1
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let A(a, 0), B(b, 2b + 1) and C(0, b), b $$\ne$$ 0, |b| $$\ne$$ 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :
A
$${{ - 2b} \over {b + 1}}$$
B
$${{2b} \over {b + 1}}$$
C
$${{2{b^2}} \over {b + 1}}$$
D
$${{ - 2{b^2}} \over {b + 1}}$$
2
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let [$$\lambda$$] be the greatest integer less than or equal to $$\lambda$$. The set of all values of $$\lambda$$ for which the system of linear equations
x + y + z = 4,
3x + 2y + 5z = 3,
9x + 4y + (28 + [$$\lambda$$])z = [$$\lambda$$] has a solution is :
A
R
B
($$-$$$$\infty$$, $$-$$9) $$\cup$$ ($$-$$9, $$\infty$$)
C
[$$-$$9, $$-$$8)
D
($$-$$$$\infty$$, $$-$$9) $$\cup$$ [$$-$$8, $$\infty$$)
3
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The set of all values of K > $$-$$1, for which the equation $${(3{x^2} + 4x + 3)^2} - (k + 1)(3{x^2} + 4x + 3)(3{x^2} + 4x + 2) + k{(3{x^2} + 4x + 2)^2} = 0$$ has real roots, is :
A
$$\left( {1,{5 \over 2}} \right]$$
B
[2, 3)
C
$$\left[ { - {1 \over 2},1} \right)$$
D
$$\left( {{1 \over 2},{3 \over 2}} \right] - \{ 1\} $$
4
JEE Main 2021 (Online) 27th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
A box open from top is made from a rectangular sheet of dimension a $$\times$$ b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :
A
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over {12}}$$
B
$${{a + b - \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
C
$${{a + b - \sqrt {{a^2} + {b^2} - ab} } \over 6}$$
D
$${{a + b + \sqrt {{a^2} + {b^2} + ab} } \over 6}$$
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