What must be subtracted from p (x) = 8x4 +14x3 – 2x2 + 7x – 8 so that the resulting polynomial is exactly divisible by g (x) = 4x2 + 3x – 2?
Let y be subtracted from p(x). (14x − 10) should be subtracted from p (x) so that it will be... View Article
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A die is tossed thrice. Find the probability of getting an odd number at least once.
Number of possible outcomes on a die = {1, 2, 3, 4, 5, 6} Favourable results getting even number =... View Article
Find the value of k in 2x2 + kx + 3 = 0 so that they have two equal roots.
It is given that the equation has two equal roots. Hence the value of the discriminant is 0. D =... View Article
Find the value of tan 480o.
tan 480 = tan (360 + 120) = tan 120 = tan (90 + 30) = – cot 30 =... View Article
Ravi made a cuboid of plasticine of dimensions 12 cm, 8 cm, and 3 cm. How many minimum number of such cuboids will be needed to form a cube of side 12cm?
The given side of cube = 12 cm, cuboid dimensions 12 cm, 8 cm, 3 cm. ⇒ Volume of cube... View Article
The matrix theory was introduced by
Matrix theory was introduced by Caley Hamilton in 1853.
The area of the triangle formed by the lines x + y = 3 and angle bisectors of the pair of straight lines x2 – y2 + 2y = 1 is
The given lines are x2 – (y – 1)2 = 0 (x + y – 1) = 0 The given... View Article
Write four integers less than – 10.
The negative integers less than – 10 are – 11, – 12, – 13, – 14.
The product of (x2 + y2) (x2 – y2) is
Since (a + b) (a – b) = a2 – b2 \(\begin{array}{l}\left(x^{2}+y^{2}\right)\left(x^{2}-y^{2}\right)\\=\left(x^{2}\right)^{2}-\left(y^{2}\right)^{2}\\=x^{4}-y^{4}\end{array} \)
Integrate sin3 x cos3 x.
Consider the given integral. \(\begin{array}{l}\int \sin ^{3} x \cos ^{3} x d x \\ =\int \sin x \cdot \sin ^{2}... View Article
Divide 184 into two parts such that one-third of one part may exceed one-seventh of another part by 8.
Let one of the numbers be ‘x’. The other number becomes 184 – x. (1 / 3)rd of one part... View Article
The fractions which have one as the numerator are called
The fractions which have one as the numerator are called unit fractions.
How many edges are there in a square pyramid?
A square pyramid has 8 edges.
Prove that sin [(π / 2) – x] = cos x.
\(\begin{array}{l}\sin \left(\frac{\pi}{2}-\mathrm{x}\right) \\ =\cos \left[\frac{\pi}{2}-\left(\frac{\pi}{2}-\mathrm{x}\right)\right] \\ \cos \left(\frac{\pi}{2}-\mathrm{x}\right)=\sin \mathrm{x} \\ =\cos (-\mathrm{x})=\cos \mathrm{x}\end{array} \)
(abcabc) ÷ (abc) = ……… (abc represents any 3-digit number).
Take abcabc ÷ abc= (abc × 1000 + abc) ÷ abc= 1000 + 1= 1001
Find the circumference of the circle with a radius of 14 cm by taking π = 22 / 7.
Radius = 14 cm Circumference = 2πr = 2 * (22 / 7) * 14 = 2 * (22 /... View Article
A square shape of the park of area 23,104 sq. m is to be enclosed with wire placed at heights 1, 2, 3, 4 m above the ground. Find the required length of the wire, if its length required for each circuit is 10% greater than the perimeter of the field.
Perimeter =4 * side \(\begin{array}{l}\text { Area of square park }=a^{2}=23104 \Rightarrow a=152 m\\ Perimeter =4 \times 152 \mathrm{~m}\\ \text... View Article
Solve the equation: (a / 5) + 3 = 2.
The given equation is \(\begin{array}{l}\frac{a}{5}+3=2 \\ \Rightarrow \frac{a}{5}=2-3 \\\Rightarrow \frac{a}{5}=-1 \\ \Rightarrow a=-1 \times 5 \\ \Rightarrow a=-5\end{array} \)
Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed, is 6 √3r.
Let ABC be isosceles is AB=AC, r is radius of circle \(\begin{array}{l}\mathbf{A F}^{2}+\mathbf{B F}^{2}=\mathbf{A B}^{2}\\ \Rightarrow(3 r)^{2}+\left(y^{2}\right)=x^{2} (1)\\ \text \... View Article
If y = 3 cos (log x) + 4 sin (log x), show that x2y2 + xy1 + y = 0.
Consider the given function. \(\begin{array}{l}y=3 \cos (\log x)+4 \sin (\log x)\\ \text { Differentiating w.r.t to } \mathrm{x}, \\ \frac{d... View Article
