NDA MATHS QUESTIONS

1.Consider a question and two statements : Question :
Is 3x + 2y positive? Statement-I : x3 = -29.8 Statement-II : y = 3x Which one of the following is correct in respect of the question and the statements? –
(a) Statement-I alone is sufficient to
answer the question
(b) Statement-II alone is sufficient to
answer the question
(c) Both Statement-I and Statement-II
are together sufficient to answer
the question
(d) Both Statement-I and Statement-II
are not sufficient to answer the
question

2. Consider a question and two statements : Question :
Does the equation ax2 + bx + c = 0
have real roots of opposite sign? Statement-I : The discriminant D> 0 Statement-II : c/a> Which one of the following is correct in respect of the question and the statements?
(a) Statement-1 alone is sufficient to
answer the question
(b) Statement-Il alone is sufficient to
answer the question le)
(c)Both Statement-I and Statement-II
are together sufficient to answer
the question
(d) Both Statement- and Statement-II
are not sufficient to answer the question

3. Consider a question and two stateme Question :
Is a? + b 2 + c2-ab-bc-ca (a, b, c are distinct real numbers) always
positive? Statement-I :a>b>C Statement-II : a+b+c=0 Which one of the following is correct in respect of the question and the statements?
(a) Statement-1 alone is required to
answer the question
(b) Statement-II alone is required to
answer the question
(c) Both Statement-I and Statement-II
are required to answer the question
(d)Neither Statement-1. nor Statement-II is required to answer the
question

4. Consider a question and two statements : Question :
Is y always greater than
** + y (x + y+0)?
x2 + y2 Statement-I : *>y Statement-II : x2 + y2 > 2xy Which one of the following is correct in respect of the question and the statements? (a)Statement-l alone is required to
answer the question
(b) Statement-Il alone is required to
answer the question
(c) Both Statement-I and Statement-II
are required to answer the question
(d) Neither Statement-I nor State
ment-II is required to answer the question

5.Sudhir purchased a chair with three consecutive discounts of 20%, 12.5% and 5%. The actual deduction will be?

(a)25.35%

(b)30.33%

(c)31.35%

(d)33.50%

6.To mainain 8 cows for 60 days, a milkman has to spend Rs. 6,400. To maintain 5 cows for n days, he has to spend Rs. 4,800. What is the value of n ?

(a)68 days

(b)70 days

(c)72 days

(d)74 days

7.A student has to secure 40% of marks to pass an examination. He gets only 45 marks and fails by 5 marks. The maximum marks are

(a)120

(b)125

(c)130

(d)135

8.Five years ago, Ram was three times as old as Shyam. Four years from now, Ram will be only twice as old as Shyam. What is the present age of Ram ?

(a)28 years

(b)30 years

(c)32 years

(d)34 years

9.A boy went to his school at a speed of 12 km/hr and returned to his house at a speed of 8 km/hr. If he has taken 50 minutes for the whole journey, whatwas the total distance walked?

(a)2 km

(b)4 km

(c)6 km

(d)8 km

10.There are 350 boys in the first three standards. The ratio of the number of boys in first and second standards is 2 : 3, while that of boys in second and third standards is 4 : 5. What is the total number of boys in first and third standards?

(a)210

(b)220

(c)230

(d)240

11.There are 8 lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersects?

(a)28

(b)26

(c)24

(d)22

12.An arc of a circle subtends an angle π at the centre . If the length of the arc is 22 cm , then what is the radius of the circle?

(a)9 cm

(b)7 cm

(c)5 cm

(d)3 cm

13.The diagonals of a rhombus are of length 20 cm and 48 cm. What is the length of a side of the rhombus?

(a)26 cm

(b)29 cm

(c)36 cm

(d)39 cm

14.A hollow cube is formed by joining six identical squares. A rectangular cello tape of length 4 cm and breadth 0.5 cm is based for joining each pair of edges. What is the total area of cello tape used?

(a)12 square cm

(b)20 square cm

(c)24 square cm

(d)36 square cm

15.If,

A = {x : x is a multiple of 7}
B = {x : x is a multiple of 5}
C = {x : x is a multiple of 35}
then which one of the following is a null set ?

(a)(A – B) ∪ C

(b)(A – B) – C

(c)(A ∩ B) ∩ C

(d)(A ∩B) – C

16.Kx + 3y + 1 = 0
2x + y + 3 = 0
The pair of linear equations given above will intersect each other, if

(a)K = 6

(b)K ≠ 6

(c)K = 0

(d)K ≠ 0

17.The number of prime numbers which are less then 100 is

(a)20

(b)25

(c)30

(d)35

18.If the equations given below have a common root

x2 – px + q = 0
x2 + qx – p = 0
then which one of the following is correct?

(a) p – q = 0

(b) p + q – 2 = 0

(c) p + q – 1 = 0

(d) p – q – 1 = 0

19.710 – 510 is divisible by

(a)5

(b)7

(c)9

(d)11

20.Which of the points P(5, -1), Q( 3, -2 ) and R(1, 1) lie in the solution of the system of inequations x + y ≤ 4 and x – y ≥ 2 ?

(a)P and Q

(b)Q and R

(c)P and R

(d)P, Q and R