The number of molecules(s) or ions(s) from the following having non-planar structure is ____.\(NO^-_3, H_2O_2, BF_3, PCl_3, XeF_4, SF_4, XeO_3, PH^+_4, SO3,[Al(OH)_4]^-\)
The area of the region enclosed by\(y≤4x^2, x2≤9y\ and\ y≤4,\)is equal to
Consider a curve y = y(x) in the first quadrant as shown in the figure. Let the area A1 is twice the area A2. Then the normal to the curve perpendicular to the line 2x – 12y = 15 does NOT pass through the point.
The equations of the sides AB, BC and CA of a triangle ABC are 2x + y = 0, x + py = 39 and x – y = 3, respectively and P(2, 3) is its circumcentre. Then which of the following is NOT true?
A circle C1 passes through the origin O and has diameter 4 on the positive x-axis. The line y = 2x gives a chord OA of circle C1. Let C2 be the circle with OA as a diameter. If the tangent to C2 at the point A meets the x-axis at P and y-axis at Q, then QA :AP is equal to
If the length of the latus rectum of a parabola, whose focus is (a, a) and the tangent at its vertex is x + y = a, is 16, then |a| is equal to :
If the length of the perpendicular drawn from the point P(a, 4, 2), a> 0 on the line\(\frac{x+1}{2} = \frac{y-3}{3} = \frac{z-1}{1}\) is \(2\sqrt6\) units and \(Q(α1, α2, α3)\)is the image of the point P in this line, then\(\alpha + \sum_{i=1}^{3} \alpha_i\)is equal to :
If the line of intersection of the planes ax + by = 3 and ax + by + cz = 0, a> 0 makes an angle 30° with the plane y – z + 2 = 0, then the direction cosines of the line are :
Let X have a binomial distribution B(n, p) such that the sum and the product of the mean and variance of X are 24 and 128 respectively. If\(P(X>n-3) = \frac{k}{2^n},\)then k is equal to :
A six faced die is biased such that3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).Let X be a random variable that counts the number of times one gets a perfect square on somethrows of this die. If the die is thrown twice, then the mean of X is :
The angle of elevation of the top P of a vertical tower PQ of height 10 from a point A on the horizontal ground is 45°, Let R be a point on AQ and from a point B, vertically above R, the angle of elevation of P is 60°. If\(∠BAQ = 30°\), AB = d and the area of the trapezium PQRB is α, then the ordered pair (d, α) is :
To light, a W, 100 V lamp is connected, in series with a capacitor of capacitance \(\frac{50}{π\sqrt{x}}\mu F\) with \(200 V\), 50 Hz AC source.The value of x will be ___.
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 :
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
