JEE Main Practice Test- 12 - JEE MCQ

The parabola y = x² – 9andy = kx² intersect each other at the points A and B. If the length AB is equal to 10 units then the value of k is equal to

An ellipse in the first quadrant is tangent to co-ordinate axes. If one focus is F₁ (3, 7), and the other focus is F₂(d, 7), then the value of  is equal to

If A is a square matrix such that A² + A + 2I = O, then which of the following is INCORRECT?
(Where I is unit matrix of order 2 and O is null matrix of order 2)

The system of equations : 
2x cos² θ + y sin 2θ – 2 sin θ = 0
x sin 2θ + 2y sin² θ = –2cos θ
x sin θ – y cos θ = 0 , for all values of θ, can

One circle has a radius of 5 and its center at (0, 5). A second circle has a radius of 12 and its centre at (12, 0). The length of a radius of a third circle which passes through the center of the second circle and both points of intersection of the first 2 circles, is equal to

Locus of a point P(x, y) satisfying the equation

P and Q are two points on the base AB of a triangle ABC whose vertices are (–2, 3), (4, – 6) and (1, 1) respectively. If the join of CP and CQ divides the triangle ABC into three triangles of equal areas, then the equation of line pair through the origin and parallel to CP and CQ is equal to

The line 4x - 7y + 10 = 0 intersects the parabola, y² = 4x at the points A and B. The sum of the co-ordinates of the point of intersection of the tangents drawn at the points A and B is

The tangent at a point whose eccentric angle 60° on the ellipse  meet the auxiliary circle at L and M. If LM subtends a right angle at the centre, then eccentricity of the ellipseis

If the curves  and x² = cy touch each other at the point (2, √2, 4) then the value of (a² + b² + c) is equal to

If the lines x + y + 1 = 0 ; 4x +3y + 4 = 0 and x + αy + β = 0, where α² + β² = 2, are concurrent then

The distance from the centre of the circle x² + y² = 2x to the straight line passing through the points of intersection of the two circles x² + y² + 5x - 8y + 1= 0, x² + y² - 3x + 7y - 25 = 0 is :

If α + β + γ = π, then the value of

Number of skew-symmetric matrices of order 3 whose elements are 0, 0, 0, 1, –1, 2, –2, 3, –3 is

In a class of 100 students few are in science stream and rest are in arts stream. 30 students took physics, 20 took chemistry, 25 took maths, 2 students took physics, chemistry and maths, 5 in physics and Chemistry, 6 in Physics and Maths and 3 in chemistry and Maths. How many took Arts if no students is common in Science & Arts

If the mean of the numbers 27 + x, 31 + x, 89 + x, 107 + x, 156 + x is 82, then the mean of 130 + x, 126 + x, 68 + x, 50 + x, 1+ x is

Let p and q be two statements. Then, (~ p v q ) ∧ (~ p∧ ~ q) is a

(Instruction to attempt numerical value (integer) type question: If your answer is 100 write 100 only. Do not write 100.0)

Two consecutive numbers from 1, 2, 3, …., n are removed, then arithmetic mean of the remaining numbers is 105/4, then n must be equal to

If S_n = 1 + 1/2 + 1/2² + .... + 1/2^n-1 and 2 - S_n < 1/100, then the least value of n must be:

Number of solutions of the equation 

If α is the common positive root of the equation
x² - ax + 12 = 0, x² - bx + 15 = 0, x² - (a + b) x + 36 = 0
and cosx + cos2x + cos3x = α, then sinx + sin2x + sin3x = ...

The least period of the function sin π[x]/12 + cos (πx/4) + tan π[x]/3 is λ, then the value of 201λ must be (where [.] denotes the greatest integer function)

The plates of a parallel plate capacitor are charged upto 100 volt. A 2 mm thick plate is inserted between the plates. To maintain the same potential difference, the distance between the capacitor plates is increased by 1.6 mm. The dielectric constant of the plate is

A conducting ring of radius R is placed in uniform inward magnetic field  as shown. If ring is moving with velocity  in its plane, the induced emf across arc PQ will be

An electron beam passes between two parallel plate electrodes as shown in the diagram. The bottom plate is kept at zero potential, while a slowly varying positive voltage is applied to the upper plate, as shown in the graph. After passing between the plates, the beam hits a screen and makes spot. Ignoring gravity, as the potential varies the spot is

In the circuit shown below, the cell is ideal, with emf = 15 V. Each resistance is of 3W. The potential difference across the capacitor is

Two particles of the same mass carry charges +3Q and –2Q respectively. They are shot into a region that contains a uniform electric field one after the other as shown. The particles have the same initial velocities in the positive x direction. The lines, numbered 1 through 4, indicate possible paths for the particles. If the electric field points in the negative y direction, what will be the resulting paths for these particles?