Column I Column II (A) In \mathbb{R}^2,if the magnitude of the projection vector of the vector \alphai^{∧}+ \betai^{∧}\text{is}\sqrt3 and if \alpha=2+\sqrt3\beta,then possible value(s) of |\alpha|is (are) (P) 1 (B) Let a and b be real numbers such that the function f(x)=\{\table-3\alphax^2-2\text{,},x<1;bx+a^2\text{,},x\geq 1is differentiable for all x ∊ \mathbb{R}.Then possible value(s) of a is (are) (Q) 2 (C) Let \omega\neq1 be a complex cube root of unity.If (3-3\omega+2\omega^2)^{4n+3}+(2+3\omega-3\omega^2)^{4n+3}+(-3+2\omega+3\omega^2)^{4n+3}=0then possible value(s) of n is (are) (R) 3 (D) Let the harmonic mean of two positive real number a\text{and}b be 4.If q is a positive real number such that a,5,q,b is an arithmetic progression then the value(s) of |q-a| is (are ) (S) 4 (T) 5 [JEE Adv 2015 P1]

Correct Answer is : (A) → (P, Q), (B) → (P, Q), (C) → (P, Q, S, T), (D) → (Q, T)

(A) → (P, Q), (B) → (P, Q), (C) → (P, R, S, T), (D) → (Q, T)

(A) → (P, Q), (B) → (P, Q), (C) → (P, Q, R, T), (D) → (Q, T)

(A) → (P, Q), (B) → (P, Q), (C) → (P, Q, S, T), (D) → (Q, T)

(A) → (P, Q), (B) → (P, Q), (C) → (P, R, S, T), (D) → (Q, T)

Vector Algebra

Section: Mathematics

Question : 19 of 38

Marks: +1, -0

Column I

Column II

(A)

In ℝ2,if the magnitude of the projection vector of the vector α

∧

+β

∧

‌is‌√3 and if α=2+√3β,then possible value(s) of |α|is (are)

(P)

(B)

Let a and b be real numbers such that the function f(x)={

−3αx2−2,	x<1
bx+a2,	x≥1

is differentiable for all x∊ℝ.Then possible value(s) of a is (are)

(Q)

(C)

Let ω≠1 be a complex cube root of unity.If (3−3ω+2ω2)4n+3+(2+3ω−3ω2)4n+3+(−3+2ω+3ω2)4n+3=0then possible value(s) of n is (are)

(R)

(D)

Let the harmonic mean of two positive real number a‌and‌b be 4.If q is a positive real number such that a,5,q,b is an arithmetic progression then the value(s) of |q−a| is (are )

(S)

(T)

[JEE Adv 2015 P1]

(A) → (P, Q), (B) → (P, Q), (C) → (P, R, S, T), (D) → (Q, T)
(A) → (P, Q), (B) → (P, Q), (C) → (P, Q, R, T), (D) → (Q, T)
(A) → (P, Q), (B) → (P, Q), (C) → (P, Q, S, T), (D) → (Q, T)
(A) → (P, Q), (B) → (P, Q), (C) → (P, R, S, T), (D) → (Q, T)

Validate

Go to Question:

Prev Question

Next Question