Question 1 :
If A is a relation on a set R, then which one of the following is correct?
Question 2 : Consider the following for triangle ABC : <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501ffb9a14448a40b9cc6"> <br> Which of the above are correct?
Question 3 : <b> </b>Consider the spheres <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50081ad67be491aba6fcc"> <br>What is the distance between the centres of the two spheres?
Question 4 : Consider the following statements : <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec5011b5bf68757b5fb87ab"> <br> Which of the above statements is/are correct?
Question 5 :
If A and B are two events such that 2P(A) = 3P(B), where 0 < P(A) < P(B) < 1, then which one of the following is correct?
Question 9 :
The equation of the line, the reciprocals of whose intercepts on the axes are m & n, is given by
Question 10 : If <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec6298755c01f053dd7aca4"> then what is the value of B ?
Question 11 :
Let the random variable X follow B(6, p). If 16 P(X = 4) = P(X = 2), then what is the value of p?
Question 12 :
If the monthly expenditure pattern of a person who earns a monthly salary of Rs. 15000 is represented in a pie diagram, then the sector angle of an item on transport expenses measures 15°. what is his monthly expenditure on transport?
Question 13 : The order and degree of the differential equation <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50275ad67be491aba72eb">
Question 14 :
A bag contains 5 black and 3 white balls. Two balls are drawn at random one after the other without replacement. What is the probability that both are white?
Question 15 :
Consider the following statements : <br> 1. The derivative where the function attains maxima or minima must be zero. <br> 2. If a function is differentiable at a point, then it must be continuous at that point. <br> Which of the above statements is/are correct?
Question 16 : sin A + 2 sin 2A + sin 3A is equal to which of the following? <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec5019fad67be491aba71c6"> <br> Select the correct answer using the code given below:
Question 17 : Given a function <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec500c3b9a14448a40b9b1c"> <br><br>What is the value of a?
Question 19 :
What is the number of different messages that can be represented by three 0’s and two 1’s?
Question 20 : A question is given to three student A, B and C whose chances of solving it are <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50231ad67be491aba7290"> respectively. What is the probability that the question will be solved?
Question 22 : <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50229b9a14448a40b9d00"> <br> Which one of the following statements is correct in respect of the above function?
Question 24 :
If sin α + sin β = 0 = cos α + cos β, where 0 < β < α < 2π, then which one of the following is correct ?
Question 25 :
<b>Consider the following for the next two (02) items that follow:</b> <br> <br> The sixth term of an AP is 2 and its common difference is greater than 1. <br> <br><br>What is the first term of the AP so that the product of the first, fourth and fifth terms is greatest?
Question 26 :
The mean weight of 150 students in a certain class is 60 kg. The mean weight of boys in the class is 70 kg and that of girls is 55 kg. what is the number of boys in the class?
Question 27 :
Two cards are drawn successively without replacement from a well-shuffled pack of 52 cards. The probability of drawing two aces is
Question 28 :
In a Binomial distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials?
Question 29 :
A basket contains 20 apples and 10 oranges out of which 5 apples & 3 oranges are defective. If a person takes out 2 at random. what is the probability that either both are apples or both are good?
Question 30 : <b> Consider the following for the next two (02) items that follow : </b> <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501acb9a14448a40b9c76"> <br> <br><br>If <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501adb9a14448a40b9c7a">then which of the following equations is/are correct? <br> 1. y – x = 4 <br> 2. 2z – 3 = 0 <br> Select the correct answer using the code given below:
Question 33 :
If f(x) = |x|+|x-1|, then which one of the following is correct?
Question 34 :
Let X be the set of all citizens of India. Elements x, y in X are said to be related if the difference of their age is 5 years. Which one of the following is correct?
Question 35 : <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec62a2d70f3072f92aad91e"> <br> What is the value of the independent term? <br>
Question 36 :
If (a, b) is at unit distance from the line 8x + 6y + 1 = 0, then which of the following conditions are correct? <br> 1. 3a – 4b – 4 = 0 <br> 2. 8a + 6b + 11 = 0 <br> 3. 8a + 6b – 9 = 0 <br> Select the correct answer using the code given below:
Question 37 :
What is the equation of a curve passing through (0, 1) and whose differential equation is given by dy = y tan x dx?
Question 38 :
Consider the set A of all matrices of order 3 × 3 with entries 0 or 1 only. Let B be the subset of A consisting of all matrices whose determinant is 1. Let C be the subset of A consisting of all matrices whose determinant is –1. The which one of the following is correct?
Question 39 :
If different words are formed with all the letters of the word ‘AGAIN’ and are arranged alphabetically among themselves as in a dictionary, the word at the 50th place with be
Question 40 :
If G is the centroid of a ∆ABC, then GA + GB + GC is equal to
Question 41 :
If A + B + C = π, then what is cos (A + B) + cos C equal to?
Question 43 :
A box contains 3 white and 2 black balls. Two balls are drawn at random one after the other. If the balls are not replaced, what is the probability that both the balls are black?
Question 44 : Consider the function <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501295bf68757b5fb87d0"> <br>The function f(x) is a decreasing function in the interval
Question 45 :
Let S be a set of all distinct numbers of the form p/q, where p, q ϵ [1, 2, 3, 4, 5, 6]. What is the cardinality of the set S?
Question 46 : <b> Consider the following for the next three (03) items that follow: </b> <br> <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501b8b9a14448a40b9c98"> <br> <br><br>Which of the following statements is/are correct? <br> 1. g(x) is differentiable at x = 0. <br> 2. g(x) is differentiable at x = 2. <br> Select the correct answer using the code given below:
Question 49 : <b> Consider the following for the next three (03) items that follow: </b> <br> <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501b8b9a14448a40b9c98"> <br> <br><br>What is the value of the differential coefficient of g(x) at x = –2?
Question 50 :
A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?
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