-1, -3, 1)

2. (- 1, 3, 2)

3. (- 2, 5, 3)

Which of the above points lie on the line joining A and B ?

1. 1 and 2 only

2. 2  and  3 only

3. 1 and 3 only

4. 1, 2 and 3

Consider the following for the next two (02) items that follow:

The position vectors of two points A and B are î -î and î + k respectively.

Question:

What  is the magnitude of →AB  ?

1. 2

2. 3

3. √6

4. √3

Consider the following for the next three (03) items that follow :

Let f (x) = Pe^x+ Qe^2x + Re^3x, where P, Q, R  are   real numbers. Further /(0)=6, f'(ln 3) 282 and f  (x)dx =11

Question:

What is the value of Q ?

1. 1

2. 2

3. 3

4. 4

Consider the following for the next three (03) items that follow :

Let f (x) = Pe^x+ Qe^2x + Re^3x, where P, Q, R  are   real numbers. Further /(0)=6, f'(ln 3) 282 and f  (x)dx =11

Question:

What is the value of R ?

1. 1

2. 2

3. 3

4. 4

Consider the following for the next three (03) items that follow :

Let f (x) = Pe^x+ Qe^2x + Re^3x, where P, Q, R  are   real numbers. Further /(0)=6, f'(ln 3) 282 and f  (x)dx =11

Question:

What is f'(0) equal to ?

1. 18

2. 16

3. 15

4. 14

Question:

What is the order of the differential equation?

1. 1

2. 2

3. 3

4. 4

Question:

What is the degree of the differential equation?

1. 2

2. 3

3. 4

4. Degree does not exist

Question:

What is f'(0) equal to ?

1. -1

2. 0

3. 1

4. 2

Question:

What is lim    f'(x) equal to ?

             x→     x

1. -1

2. 0

3. 1

4. 2

Question:

What is lim      f'(x)  equal to ?

          x→0       x²

1. -1

2. 0

3. 1

4. 2

Consider the following for the next two (02) items that follow :

Question:

1. -1

2. 0

3. 1

4. 2

Consider the following for the next two (02) items that follow :

Question:

What is f {π/4} equal to ? 

1. 0

2. -1

3. 1

4. 1/√2

    

Consider the following for the next three (030 items that follow :

Question:

What is value of I₁+I₂/I₁-I₂

1. 1

2.  π

3.  π²

4.  π³

Consider the following for the next three (030 items that follow :

Question:

What is the value of 8I²₁ ?

1. π

2. π²

3. π³

4. π⁴

Consider the following for the next three (030 items that follow :

Question:

What is value of I₂?

Consider the fdollowing for next tgwo (02) itemks that follow:

Question:

1. a

2. b

3. c

4. d

Consider the fdollowing for next tgwo (02) itemks that follow:

Question:

What is I equal to when a < b < 0 ?

1. a + b

2. a - b

3. b - a

4. a + - b

Considering the following for the next three (03) items that follow:

Let f'(x) = |Inx|,x ≠1

Question:

What is the derivative of f'(x) at x=0.5?

1. -2

2. -1

3. 1

4. 2

Considering the following for the next three (03) items that follow:

Let f'(x) = |Inx|,x ≠1

Question:

What is the derivative of f'(x) atx = 2?

1. 

2. -1

3. 

4. 2

Considering the following for the next three (03) items that follow:

Let f'(x) = |Inx|,x ≠1

Question:

What is the derivative of f°f(x), where 1

Consider the following for next (2) two items that follow :

                  |  x + 6, x ≤ 1 
 Let f'(x) =  |  px + q, 1 < x < 2
                  |  5x, x ≥ 2  

and f'(x) is continuous

Question:

What is the value of p ?

1. 2

2. 3

3. 4

4. 5

Consider the following for next (2) two items that follow :

                  |  x + 6, x ≤ 1 
 Let f'(x) =  |  px + q, 1 < x < 2
                  |  5x, x ≥ 2  

and f'(x) is continuous

Question:

What is the value of q ?

