Can I Crack NDA Written Exam- Part- I Compiled by www.ssbcoaching.com
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CAN I CRACK NDA- SET-02. Compiled by www.ssbcoaching.com- This is an aptitude finding test.
1. What is the number of different Messages that can be represented by three 0's and two 1's?
a) 10
b) 9
c) 8
d) 7
2. If Loga (ab) = x, then what is logb (ab) equal to ?
a) 1/x
b) x / ( x+1)
c) x / ( x-1)
d) x ( x-1)
3. What is the acute angle between the lines represented by the equations
( y - √ 3x - 5 = 0) and ( √ 3y - x +6) = 0 ?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 75 degrees
4. The system of linear equations kx + y +z =1, x +ky +z = 1 and x +y +kz = 1 has a unique solutions under which one of the following conditions?
a) K not equal to 1 anad K not equal to - 2
b) k not equal i q and k not equal to 2
c) k not equal to - 1 and k not equal to -2
d) k not equal to -1 and k not equal to 2
5. What is the number of four digit decimal numbers ( < 1 ) in which no digit is repeated?
a) 3024
b) 4536
c) 5040
d) None of the above
6. If one root of the equation ( l -m) x² + lx +1 = 0, is double the other and l is real, then what is the greatest value of m ?
a) - 9/8
b) 9 / 8
c) - 8 /9
d) 8/9
7. What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?
a) 60
b) 120
c) 500
d) 1000
8. A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?
a) 1/2
b) 3/8
c) 1/4
d) 1/8
9. For the data, 3, 5, 1, 6, 5, 9, 5, 2, 8, 6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?
a) x = y Not equal to z
b) x not equal to z
c) x not equal to z
d) x = y = z
10. A point is chosen at random inside a rectangle measuring 6 inches by 5 inches, What is the probability that the randomly selected point is at least one inch from the edge of the Rectangle?
a) 2/3
b) 1/3
c) 1/4
d) 2/5
11. A certain type of missible hits the target with probability = 0.3, what is the least number of missiles should be fires so that there is at least an 80% probability that the target is hit?
a) 5
b) 6
c) 7
d) None of the above
12. If two dice are thrown , then what is the probability that the sum on the two faces is greater than or equal to 4?
a) 13 /18
b) 5 /6
c) 11 / 12
d) 35 / 36
13. What is the probability of 5 Sundays in the month of December?
a) 1/7
b) 2/7
c) 3/ 7
d) None of these
14. What is the mean deviation from the mean of the numbers, 10, 9, 21, 16 and 24 ?
a) 5.2
b) 5.0
c) 4.5
d) 4.0
15. If A = ( cos12 ° - cos 36°) ( sin 96° +sin 24°) and
B = ( sin60° - sin 12 °) ( cos 48° - cos 72°), then what is A/ B equal to ?
a) - 1
b) 0
c) 1
d) 2
16. ( a, 2b ) is the mid-point of the line seqment joining the points ( 10, -6) and ( k,4). If a - 2b = 7, then what is the value of k ?
a) 2
b) 3
c) 4
d) 5
17. What is the number of natural numbers less than or equal to 1000 which are neiterh divisble by 10 nor 15 nor 25?
a) 860
b) 854
c) 840
d) 824
18.
Consider the following statements :
1. If ABC is an equilateral triangle, then 3 tan (A+B) tan C =1
2. If ABC is a triangle in which A = 78 Degrees, and B = 66 degrees, then
tan (A/2 + C) < tan A
3. If ABC is any Triangle, then tan ( A+B/ 2) sin(C/2) < cost (C/2), which of the following of the above statements is / are correct?
a) 1 only
b) 2 only
c) 1 and 2
d) 2 and 3
19. What is the binary equivalent of the decimal number 0.3125?
a) 0.0111
b) 0.1010
c) 0.0101
d) 0.1101
20. If A is a square matrix, then what is ad [A ¯¹ ] - (adj A) ¯¹ equal to ?
a) 2 I A I
b) Null Matrix
c) Ubnit Matrix
d) None of the above
21. What are the order and degree respectively of the differential euqation whose solution is y = cx + c² - 3 c pwer 3 by 2 + 2 , where c is a parameter?
a) 1, 2
b) 2, 2
c) 1, 3
d) 1, 4
22. Consider a circle passing through the origin and the points ( a,b) and ( -b, -a)
On which line does the centre of the circle lie?
What is the sum of the squares of the intercepts cut off by the circle on the axes ?
a) { (a² + b²) / ( a² - b²) } ²
b) 2{ (a² + b ²) / ( a-b) } ²
c) 4 ( (a² +b²) / ( a - b)}²
d) None of the above
23. Consider a circle passing through the origin and the points ( a,b) and ( -b, -a)
On which line does the centre of the circle lie?
a) x + y = 0
b) x - y = 0
c) x + y = a +b
d) x - y = a² - b²
24. A plane P passes through the line of intersection of the planes 2x -y + 3z =2, x + y -z = 1 and the point (1,0,1).
From the above statement find out,
what are the direction ratios of the tline of intersection of the given planes?
a) {2, -5, -3}
b) {1. -5. -3}
c) {2, 5, 3}
d) { 1, 3, 5}
25. What is the area of the Parallelogram ?
a) 7/2 square units
b) 4 suqare units
c) 11/ 2 square units
d) 7 square units.
CAN I CRACK NDA- SET-02. Compiled by www.ssbcoaching.com- This is an aptitude finding test.
1. What is the number of different Messages that can be represented by three 0's and two 1's?
a) 10
b) 9
c) 8
d) 7
2. If Loga (ab) = x, then what is logb (ab) equal to ?
a) 1/x
b) x / ( x+1)
c) x / ( x-1)
d) x ( x-1)
3. What is the acute angle between the lines represented by the equations
( y - √ 3x - 5 = 0) and ( √ 3y - x +6) = 0 ?
a) 30 degrees
b) 45 degrees
c) 60 degrees
d) 75 degrees
4. The system of linear equations kx + y +z =1, x +ky +z = 1 and x +y +kz = 1 has a unique solutions under which one of the following conditions?
a) K not equal to 1 anad K not equal to - 2
b) k not equal i q and k not equal to 2
c) k not equal to - 1 and k not equal to -2
d) k not equal to -1 and k not equal to 2
5. What is the number of four digit decimal numbers ( < 1 ) in which no digit is repeated?
a) 3024
b) 4536
c) 5040
d) None of the above
6. If one root of the equation ( l -m) x² + lx +1 = 0, is double the other and l is real, then what is the greatest value of m ?
a) - 9/8
b) 9 / 8
c) - 8 /9
d) 8/9
7. What is the number of ways in which 3 holiday travel tickets are to be given to 10 employees of an organization, if each employee is eligible for any one or more of the tickets?
a) 60
b) 120
c) 500
d) 1000
8. A fair coin is tossed 100 times. What is the probability of getting tails an odd number of times?
a) 1/2
b) 3/8
c) 1/4
d) 1/8
9. For the data, 3, 5, 1, 6, 5, 9, 5, 2, 8, 6 the mean, median and mode are x, y and z respectively. Which one of the following is correct?
a) x = y Not equal to z
b) x not equal to z
c) x not equal to z
d) x = y = z
10. A point is chosen at random inside a rectangle measuring 6 inches by 5 inches, What is the probability that the randomly selected point is at least one inch from the edge of the Rectangle?
a) 2/3
b) 1/3
c) 1/4
d) 2/5
11. A certain type of missible hits the target with probability = 0.3, what is the least number of missiles should be fires so that there is at least an 80% probability that the target is hit?
a) 5
b) 6
c) 7
d) None of the above
12. If two dice are thrown , then what is the probability that the sum on the two faces is greater than or equal to 4?
a) 13 /18
b) 5 /6
c) 11 / 12
d) 35 / 36
13. What is the probability of 5 Sundays in the month of December?
a) 1/7
b) 2/7
c) 3/ 7
d) None of these
14. What is the mean deviation from the mean of the numbers, 10, 9, 21, 16 and 24 ?
a) 5.2
b) 5.0
c) 4.5
d) 4.0
15. If A = ( cos12 ° - cos 36°) ( sin 96° +sin 24°) and
B = ( sin60° - sin 12 °) ( cos 48° - cos 72°), then what is A/ B equal to ?
a) - 1
b) 0
c) 1
d) 2
16. ( a, 2b ) is the mid-point of the line seqment joining the points ( 10, -6) and ( k,4). If a - 2b = 7, then what is the value of k ?
a) 2
b) 3
c) 4
d) 5
17. What is the number of natural numbers less than or equal to 1000 which are neiterh divisble by 10 nor 15 nor 25?
a) 860
b) 854
c) 840
d) 824
18.
Consider the following statements :
1. If ABC is an equilateral triangle, then 3 tan (A+B) tan C =1
2. If ABC is a triangle in which A = 78 Degrees, and B = 66 degrees, then
tan (A/2 + C) < tan A
3. If ABC is any Triangle, then tan ( A+B/ 2) sin(C/2) < cost (C/2), which of the following of the above statements is / are correct?
a) 1 only
b) 2 only
c) 1 and 2
d) 2 and 3
19. What is the binary equivalent of the decimal number 0.3125?
a) 0.0111
b) 0.1010
c) 0.0101
d) 0.1101
20. If A is a square matrix, then what is ad [A ¯¹ ] - (adj A) ¯¹ equal to ?
a) 2 I A I
b) Null Matrix
c) Ubnit Matrix
d) None of the above
21. What are the order and degree respectively of the differential euqation whose solution is y = cx + c² - 3 c pwer 3 by 2 + 2 , where c is a parameter?
a) 1, 2
b) 2, 2
c) 1, 3
d) 1, 4
22. Consider a circle passing through the origin and the points ( a,b) and ( -b, -a)
On which line does the centre of the circle lie?
What is the sum of the squares of the intercepts cut off by the circle on the axes ?
a) { (a² + b²) / ( a² - b²) } ²
b) 2{ (a² + b ²) / ( a-b) } ²
c) 4 ( (a² +b²) / ( a - b)}²
d) None of the above
23. Consider a circle passing through the origin and the points ( a,b) and ( -b, -a)
On which line does the centre of the circle lie?
a) x + y = 0
b) x - y = 0
c) x + y = a +b
d) x - y = a² - b²
24. A plane P passes through the line of intersection of the planes 2x -y + 3z =2, x + y -z = 1 and the point (1,0,1).
From the above statement find out,
what are the direction ratios of the tline of intersection of the given planes?
a) {2, -5, -3}
b) {1. -5. -3}
c) {2, 5, 3}
d) { 1, 3, 5}
25. What is the area of the Parallelogram ?
a) 7/2 square units
b) 4 suqare units
c) 11/ 2 square units
d) 7 square units.
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