The number of elements in the set {(a, b): 2a² + 3b² = 35, a, b ∈ Z}, where Z is the set of all integers, is

If f': R → S, defined by f(x)= sin x -√3 cos x + 1, is onto, then the interval of S is

The straight lines x + y = 0, 3x + y – 4 = 0, x + 3y – 4 = 0 form a triangle which is

The current voltage relation of diode is given by I = (e^1000V/T – 1) mA, where the applied V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ±0.01 V while measuring the current of 5 mA at 300K, what will be the error in the value of current in mA ?

Line L has intercepts a and b on the coordinate axes. When the axes are rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q, then

If z₁ is a fixed point on the circle of radius 1 centred at the origin in the argand plane and z₁ ≠ ± 1. Consider an equilateral triangle inscribed in the circle with z₁,z₂, z₃ as the vertices taken in the counter clockwise direction. Then, z₂ z₃ is equal to

The number of digits in 20 ³⁰¹

If Avogadro number N_A, is changed from 6.022 ×10²³ mol^–1 to 6.022 × 10²⁰ mol^–1 this would change :

Two spherical bodies of mass M and 5 M and radii R and 2 R, respectively are released in free space with initial separation between their centres equal to 12 R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is

The third term of a geometric progression is 4. The product of the first five terms is