1. 2

2. 3

3. 4

4. 5

1. 1 only

2. 2 only

3. Both l and 2

4. Neither I nor 2

What is the derivative of sin²x with respect to cos²x ?

1. -1

2. 1

3. sin2x

4. cos2x

For what value of m with m < 0, is the area bounded by the lines y = x, y = mx and x = 2 equal to 3 ?

1. 

2. -1

3. 

4. -2

1. a

2. b

3. c

4. d

A solution of the differential equation

(dy/dx)²  - x dy/dx=0 is

1. y = 2x

2. y = 2x+4

3. y = 2x-1

4. y = x²-2)/2

If f'(x) = x² + 2 and g(x) = 2x - 3, then what is (fg)(1) equal to ?

1. 3

2. 1

3. -2

4. -3

What is the range of the function f(x)=x +lxl if the domain is the set of real numbers ?

1. (0, oo)
    

2. [0, oo)

3. (- co, co)

4. (1, co)

If f'(x) =x(4x² - 3 ), then what is /(sinθ) equal to ?

1. - sin3θ

2. - cos3θ

3. sin3θ

4. - sin4θ

What is lim 

equal to 

1. -1

2. 0

3. 1

4. Limit does not exist

What is lim  equal to

1. -1

2. -3

3. 3

4. Limit does not exist

The mean and variance of five obser­ vations are 14 and 13.2 respectively. Three of the five observations are 11, 16 and 20. What are the other two observations ?

1. 8 and 15

2. 9 and 14

3. 10 and 13

4. 11  and 12

Let A and B be two independent events such that 

P(A) = 0.7, P(B) = k, P(AUB) = 0.8. 

What is the value of k ?

A biased coin with the probability of getting head equal to ¼ is tossed five times. What is the probability of getting tail in all the first four tosses followed by head ?

A coin is bised so that heads comes up thrice as likely as tails. In four independent tosses of coin, what is probability of getting exactly three heads?

If X and Y be two random variables such that X + Y = 100. If X follows Binomial distribution with parameters n = 100 and  p = 4/5, what is the variance of Y?

1. 1

2. 

3. 16

4. 

If  two   lines    of    regression    are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y=-3?

1. -13

2. -5

3. 5

4. 7

The central  angles  p,  q,  r  and  s  (in degrees)  of  four  sectors   in   a Pie Chart satisfy the relation 9p = 3q = 2r =6s. What is the value of 4p - q ?

1. 12

2. 24

3. 30

4. 36

The observations 4, 1, 4, 3, 6,  2, 1, 3, 4, 5, 1, 6 are outputs of 12 dices thrown simultaneously. If m and M are means of lowest 8 observations and highest 4 observations respectively, then what is (2m + M) equal to ?

1. 10

2. 12

3. 17

4. 21

A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?

1. x-4y+5=0

2. 3x + 2y - I = 0 

3. x + 4y + 1 = 0 

4. 5x - 4y + 1 = 0

A die is thrown 10 times and obtained the following outputs :

1, 2, 1, 1, 2, 1, 4, 6, 5, 4

What will be the mode of data so obtained?

1. 6

2. 4

3. 2

4. 1

Waht is following frequency distribution : 

What is the value of median of the distribution ?

1. 1

2. 2

3. 3

4. 3.5

For data -1, I, 4, 3, 8, 12, 17, 19, 9,

11; if M is the median of first 5 observations and N is the median of last five observations, then  what  is the value of 4M - N?

1. 7

2. 4

3. 1

4. 0

Let P, Q, R represent mean median and mode. If for some distribution 5P = 4Q   = R/2, then what is P+Q/2P+0.7R equal to?

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

1. a

2. b

3. c

4. d

One bag contains 3 white and 2 black balls, another bag contains 2  white and 3 black balls. Two balls  are drawn from the first bag and put  it  into the second bag and then a ball is drawn from the second bag. What is the probability that it is white ?

Three dice are thrown. What is the probability that each face shows only multiples of 3 ?

What is the probability that the month of December has 5 Sundays ?

1. 1

2. 

3. 

4. 

A natural number n is choosen from the first 50 natural numbers. What is the probability that n + 50/n < 50 ?