List of practice Questions

Paton described Realism as left wing of

Identify the Rupee symbol from the images given below.

If the value of real number a> 0 for which \(x^2\)-5ax+1-0 and \(x^2-a x-5-0\) have a common real root is \(\frac{3}{\sqrt{2 \beta}}\) then \( \beta\) is equal to_______

Let \(A=\) [\(a_{ij}\)]\(_{2\times2}\) be a matrix and \(A^2 = I\) where \(a_{ij} \neq0\). If a sum of diagonal elements and b=det(A), then \(3a^2+4b^2\) is

Maria said ‘please lend me a pen’. (Convert the sentence into indirect speech)

Three dice are thrown. The probability of getting a sum of numbers which is a perfect cube, is:

In the displacement method of \(l_1\) and \(l_1\) be the sizes of two images, then the size of the object is:

The tangent to the curve \(x=cost(3-2cos^2t),y=sint(3-2sin^2t)\) at \(t=\frac{\pi}{4}\),makes with the \(x-axis\) an angle:

The number of S-S bonds and the number of lone pairs in S₈molecule,respectively,are:

Who was the first PM of India to visit China after the war of 1962?

Let S = (0,1) ∪ (1,2) ∪ (3,4) and T = {0,1, 2,3} . Then which of the following statements is(are) true?

Let P be a point on the parabola y² = 4ax, where a > 0. The normal to the parabola at P meets the x -axis at a point Q. The area of the triangle PFQ where F is the focus of the parabola, is 120. If the slope m of the normal and a are both positive integers, then the pair (a, m) is

f domain of the function \[ f(x) = \log_e \left(\frac{6x^2 + 5x + 1}{2x - 1}\right) + \cos^{-1}\left(\frac{2x^2 - 3x + 4}{3x - 5}\right) \] is \( (\alpha, \beta) \cup (\gamma, \delta) \), then \( 18(\alpha^2 + \beta^2 + \gamma^2 + \delta^2) \) is equal to __________.

A positively charged particle of mass m is passed through a velocity selector. It moves horizontally rightward without deviation along the line y = \(\frac{2mv}{qB}\) with a speed v. The electric field is vertically downwards and magnetic field is into the plane of the paper. Now, the electric field is switched off at t = 0. The angular momentum of the charged particle about origin O at t = \(\frac{\pi m}{qB}\) is

An electric dipole is placed as shown in the figure.

The electric potential (in 102 V) at point P due to the dipole is (ε₀ = permittivity of free space and \(\frac{1}{4\pi\epsilon_0}=K\)):

If \[ \cos \alpha = k \cos \beta \] then \[ \cot \left( \frac{\alpha + \beta}{2} \right) \] is equal to

In a class of 165 students, 45 students are passed in Mathematics as well as in English, whereas 60 students are failed in Mathematics and 65 students are failed in English. How many students are passed in exactly one subject?

Let the equation of the tangent at a point \( P \) on the parabola \( x^2 - 4x - 4y + 16 = 0 \) be \( 2x - y - 5 = 0 \). If the equation of the normal drawn at \( P \) to this parabola is \( ax + y + c = 0 \), then find \( ac \):

If \( \theta \) is the acute angle between the tangents drawn from the point \( (2, 3) \) to the hyperbola \( 5x^2 - 6y^2 - 30 = 0 \), then \( \tan \theta \) is:

The difference between the focal distances of any point on the hyperbola \[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \text{ is } 6. \text{ If } (\sqrt{13}, k) \text{ is an end point of a latus rectum of this hyperbola, then } k = \]

If \( f(x) = \begin{cases} 1 + 6x - 3x^2, & x \leq 1 \\ x + \log_2(b^2 + 7), & x > 1 \end{cases} \) is continuous at all real \( x \), then \( b \) is:

Let \( f(x) \) be a real valued function. If \( f'(x) \) is a constant for all \( x \in \mathbb{R}, f(0) = 1 \) and \( f'(0) = 2 \), then

If \( f : \mathbb{R} \to \mathbb{R} \) is defined by: \[ f(x) = \begin{cases} \sin x - \sin \left( \frac{x}{2} \right), & x<0 \\ \frac{x}{\sqrt{x^2 + \sqrt{x^2}}}, & x>0 \end{cases} \] If \( f \) is continuous on \( \mathbb{R} \), then \( f(0) = \)

If \( f(x) \) is a differentiable function, \( f'(x) \geq 5 \) for \( x \in [2,6] \), \( f(2) = 4 \) and \( f(3) = 15 \), then a possible value of \( f(6) \) is:

If \( f(x) = \sqrt{x} + \sin x \), then all the points of the set \( \left( x, f(x) \right)/f'(x) = 0 \) lie on: