NTA JEE Main 7th January 2020 Shift 2
For the following questions answer them individually
NTA JEE Main 7th January 2020 Shift 2 - Question 51
Let $$\alpha$$ and $$\beta$$ be the roots of the equation $$x^2 - x - 1 = 0$$. If $$p_k = (\alpha)^k + (\beta)^k$$, $$k \ge 1$$, then which one of the following statements is not true?
NTA JEE Main 7th January 2020 Shift 2 - Question 52
If $$\frac{3+i\sin\theta}{4-i\cos\theta}$$, $$\theta \in [0, 2\pi]$$, is a real number, then an argument of $$\sin\theta + i\cos\theta$$ is
NTA JEE Main 7th January 2020 Shift 2 - Question 53
Let $$a_1, a_2, a_3, \ldots$$ be a G.P. such that $$a_1 < 0$$, $$a_1 + a_2 = 4$$ and $$a_3 + a_4 = 16$$. If $$\sum_{i=1}^{9} a_i = 4\lambda$$, then $$\lambda$$ is equal to.
NTA JEE Main 7th January 2020 Shift 2 - Question 54
If the sum of the first 40 terms of the series, $$3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + \ldots$$ is $$(102)m$$, then $$m$$ is equal to
NTA JEE Main 7th January 2020 Shift 2 - Question 55
The coefficient of $$x^7$$ in the expression $$(1 + x)^{10} + x(1 + x)^9 + x^2(1 + x)^8 + \ldots + x^{10}$$, is
NTA JEE Main 7th January 2020 Shift 2 - Question 56
The number of ordered pairs $$(r, k)$$ for which $$6 \cdot {}^{35}C_r = (k^2 - 3) \cdot {}^{36}C_{r+1}$$, where $$k$$ is an integer is
NTA JEE Main 7th January 2020 Shift 2 - Question 57
The locus of the mid-points of the perpendiculars drawn from points on the line $$x = 2y$$, to the line $$x = y$$, is
NTA JEE Main 7th January 2020 Shift 2 - Question 58
Let the tangents drawn from the origin to the circle, $$x^2 + y^2 - 8x - 4y + 16 = 0$$ touch it at the points A and B. Then $$(AB)^2$$ is equal to
NTA JEE Main 7th January 2020 Shift 2 - Question 59
If $$3x + 4y = 12\sqrt{2}$$ is a tangent to the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{9} = 1$$ for some $$a \in R$$, then the distance between the foci of the ellipse is
NTA JEE Main 7th January 2020 Shift 2 - Question 60
Let $$A, B, C$$ and $$D$$ be four non-empty sets. The contrapositive statement of "If $$A \subseteq B$$ and $$B \subseteq D$$, then $$A \subseteq C$$" is
