If \(\sum\limits_{k=1}^{31}\) \((^{31}C_k) (^{31}C_{k-1})\) \(-\sum\limits_{k=1}^{30}\) \((^{30}C_k) (^{30}C_{k-1})\) \(= \frac{α (60!)} {(30!) (31!)}\)where \(α ∈ R\), then the value of 16α is equal to
The number of \(\theta \in(0,4 \pi) \)for which the system of linear equations \(3(\sin 3 \theta) x-y+z=2\) \(3(\cos 2 \theta) x+4 y+3 z=3\) \(6 x+7 y+7 z=9\) has no solution is :
Choose the correct answer :
1. The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :
Two numbers are selected at random from the first six positive integers. If X denotes the larger of two numbers, then Var (X) =?
If the slope of one of the lines given by ax2 + 2hxy + by2 = 0 is two times the other, then
If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154 sq. units, then equation of the circle is (Taken π=\(\frac {22}{7}\))
∫\(\frac {e^x}{(2+e^x)(e^x +1)}\)dx = (where C is a constant of integration.)
If the position vectors of the points A and B are 3\(\hat {i}\) + \(\hat {j}\) + 2\(\hat {k}\) and \(\hat {i}\) -2\(\hat {j}\) -4\(\hat {k}\) respectively, then the equation of the plane through B and perpendicular to AB is
If matrix A =\(\begin{bmatrix} 1 & 2 \\ 4 & 3 \end{bmatrix}\) is such that AX = I, where I is 2 x 2 unit matrix, then X =
A random variable X has the following probability distribution then P (X ≥ 2) =?
If y = sec–1\((\frac {x + x^{-1}}{x - x^{-1}})\), then \(\frac {dy}{dx}\) =?
Let cos (α + β) = \(\frac {4}{5}\) and sin (α - β) = \(\frac {5}{13}\), where 0 < α, β < \(\frac {π}{4}\) , then tan 2α=?
