NTA JEE Mains 23rd Jan 2025 Shift 2

The variance of the numbers 8, 21, 34, 47,…, 320 is

The roots of the quadratic equation $$3x^{2} - px + q = 0$$ are $$10^{th}$$ and $$11^{th}$$ terms of an arithmetic progression with common difference $$\frac{3}{2}$$. If the sum of the first 11 terms of this arithmetic progression is 88 , then q - 2p is equal to

The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is

The focus of the parabola $$y^{2}=4x+16$$ is the centre of the circle C of radius 5 . If the values of $$\ambda$$, for which C passes through the point of intersection of the lines 3x − y = 0 and $$x + \lambda y = 4$$, are $$\lambda_{1}$$ and $$\lambda_{2},\lambda_{1} < \lambda_{2}$$, then $$12\lambda_{1}+29\lambda_{2}$$ is equal to

Let $$\alpha,\beta$$ be the roots of the equation $$x^{2}-ax-b=0$$ with $$Im(\alpha) < Im(\beta)$$. Let $$P_{n}=\alpha^{n}-\beta^{n}$$. If $$P_{3}=-5\sqrt{7}i,P_{4}-3\sqrt{7}i,P_{5}=11\sqrt{7}i\text{ and }P_{}=45\sqrt{7}i$$.then $$|\alpha^{4}+\beta^{4}|$$ is equal to

A galvanometer having a coil of resistance 30Ω need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be $$\frac{30}{X}$$Ω.where X is Options

A ball having kinetic energy KE, is projected at an angle of $$60^{\circ}$$ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ?

Two charges $$7\mu c$$ and $$-4\mu c$$ are placed at (−7 cm, 0, 0) and (7 cm, 0, 0) respectively. Given, $$\epsilon_{\circ}=8.85\times 10^{-12}C^{2}m^{-2}$$, the electrostatic potential energy of the charge configuration is :

Two point charges $$-4\mu c$$ and $$4\mu c$$, constituting an electric dipole, are placed at (−9, 0, 0)cm and (9, 0, 0)cm in a uniform electric field of strength $$10^{4}NC^{-1}$$. The work done on the dipole in rotating it from the equilibrium through $$180^{\circ}$$ is :

A massless spring gets elongated by amount $$x_{1}$$ under a tension of 5 N . Its elongation is $$x_{2}$$ under the tension of 7 N . For the elongation of $$(5x_{1}-2x_{2})$$,the tension in the spring will be,