JEE (Main)-2023 Exam Instructions

The distance between points C1 and C2, represented by 'd', is calculated as d = C1C2 = (9 − 3)2 + ( ______ - 3 )2

What is the final value of 'd' after carrying out the calculations?

What does the symbol 'r1' represent in the given context?

The equation r1 + r2 = C1C2 suggests that the two circles intersect at two distinct points.

Based on the given information, how many common tangents can be drawn to the two circles?

Match the following terms with their corresponding definitions:

What is the final simplified expression for f(y)?

The function f(y) is defined for all real values of y.

What is the value of 𝜆 in the equation –3x + y + 13z = 𝜆, given that x = –3, y = 2, and z = 0?

The distance between the point (–3, 2, 0) and the plane 2x – 2y + z = 11 is 7.

What is the cross product of vectors n1 and n2?

The ______ between the point and the plane is calculated using the formula: d = |ax + by + cz + d|/√(a² + b² + c²), where (a, b, c) is the normal vector of the plane and (x, y, z) is the point, and d is the constant in the plane equation.

Match the following equations to their corresponding variables:

The equation ( 2iˆ + 3 jˆ – 12kˆ )  ( 4iˆ + 3 ˆj – 12kˆ ) = 8 is used to solve for 𝜆.

What is the total number of possible numbers that can be formed with the sum of digits equal to 24?

What is the equation of the plane that passes through the point (-3, 2,0)?

The range of the function f(y) is given as (– 0.125, 1.125]. Therefore, the value of (\beta - \alpha) is equal to ______.

The number of possible numbers that can be formed with a sum of digits equal to 12 is 12.

Match the following expressions with their corresponding values based on the given information.

What is the value of 2(a + b + c) if (p_1 = 20) and (p_2 = 210) in the expression (a + bx + cx^2 = \sum_{i=10}^{20} p_i x^i)?

The given differential equation involves a function x that is a function of y, denoted as x(y). This means that x is the ______ variable and y is the ______ variable.

The set (Re(\frac {z^2}{3z - 5z})) where (Re(z)) is the real part of (z), equals the interval ((\alpha), (\beta)]. What is the value of 24((\beta - \alpha))?

The total number of possible numbers that can be formed with the sum of digits equal to 3, 9, 12, 15, 18, and 21 is 10.

The value of the expression (a - b) + (a^2 - ab + b^2) + (a^3 - a^2b + ab^2 - b^3) + ... is given by the formula ______ .

What is the simplified expression for (a + b)/(1 - a/b) * (a^2 - b^2 + a^3 + b^3 + a^4 - b^4 + ...)?

Which of the following equations represents the plane P?

The point B lies on the plane P.

What is the value of  + 3, where  and  are the direction ratios of the line AB?

Match the following terms with their corresponding values:

The equation of the plane P is given by ______x + ______y + ______z + ______ = 0.

The line AB intersects the plane P at a single point.

A single slit of width 'a' is illuminated by monochromatic light of wavelength 600 nm. The value of 'a' for which the first minimum appears at θ = 30° on the screen is:

The work done in moving a charge of 2 coulomb between two points having a potential difference of 150 volts is ______ joules.

For a voltmeter to be accurate, its internal resistance should be very high compared to the resistance of the circuit it is connected to.

What is the condition for the first minimum in a single-slit diffraction pattern?

Which of the following conditions would result in a higher internal resistance for an ammeter?

What is the primary type of equation represented in the content?

The variable 'x' is independent of 'y' in the given differential equation.

In the given differential equation, what is the expression that represents the integration bounds?

The differential equation mentioned is valid for values of y such that y > ______.

Match the following components of the differential equation with their descriptions: