Differentiate tan x2 with respect to x.
The given function is \(\begin{array}{l}\begin{array}{l} y=\tan x^{2}\\ \text { Differentiation w.r.t. } \mathbf{x}\\ \frac{d y}{d x}=\sec ^{2}\left(x^{2}\right) \times 2 x\\... View Article
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Resolve a3 – b3 + c3 + 3abc into factors.
The given expression can be rewritten as \(\begin{array}{l}\mathbf{a}^{3}+(-\mathbf{b})^{3}+\mathbf{c}^{3}-\mathbf{3 a}(-\mathbf{b}) \mathbf{c}\\ \text { This in the familiar form, where b is... View Article
One centimetre is equal to
1 cm = 10 mm
For what value of k, are the roots of the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 equal?
The roots of the quadratic equation are found as follows. \(\begin{array}{l}\begin{array}{l} \Rightarrow \boldsymbol{\Delta }=\mathbf{b}^{2}-\mathbf{4 a c}=\mathbf{0} \\ \Rightarrow(\mathbf{k}+\mathbf{1})^{2}-4(\mathbf{k}+\mathbf{4}) \times \mathbf{1}=\mathbf{0}... View Article
The value of ∫e2x (2 sin 3x + 3 cos 3x)dx is
Answer: The value of \(\begin{array}{l}\int e^{2x}(2\sin 3 x+3\cos 3 x) d x\end{array} \) is e2xsin3x + c. \(\begin{array}{l}\begin{array}{l} \int e^{2 x}(2 \sin... View Article
Find the LCM of 4, 5 and 6.
4 = 2 × 2 5 = 5 6 = 2 × 3 LCM (4, 5, 6) = 2 ×... View Article
What is the radius of the circumcircle of a triangle whose sides are 30 cm, 36 cm and 30 cm?
Dimension of triangle is given by \(\begin{array}{l}=30 \mathrm{~cm}, 36 \mathrm{~cm}, 30 \mathrm{~cm}\\ \text \ In \ \triangle \ \mathrm{ABC}\\ \text... View Article
The difference between the sum of prime numbers from 21 to 30 and the sum of composite from 21 to 30 is divisible by which of the following numbers? A) 3 B) 7 C) 151 D) 17
The sum of prime numbers from 21 to 30 = 23 + 29 = 52 The sum of composite numbers... View Article
If θ is an acute angle and sin θ = cos θ. The value of 2 tan2 θ + sin2 θ – 1 is
sin θ = cos θ sin θ / cos θ = cos θ / cos θ [dividing both sides by... View Article
Say true or false: The diagonals of a square are perpendicular.
The given statement is true. The diagonals of a square are perpendicular.
Determine the degree of the following polynomials: 2x – 1.
The highest power of x is 1, hence the degree of the polynomial 2x – 1 is 1.
Robin purchased an old car for ₹73500. He spent ₹10300 on repairs and paid ₹2600 for its insurance. Then he sold it to a mechanic for ₹84240. What was his percentage gain or loss? Hint: overheads = ₹ 10300 + ₹ 2600 = ₹ 12900
Actual price of old car = purchase price + overheads = 73500 + 12900 = 86400 Cost price = ₹... View Article
Find the square of 85.
We have to find the square of 85. To find the square of number, multiply the number by itself. So... View Article
Prove that tan 225° cot 405° + tan 765° cot 675° = 0.
tan 225° cot 405° + tan 765° cot 675° = tan (90° × 2 + 45°) cot (90° × 4... View Article
Using distributivity of multiplication over the addition of whole numbers, find the following product: 736 × 103
736 × 103 = 736 × (100 + 3) By using distributivity of multiplication over the addition of whole numbers ... View Article
The number of six-digit numbers that can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 so that digits do not repeat and the terminal digits are even is
The first position can be occupied in 3 ways, the last place in 2 ways and the remaining places can... View Article
A person invests Rs. 5,000 for two years at a certain rate of interest compounded annually. At the end of one year, this sum amounts to Rs. 5,600. Calculate : (i) the rate of interest per year. (ii) the amount at the end of the second year.
Principal (P) = Rs. 5000 Time = 2 Years Amount at the end of one year = Rs. 5600 Interest... View Article
Find the percentage increase in the area of a triangle if each side is doubled.
Semi-perimeter of the triangle \(\begin{array}{l}\begin{array}{l} \mathrm{s}=\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{2}\\ \text { Area of triangle }=\sqrt{\mathrm{s}(\mathrm{s}-\mathrm{a})(\mathrm{s}-\mathrm{b})(\mathrm{s}-\mathrm{c})}\\ \text { When each side is doubled, the... View Article
Which Of The Following Polymers Occur Naturally (A) Protein And Pvc (B) Starch And Nylon (C) Proteins And Nylon (D) Starch And Cellulose
The correct answer is (D) Starch And Cellulose. Starch, cellulose and proteins are purely polymeric or naturally occurring polymers composed... View Article
What Is The Symbol Of Switch In On Position Is
The switch symbol in the ON position is represented by two small circled connected by a straight line. When a... View Article
