Question 1 :
If A is a relation on a set R, then which one of the following is correct?

Question 2 :
<b> Consider the following for the next two (02) items that follow : </b> <br> 2x² + 3x - α = 0 has roots –2 and β while the equation x² - 3mx + 2m² = 0 has both roots positive, where α&gt;0 and β&gt;0. <br> <br><br>What is the value of α?

Question 4 :
<b> A straight line passes through (1, –2, 3) and perpendicular to the plane 2x + 3y – z = 7. </b> <br>What is the image of the point (1, –2, 3) in the plane?

Question 5 :
The vertices of a triangle ABC are A (2, 3, 1), B (–2, 2, 0), and C(0, 1, –1). <br>What is the cosine of angle ABC?

Question 7 :
If the ratio AM to GM of two positive numbers a and b is 5 : 3, then a : b is equal to

Question 8 :
What is the diameter of the sphere <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec6298e55c01f053dd7acb7">

Question 9 :
If A is a square matrix, then what is adj <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50175ad67be491aba7185"> equal to?

Question 10 :
<b>The general solution of the differential equation</b> <br> <b> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec500995bf68757b5fb8740">where B, C and D are constants and A is parameter. </b> <br>What is B equal to?

Question 11 :
A survey of 850 students in a University yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance?

Question 13 :
Two straight lines passing through the point A(3, 2) cut the line 2y = x + 3 and x-axis perpendicularly at P and Q respectively. The equation of the line PQ is

Question 14 :
<b>Consider the following for the next three (03) items that follow:</b> <br> <br> Let a, x, y, z, b be in AP, where x + y + z = 15. Let a, p, q, r, b be in HP, where <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50194b9a14448a40b9c28"> <br> <br><br>What is the value of xyz?

Question 15 :
If x = sin 70°. Sin 50° and y = cos 60°. cos 80°, then what is xy equal to?

Question 16 :
The co-ordinates of incentre of ∆ ABC with vertices A(0, 6), B(8, 12) and C(8, 0) is.

Question 18 :
It has been found that if A and B play a game 12 times, A wins 6 times, B wins 4 times and they draw twice. A and B take part in a series of 3 games. The probability that they win alternately, is :

Question 19 :
In throwing of two dice, the number of exhaustive events that ‘5’ will never appear on any one of the dice is

Question 20 :
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec62a5e70f3072f92aad958"> <br> What is the minimum value of the function?

Question 21 :
What is the median of the number <br> 4.6, 0, 9.3, –4.8, 7.6, 2.3, 12.7, 3.5, 8.2, 6.1, 3.9, 5.2 ?

Question 22 :
Consider the function <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501265bf68757b5fb87c8"> <br>At what value of x does the function attain maximum value?

Question 23 :
Number of telephone calls received in 245 succesive one minute intervals at an exchange is given below in the following frequency distribution. <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec62a6cee5c6e2f33eeaa9d"> <br>What is the median of the distribution?

Question 24 :
<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 26 :
Given two points A(-2,0) and B(0, 4), M is a point with coordinates <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec62975ee5c6e2f33eea992"> <br> P divides the joining of A &amp; B in the ratio 2 : 1. C &amp; D are the mid points of BM and AM respectively. <br>Area of the ∆AMB is minimum, if the coordinates of M are

Question 28 :
Consider any point P on the ellipse <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec5010d5b3cce58210939b5">in the first quadrant. Let r and s represent its distances from (4, 0) and (–4, 0) respectively, then (r + s) is equal to

Question 30 :
The hyperbola <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec500bbad67be491aba704e">passes through the point (3√5, 1) and the length of its latus rectum is 4/3 units. The length of the conjugate axis is

Question 31 :
In a college of 300 students, every student reads 5 newspapers and every newspaper is read by 60 students. The number of newspapers is

Question 35 :
What is the area of the parallelogram having diagonals <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501835b3cce5821093a7c">

Question 37 :
<b>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). </b> <br>What are the direction ratios of the line of intersection of the given planes?

Question 41 :
A force <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec500d7b9a14448a40b9b58"> is applied at the point P, whose position vector is <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec500d7ad67be491aba70a2">What is the magnitude of the moment of the force about the origin?