1
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If the sum of ' $n$ ' terms of an A.P. is $3 n^2+5 n$ and its $m$ th term is 164 , then the value of $m$ is

A
26
B
27
C
28
D
29
2
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If $x=\int\limits_0^y \frac{1}{\sqrt{1+9 t^2}} d t$ and $\frac{d^2 y}{d x^2}=a y$, then $a$ is equal to

A
3
B
6
C
9
D
1
3
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is

A
4
B
8
C
5
D
7
4
WB JEE 2025
MCQ (Single Correct Answer)
+1
-0.25
Change Language

If ' $\theta$ ' is the angle between two vectors $\vec{a}$ and $\vec{b}$ such that $|\vec{a}|=7,|\vec{b}|=1$ and $|\vec{a} \times \vec{b}|^2=k^2-(\vec{a} \cdot \vec{b})^2$, then the values of $k$ and $\theta$ are

A
$k=1, \theta=45^{\circ}$
B
$k=7, \theta=60^{\circ}$
C
$k=49, \theta=90^{\circ}$
D
$k=7$ and $\theta$ is arbitrary
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