Question 2 :
<b>Matrix A has x rows and x+5 columns. Matrix B has y rows &amp; 11–y columns. Both AB &amp; BA exist. </b> <br> <br>Find the value of x.

Question 4 :
A bag contains 10 white and 15 black balls. <br> Two balls are drawn in succession without replacement. What is the probability that first is white and second is black ?

Question 5 :
Let f(x) &amp; g(x) be twice differentiable functions on [0,2] satisfying <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec6297eaf172b04d746c15d">(1)= 6, <br> f(2) = 3 &amp; g(2)= 9. Then what is f(x) – g(x) at x = 4 equal to ?

Question 7 :
Consider the lines <br> y = 3x, y = 6x and y = 9 <br>What is the area of the triangle formed by these lines?

Question 8 :
What are the coordinates of the point on the parabola which is closest to the straight line?

Question 10 :
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec6297aee5c6e2f33eea9a1"> <br> <br>The value of a and b are respectively

Question 11 :
A straight line passes through (1, –2, 3) and perpendicular to the plane 2x + 3y – z = 7. <br>What is the image of the point (1, –2, 3) in the plane?

Question 12 :
If A = {x, y}, B = {2, 3}, C = {3, 4}, then what is the number of elements in A × (B ∪ C) ?

Question 13 :
<b> Consider the following for the next three (03) items that follow : </b> <br> <br> Let f(x) = [x], where [.] is the greatest integer function and g(x) = sin x be two real valued functions over R. <br> <br><br>Which of the following statements are correct? <br> 1. (fof) (x) = f(x). <br> 2. (gog) (x) = g(x) only when x = 0. <br> 3. (go(fog)) (x) can take only three values. <br> Select the correct answer using the code given below:

Question 16 :
<b>Consider the following for the next two (02) items that follow : </b> <br> <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50195ad67be491aba71a6"> <br> <br><br>What is the value of c?

Question 17 :
<b> Consider the following for the next two (02) items that follow: </b> <br> <br> <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501aead67be491aba71f3"> <br> <br><br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec501aeb9a14448a40b9c7c">

Question 19 :
If x dy = y dx + y² dy, y &gt; 0 and y(1) = 1, then what is y(–3) equal to?

Question 20 :
In a triangle ABC if a = 2, b = 3 and sin A = 2/3, then what is angle B equal to?

Question 21 :
<img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50103b9a14448a40b9bb5"> <br>If the coefficients of <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50103ad67be491aba712c"> are equal in the expansion, then r is equal to

Question 22 :
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 25 :
If <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/NDA/5ec50197ad67be491aba71ac">, then which of the following are correct? <br> 1. f(θ) × f(ϕ) = f(θ + ϕ). <br> 2. The value of the determinant of the matrix f(θ) × f(ϕ) is 1. <br> 3. The determinant of f(x) is an even function. <br> Select the correct answer using the code given below: