List of top Questions asked in Jammu And Kashmir Board Of Professional Entrance Examinations Common Entrance Test- 2024

In a G.P. of $ (m + n)^{\text{th}} $ term is $ P $ and the $ (m - n)^{\text{th}} $ term is $ q $, then its $ m^{\text{th}} $ term is

If $ \theta $ is the angle between two vectors $ \vec{a} $ and $ \vec{b} $, then $ | \vec{a} \times \vec{b} | = | \vec{a} \cdot \vec{b} | $ equals to
If $ \vec{a} $ is a non-zero vector and $ k $ is a scalar such that $ |k \vec{a}| = 1 $, then $ k $ is equal to
The standard deviation of 25 numbers is $ \sigma $. If each of the numbers is increased by 5, then the new standard deviation will be
If $ P[E_1] = P_1 $ and $ E_1 $ and $ E_2 $ are mutually exclusive, then $ P[\text{neither } E_1 \text{ nor } E_2] $ is equal to
A bag contains 5 white, 7 red, and 4 black balls. Four balls are drawn one by one with replacement. The chance that at least two balls are black is
A die is tossed 5 times, getting an odd number is considered a success. Then the variance of the distribution of number of successes is
The points $ (-a, -b), (0, 0), (a, b), \text{ and } (a^2, ab) $ are
The inclination of the straight line passing through the point (-3, 6) and the mid point of the line joining the points (4,-5) and (-2,9) is
The coordinates of the foot of the perpendicular from $ (a, 0) $ on the line $ y = mx + \frac{a}{m} $ are
If the line $ x - 1 = 0 $ is the direction of the parabola $ y^2 - kn + 8 = 0 $, then one of the values of $ k $ is
Equation of the ellipse with eccentricity $ \frac{1}{2} $ and foci at $ (\pm 1, 0) $ is
For a frequency distribution, the mean deviation about the mean is computed by
The area enclosed between the curve $ y^2 = 4x, \quad \text{and the line } y = x \text{ is} $
The integral $ \int \sqrt{x^2 + a^2} \, dx $ is equal to
The value of $ \int_0^{2\pi} \sqrt{1 + \sin^2 \frac{x}{2}} \, dx \text{ is} $
If $ \int_0^{2a} f(x) \, dx = 2 \int_0^a f(x) \, dx, \text{ then} $
The value of $ \int_0^{\frac{\pi}{2}} \frac{\tan x}{\tan x + \cot x} \, dx \text{ is} $
The domain of the function $ \sin^{-1} x $ is
The derivative of $ \frac{d}{dx} \left( \tan^{-1} \left( \frac{3x - x^3}{1 - 3x^2} \right) \right) \text{ is equal to} $
The derivative of $ \frac{d}{dx} \left( x \sqrt{a^2} - x^2 + a^2 \sin^{-1} \left( \frac{x}{a} \right) \right) \text{ is equal to} $
Let $ f(x) = x^3 - 6x^2 + 9x + 8 $, then $ f(x) $ is decreasing in
The function $ f(x) = 2 + 4x^2 + 6x^4 + 8x^6 $ has
The system of linear equations $ x + y + z = 2, \quad 2x + y - 2 = 3, \quad 3x + 2y + kz = 4 \text{ has a unique solution if} $
If a matrix $ A $ is symmetric as well as skew symmetric then $ A $ is