1
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The shortest distance between the lines $$x+1=2y=-12z$$ and $$x=y+2=6z-6$$ is :

A
3
B
$$\frac{5}{2}$$
C
$$\frac{3}{2}$$
D
2
2
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let T and C respectively be the transverse and conjugate axes of the hyperbola $$16{x^2} - {y^2} + 64x + 4y + 44 = 0$$. Then the area of the region above the parabola $${x^2} = y + 4$$, below the transverse axis T and on the right of the conjugate axis C is :

A
$$4\sqrt 6 - {{28} \over 3}$$
B
$$4\sqrt 6 - {{44} \over 3}$$
C
$$4\sqrt 6 + {{28} \over 3}$$
D
$$4\sqrt 6 + {{44} \over 3}$$
3
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let the function $$f(x) = 2{x^3} + (2p - 7){x^2} + 3(2p - 9)x - 6$$ have a maxima for some value of $$x < 0$$ and a minima for some value of $$x > 0$$. Then, the set of all values of p is

A
$$\left( { - {9 \over 2},{9 \over 2}} \right)$$
B
$$\left( {{9 \over 2},\infty } \right)$$
C
$$\left( {0,{9 \over 2}} \right)$$
D
$$\left( { - \infty ,{9 \over 2}} \right)$$
4
JEE Main 2023 (Online) 25th January Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language

Let $$\Delta ,\nabla \in \{ \wedge , \vee \} $$ be such that $$\mathrm{(p \to q)\Delta (p\nabla q)}$$ is a tautology. Then

A
$$\Delta = \vee ,\nabla = \vee $$
B
$$\Delta = \vee ,\nabla = \wedge $$
C
$$\Delta = \wedge ,\nabla = \wedge $$
D
$$\Delta = \wedge ,\nabla = \vee $$
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