1
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the line x + y = 1 meet the axes of x and y at A and B, respectively. A right angled triangle AMN is inscribed in the triangle OAB, where O is the origin and the points M and N lie on the lines OB and AB, respectively. If the area of the triangle AMN is $ \frac{4}{9} $ of the area of the triangle OAB and AN : NB = $ \lambda : 1 $, then the sum of all possible value(s) of $ \lambda $ is:

A

$\frac{1}{2}$

B

$\frac{5}{2}$

C

2

D

$\frac{13}{6}$

2
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Bag 1 contains 4 white balls and 5 black balls, and Bag 2 contains n white balls and 3 black balls. One ball is drawn randomly from Bag 1 and transferred to Bag 2. A ball is then drawn randomly from Bag 2. If the probability, that the ball drawn is white, is $ \frac{29}{45} $, then n is equal to:

A

5

B

6

C

4

D

3

3
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The remainder, when $7^{103}$ is divided by 23, is equal to:

A

9

B

6

C

14

D

17

4
JEE Main 2025 (Online) 29th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $\alpha x+\beta y=109$ is the equation of the chord of the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$, whose mid point is $\left(\frac{5}{2}, \frac{1}{2}\right)$. then $\alpha+\beta$ is equal to :
A

37

B

46

C

72

D

58

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