Question 2 :
The point at which the maximum value of {tex} ( 3 x + 2 y ) {/tex} subject to the constraints {tex} x + y \leq 2 ,\ x \geq 0 ,\ y \geq 0 {/tex} is obtained, is
Question 3 :
The vertex of common graph of inequalities {tex} 2 x + y \geq 2 {/tex} and {tex} x - y \leq 3 , {/tex} is
Question 4 :
The solution for minimizing the function {tex} z = x + y {/tex} under a L.P.P. with constraints {tex} x + y \geq 1 ,\ x + 2 y \leq 10 ,\ y \leq 4 {/tex} and {tex} x ,\ y \geq 0 {/tex}, is
Question 5 :
For the constraint of a linear optimizing function {tex} z = x _ { 1 } + x _ { 2 } , {/tex} given by {tex} x _ { 1 } + x _ { 2 } \leq 1,3 x _ { 1 } + x _ { 2 } \geq 3 {/tex} and {tex} x _ { 1 } , x _ { 2 } \geq 0 {/tex}
Question 6 :
On maximizing {tex} z = 4 x + 9 y {/tex} subject to {tex} x + 5 y \leq 200 {/tex}, {tex} 2 x + 3 y \leq 134 {/tex} and {tex} x , y \geq 0 {/tex}, {tex} z = {/tex}
Question 8 :
The maximum value of {tex} 10 x + 5 y {/tex} under the constraints {tex} 3 x + y \leq 15 ,\ x + 2 y \leq 8 ,\ x ,\ y \geq 0 {/tex} is
Question 9 :
The maximum value of {tex} z = 4 x + 2 y {/tex} subject to the constraints {tex} 2 x + 3 y \leq 18 ,\ x + y \geq 10 ;\ x ,\ y \geq 0 , {/tex} is
Question 10 :
The intermediate solutions of constraints must be checked by substituting them back into
Question 12 :
The solution set of the inequation {tex} 2 x + y > 5 , {/tex} is
Question 13 :
The necessary condition for third quadrant region in {tex} x y {/tex}-plane, is
Question 14 :
The point at which the maximum value of {tex} ( x + y ) {/tex} subject to the constraints {tex} 2 x + 5 y \leq 100, \ \frac { x } { 25 } + \frac { y } { 49 } \leq 1, \ x ,\ y \geq 0 {/tex} is obtained, is
Question 17 :
{tex} z = a x + b y ,\ a ,\ b {/tex} being positive, under constraints {tex} y \geq 1 {/tex}, {tex} x - 4 y + 8 \geq 0 ,\ x ,\ y \geq 0 {/tex} has
Question 18 :
If the number of available constraints is 3 and the number of parameters to be optimized is 4, then
Question 19 : The feasible region for the following constraints {tex} L _ { 1 } \leq 0 ,\ L _ { 2 } \geq 0 ,\ L _ { 3 } = 0 ,\ x \geq 0 ,\ y \geq 0 {/tex} in the diagram shown is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd6826ef197791516a5f269"><br>
Question 20 :
The region represented by {tex} 2 x + 3 y - 5 \leq 0 {/tex} and {tex} 4 x - 3 y + 2 \leq 0 {/tex}, is
Question 21 :
In which quadrant, the bounded region for inequations {tex} x + y \leq 1 {/tex} and {tex} x - y \leq 1 {/tex} is situated
Question 22 :
The position of points {tex} O ( 0,0 ) {/tex} and {tex} P ( 2 , - 2 ) {/tex} in the region of graph of inequation {tex} 2 x - 3 y < 5 , {/tex} will be
Question 23 : The minimum value of objective function {tex} c = 2 x + 2 y {/tex} in the given feasible region, is<br><img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5dd682ccf197791516a5f2b1"><br>
Question 24 :
A vertex of bounded region of inequalities {tex} x \geq 0 {/tex}, {tex} x + 2 y \geq 0 {/tex} and {tex} 2 x + y \leq 4 , {/tex} is
Question 26 :
For the L.P. problem {tex} { Min }\ z = 2 x - 10 y {/tex} subject to {tex} x - y \geq 0 ,\ x - 5 y \geq - 5 {/tex} and {tex} x , y \geq 0 ,\ z = {/tex}
Question 27 :
For the L.P. problem {tex} { Min }\ z = 2 x + y {/tex} subject to {tex} 5 x + 10 y \leq 50 ,\ x + y \geq 1 ,\ y \leq 4 {/tex} and {tex} x ,\ y \geq 0 ,\ z = {/tex}
Question 28 :
The solution of a problem to maximize the objective function {tex} z = x + 2 y {/tex} under the constraints {tex} x - y \leq 2 {/tex}, {tex} x + y \leq 4 {/tex} and {tex} x , y \geq 0 {/tex}, is
Question 29 :
The maximum value of {tex} \mu = 3 x + 4 y , {/tex} subject to the conditions {tex} x + y \leq 40 ,\ x + 2 y \leq 60 ,\ x ,\ y \geq 0 {/tex} is
Question 30 :
The sum of two positive integers is at most 5. The difference between two times of second number and first number is at most 4. If the first number is {tex} x {/tex} and second number {tex} y , {/tex} then for maximizing the product of these two numbers, the mathematical formulation is
Question 31 :
Three like parallel forces P, Q, R act at the corner points of a triangle ABC. Their resultant passes through the circumcenter, if
Question 32 :
A hockey stick pushes a ball at rest for 0.01 second with an average force of 50 N. If the ball weighs 0.2 kg, then the velocity of the ball just after being pushed is
Question 33 :
A train of length 200 m travelling at 30 m/sec. overtakes another of length 300 m travelling at 20 m/sec. The time taken by the first train to pass the second is
Question 34 :
If the resultant of two forces of magnitude P and 2P is perpendicular to P, then the angle between the forces is
Question 36 :
If for a slightly assymetric distribution, mean and median are 5 and 6 respectively. What is its mode
Question 37 :
In a class of 100 students, there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class are 72, then what are the average marks of the girls
Question 38 :
S.D. of data is 6 when each observation is increased by 1, then the S.D. of new data is
Question 39 : The mode of the distribution <table>
<tr><th>Marks</th> <th>students</th> </tr>
<tr><td>(A) 4</td> <td>(i) 6</td> </tr>
<tr><td>(B) 5</td> <td>(ii) 7</td> </tr>
<tr><td>(C) 6</td> <td>(iii)10</td> </tr>
<tr><td>(D) 7</td> <td>(iv)8</td> </tr>
<tr><td>(E) 8</td> <td>(v)3</td> </tr>
Question 40 :
A man of mass 80 kg. is travelling in a lift. The reaction between the floor of the lift and the man when the lift is ascending upwards at 4 m/sec<sup>2</sup> is
Question 41 :
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observation of the set is increased by 2, then the median of the new set
Question 42 :
Coefficient of correlation between observations(1, 6),(2, 5),(3, 4), (4, 3), (5, 2), (6, 1) is
Question 43 :
Two bodies of masses m and 4m are moving with equal momentum. The ratio of their K.E. is
Question 44 :
The quartile deviation of daily wages (in Rs.) of 7 persons given below 12, 7, 15, 10, 17, 19, 25 is
Question 45 :
The resultant of three forces represented in magnitude and direction by the sides of a triangle ABC taken in order with BC = 5 cm, CA = 5 cm, and AB = 8 cm, is a couple of moment
Question 46 :
Given that the regression coefficients are - 1.5 and 0.5, the value of the square of correlation coefficient is
