Section-A

One Options Correct Type

Question 1:

The sum of solutions of the equation  is:

(A)

(B)

(C)

(D)

 

Question 2:

Let . Then:

(A)

(B)

(C)

(D)

 

Question 3:

Out of all the patients in a hospital  are found to be suffering from heart ailment and  are suffering from lungs infection. If  of them are suffering from both ailments, then  can not belong to the set:

(A)

(B)

(C)

(D)

 

Question 4:

The equation  represents a circle with:

(A) centre at  and radius 2

(B) centre at  and radius

(C) centre at  and radius

(D) centre at  and radius

 

Question 5:

Let . If the system of linear equations.

has a non trivial solution, then the value of  is:
(A)
(B)
(C)
(D)

 

Question 6:

A plane  contains the line , and is perpendicular to the plane . Then which of the following points lies on  ?

(A)

(B)

(C)

(D)

 

Question 7:

The sum of the series  when  is:

(A)
(B)
(C)
(D)

 

Question 8:

If  is the co-efficient of  in the expansion of , then the value of  is equal to

(A)

(B)

(C)

(D)

 

Question 9:

If , and , then the inverse of the matrix  is equal to

(A)

(B)

(C)

(D)

 

Question 10:

The value of  is:

(A)

(B)

(C)

(D)

 

Question 11:

On the ellipse  let  be a point in the second quadrant such that the tangent at  to the ellipse is perpendicular to the line . Let  and  be the foci of the ellipse and e be its eccentricity. If  is the area of the triangle SPS' then, the value of  is:

(A) 24

(B) 6

(C) 12

(D) 14

Question 12:

Let  and  be independent events such that . The largest value of , for which  (exactly one of  occurs) , is:
(A)
(B)
(C)
(D)

 

Question 13:

If a line along a chord of the circle , passes through the point  and is tangent to the parabola , then the length of this chord is:

(A) 7

(B) 5

(C)

(D)

 

Question 14:

If the truth value of the Boolean expression  is false, then the truth values of the statements  respectively can be:

(A) F T F

(B) T F F

(C) FF T

(D) T F T

 

Question 15:

The mean and standard deviation of 20 observations were calculated as 10 and 2.5 respectively. It was found that by mistake one data value was taken as 25 instead of 35 . If  and  are the mean and standard deviation respectively for correct data, then  is:

(A)

(B)

(C)

(D)

 

Question 16:

Let  be a triangle with  and . If the equation of the median through  is  and the equation of angle bisector of  is , then  is equal to:
(A)
(B)
(C)

(D) 2

 

Question 17:

Let  be a solution curve of the differential equation . If , then the value of  is:

(A)

(B)

(C)

(D)

 

Question 18:

Let  and . If  is a vector such that  and , then  is equal to

(A) -2

(B) 6

(C) -6

(D) 2

 

Question 19:

If the sum of an infinite GP  Is 15 and the sum of the squares of its each term is 150,then …. is :

(A)

(B)

(C)

(D)

 

Question 20:

If  , the ratio  is  

(A) 

(B)

(C)

(D)

Section-B

Numerical Answer Type

Question 1:

A wire of length  is cut into two pieces, one of the pieces is bent to form a square and the other is bent to form a circle. If the sum of the areas of the two figures is minimum, and the circumference of the circle is  (meter), then  is equal to

 

Question 2:

The sum of all integral values of  for which the equation  in  has no real roots, is

 

Question 3:

The area of the region  is

 

Question 4:

If  , then   is equal to

 

Question 5:

Let the line  be the projection of the line  in the plane . If  is the distance of the point  from , then  is equal to

 

Question 6:

If  is an implicit function of  such that , then  at  is equal to

 

Question 7:

The locus of a point which moves such that the sum of squares of its distances from the points , 0),(1,0),(0,1),(1,1)  is 18 units, is a circle of diameter . Then  is equal to

 

Question 8:

Let . Then the value of

 is

 

Question 9:

Let . Define a function  If  is continuous at , then  is equal to

 

Question 10:

The number of three digit even numbers, formed by the digits  if the repetition of digits is not allowed, is    

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