1
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the equation cos4 $$\theta $$ + sin4 $$\theta $$ + $$\lambda $$ = 0 has real solutions for $$\theta $$, then $$\lambda $$ lies in the interval :
A
$$\left[ { - {3 \over 2}, - {5 \over 4}} \right]$$
B
$$\left( { - {1 \over 2}, - {1 \over 4}} \right]$$
C
$$\left( { - {5 \over 4}, - 1} \right]$$
D
$$\left[ { - 1, - {1 \over 2}} \right]$$
2
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$ \to $$ R be a function which satisfies
f(x + y) = f(x) + f(y) $$\forall $$ x, y $$ \in $$ R. If f(1) = 2 and
g(n) = $$\sum\limits_{k = 1}^{\left( {n - 1} \right)} {f\left( k \right)} $$, n $$ \in $$ N then the value of n, for which g(n) = 20, is :
A
20
B
9
C
5
D
4
3
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a, b, c $$ \in $$ R be all non-zero and satisfy
a3 + b3 + c3 = 2. If the matrix

A = $$\left( {\matrix{ a & b & c \cr b & c & a \cr c & a & b \cr } } \right)$$

satisfies ATA = I, then a value of abc can be :
A
3
B
$${1 \over 3}$$
C
-$${1 \over 3}$$
D
$${2 \over 3}$$
4
JEE Main 2020 (Online) 2nd September Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If the sum of first 11 terms of an A.P.,
a1, a2, a3, .... is 0 (a $$ \ne $$ 0), then the sum of the A.P.,
a1 , a3 , a5 ,....., a23 is ka1 , where k is equal to :
A
$${{121} \over {10}}$$
B
-$${{121} \over {10}}$$
C
$${{72} \over 5}$$
D
-$${{72} \over 5}$$
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