1
JEE Main 2024 (Online) 1st February Morning Shift
+4
-1
Let $3, a, b, c$ be in A.P. and $3, a-1, b+1, c+9$ be in G.P. Then, the arithmetic mean of $a, b$ and $c$ is :
A
-4
B
-1
C
13
D
11
2
JEE Main 2024 (Online) 31st January Evening Shift
+4
-1

Let $$2^{\text {nd }}, 8^{\text {th }}$$ and $$44^{\text {th }}$$ terms of a non-constant A. P. be respectively the $$1^{\text {st }}, 2^{\text {nd }}$$ and $$3^{\text {rd }}$$ terms of a G. P. If the first term of the A. P. is 1, then the sum of its first 20 terms is equal to -

A
990
B
980
C
960
D
970
3
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

For $$0 < c < b < a$$, let $$(a+b-2 c) x^2+(b+c-2 a) x+(c+a-2 b)=0$$ and $$\alpha \neq 1$$ be one of its root. Then, among the two statements

(I) If $$\alpha \in(-1,0)$$, then $$b$$ cannot be the geometric mean of $a$ and $$c$$

(II) If $$\alpha \in(0,1)$$, then $$b$$ may be the geometric mean of $$a$$ and $$c$$

A
only (II) is true
B
Both (I) and (II) are true
C
only (I) is true
D
Neither (I) nor (II) is true
4
JEE Main 2024 (Online) 31st January Morning Shift
+4
-1

The sum of the series $$\frac{1}{1-3 \cdot 1^2+1^4}+\frac{2}{1-3 \cdot 2^2+2^4}+\frac{3}{1-3 \cdot 3^2+3^4}+\ldots$$ up to 10 -terms is

A
$$\frac{45}{109}$$
B
$$-\frac{55}{109}$$
C
$$\frac{55}{109}$$
D
$$-\frac{45}{109}$$
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