If tan A = √3, find other trigonometric ratios of ∠A.
tan A = Perpendicular / base = √3 / 1 \(\begin{array}{l} \text { Using pythagoras theorem, } \mathbf{A C}^{2}=\mathbf{A B}^{2}+\mathbf{B... View Article
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Lipika reads a book for 1 (3 / 4) hours every day. She reads the entire book in 6 days How many hours in all were required by her to read the book?
Number of hours per days \(\begin{array}{l}\begin{array}{l} =1 \frac{3}{4} hr \\ =\frac{7}{4} h r \\ \text { Number of hours for... View Article
Without drawing a diagram, find (i) 10th square number (ii) 6th triangular number
To find \(\begin{array}{l}\begin{array}{l} \text { i) } 10^{\text {th }} \text { square number } \\ = 10 \times 10... View Article
If [a2 – 1] / a = 2, then the value of [a6 – 1] / a3 is
On raising the given expression to the power 3 on both sides, \(\begin{array}{l}\begin{array}{l} \left(\frac{a^{2}-1}{a}\right)^{3}=(2)^{3} \\ \Rightarrow \frac{\mathbf{a}^{6}-1-3 \mathbf{a}^{4}+3 \mathbf{a}^{2}}{\mathbf{a}^{3}}=8 \\... View Article
Write the first five multiples of the number 25.
25 × 1= 25 25 × 2 = 50 25 × 3 = 75 25 × 4 = 100 25... View Article
The value of cos 66 + sin 84 is
The given expression can be written as \(\begin{array}{l}\begin{array}{l} \cos 66^{\circ}+\sin 84^{\circ}=\cos 66^{\circ}+\sin (90-6)^{\circ} \\ =\cos 66^{\circ}+\cos 6^{\circ}[\text { because }... View Article
Write any three numbers of two digits and find their LCM.
LCM (50, 75, 90) 50 = 2 × 5 × 5 75 = 3 × 5 × 5 90 =... View Article
In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: (i) How many can speak both Hindi and English? (ii) How many can speak Hindi only? (iii) How many can speak English only?
The people who can speak English n (E) = 460 The people who can speak Hindi n (H) = 750 ... View Article
Find the mode of the data : (i) 10, 8, 4, 7, 8, 11, 15, 8, 6, 8. (ii) 27, 23, 39, 18, 27, 21, 27, 27, 40, 36, 27.
(i) 10, 8, 4, 7, 8, 11, 15, 8, 6, 8. Mode = 8 (ii) 27, 23, 39, 18, 27,... View Article
A man sells an article at a profit of 25% if he had bought it 20% less and sold it for Rs 10.50 less, he would have gained 30% find the cost price of the article.
Let the C.P be Rs x. First selling price = 125% of x = (125x / 100) = 5x /... View Article
Determine the LCM of 225 and 300.
225 = 3 × 3 × 5 × 5 300 = 2 × 2 × 3 × 5 × 5... View Article
The volume of a solid hemisphere is 1152π cu.cm. Find its curved surface area.
The volume of a solid hemisphere is given by \(\begin{array}{l}\mathbf{V}=\mathbf{1 1 5 2 \pi} \mathrm{cm}^{3}\\ \text {Volume of the hemisphere}... View Article
Find the square of 71 without multiplication.
712 = 71 × 71 712 = 5041 Use the following method to make calculations simple: 71 = (70 + 1) \(\begin{array}{l}\begin{array}{l}... View Article
If 8R2 = a2 + b2 + c2, then prove that the triangle is a right angled triangle.
The given condition is \(\begin{array}{l}\begin{array}{l} 8 R^{2}=a^{2}+b^{2}+c^{2} \\ \Rightarrow 8 R^{2}=4 R^{2} \sin ^{2} A+4 R^{2} \sin ^{2} B+4 \sin... View Article
The place value of 3 in 4.375 is
4.375 = 4 + 0.3 + 0.07 + 0.005 4 is in the units place 3 is in the one-tenth... View Article
Find the derivative of x2 – 2 at x = 10 from first principle.
The given function is \(\begin{array}{l}\begin{array}{l} f(x)=x^{2}-2 \\ f^{\prime}(x)=\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h} \\ =\lim _{h \rightarrow 0} \frac{\left[(x+h)^{2}-2\right]-\left(x^{2}-2\right)}{h} \\ =\lim... View Article
What is a point?
A point is a location on a plane.
Factorize 6x2 + 17x + 5 by using the factor theorem.
The given expression is \(\begin{array}{l}p(x)=6 x^{2} +17 x+5\\=6 x^{2}+15 x+2 x+5 \\ =2 x(3 x+1)+5(3 x+1) \\ =(2 x+5)(3 x+1)\end{array}... View Article
Complete the following series: 90, 180, 12, 50, 100, 200, ?, 3, 50, 4, 25, 2, 6, 30, 3.
90 = 30 × 3, 180 = 6 × 30, 12 = 2 × 6, 50 = 25 × 2,... View Article
Two dice were thrown and it is known that the numbers which come up were different. Find the probability that the sum of the two numbers was 5.
A is the event such that the sum of the two numbers that came up is 5 and B is... View Article
