Factorise 1 + 2ab – (a2 + b2)
Solution: 1 + 2ab – (a2 + b2) = 1 – (a2 + b2 – 2ab) = 1 – (a... View Article
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State whether the statement given is true or false. Zero is the smallest rational number.
Solution: A number that can be expressed in the form p/q where q is not equal to zero is called... View Article
Find the cube of 21.
Solution: The cube of a number means a number multiplied by itself three times. So we multiply 21 by itself... View Article
Find 1% of 1 hour.
Solution: 1 hour = 60 min = 3600 sec 1% of 3600 = (1/100)3600 = 36 sec So 1% of... View Article
How many vertices does an angle have?
Solution: An angle can be defined as the figure formed by two rays meeting at a common endpoint. The point... View Article
In a division sum, we have dividend = 199, quotient = 16 and remainder = 7. The divisor is
(a) 11 (b) 12 (c) 23 (d) none of these Solution: We know dividend = (Divisor × Quotient) + remainder... View Article
The total number of injective mappings from a set with m elements to a set with n elements, m ≤ n, is
(a) mn (b) nm (c) n!/(n-m)! (d) n! Solution: Let A= {a1, a2 …am} B = {b1, b2 …bn} m... View Article
A shopkeeper purchased 200 bulbs for Rs.10 each. However, 5 bulbs were fused and put them into scrap. The remaining were sold at Rs.12 each. Find the gain or loss percent.
Solution: The cost price of 200 bulbs = 200×10 = Rs. 2000 5 bulbs were fused. Remaining 195 bulbs are... View Article
A dealer sells a toy for Rs. 24 and gains as much percent as the cost price of the toy. Find the cost price of the toy.
Solution: Given selling price, SP = Rs. 24 Dealer gains as much percent as the cost price of the article.... View Article
Prove that : sin 2x + 2 sin 4x + sin 6x = 4 cos2x sin 4x
Solution: LHS = sin 2x + 2 sin 4x + sin 6x = (sin 6x + sin 2x) + 2... View Article
If the area of a rectangle is equal to the area of a square and the length of the rectangle is equal to the perimeter of the square, then the breadth of the rectangle is
(a) side/2 (b) side2/2 (c) side/4 (d) side/3 Solution: Let l be length and b be the breadth of the... View Article
If G be the centroid of a triangle ABC, prove that AB2+ BC2 + AC2 = 3(GA2 + GB2 + GC2).
Solution: Let A (x1, y1), B(x2, y2), and C(x3, y3) be the vertices of ∆ABC. Without the loss of Generality,... View Article
Find the condition for the line x cos α + y sin α = p to be a tangent to the ellipse x2/a2 +y2/b2 = 1
Solution: Given equation of line is x cos α + y sin α = p => y sin α =... View Article
A shopkeeper sells 25 articles at Rs.45 per article after giving 10% discount and earns 50% profit. If the discount is not given the profit gained is
(a) 60% (b) 66% (c) \(\begin{array}{l}66\frac{2}{3}%\\\end{array} \) (d) none of these Solution: Selling price = Rs. 45 Let marked price... View Article
The equation of the plane containing the two lines (x-1)/2 = (y+1)/-1 = z/3 and x/-1= (y-2)/3 = (z+1)/-1 is
(a) 8x + y – 5z – 7 = 0 (b) 8x + y + 5z – 7 = 0... View Article
The area of a right-angled isosceles triangle whose hypotenuse is equal to 270 m is :
(A) 19000 m2 (B) 18225 m2 (C) 17256 m2 (D) 18325 m2 Solution: Given hypotenuse = 270 m Let ABC... View Article
What is the Past Participle form of the verb ‘sow’?
a) sow b) sowed c) sowden d) sown Answer: The past participle of the verb sow is sown. Hence option... View Article
In the question below is given a group of letters followed by four combinations of digits/symbols numbered (a), (b), (c), and (d)
You have to find out which of the combinations correctly represents the group of letters based on the coding system... View Article
A line intersects the Y-axis and X-axis at the points P and Q, respectively. If (2, – 5) is the mid-point of PQ, then the coordinates of P and Q are, respectively
(a) (0,-5) and (2, 0) (b) (0, 10) and (- 4, 0) (c) (0, 4) and (- 10, 0) (d)... View Article
Find the slant height of a frustum cone whose top radius is 12 m and bottom radius is 10 m. The height of the cone is 13 m.
(A) 13.15 m (B) 12.15 m (C) 10.15 m (D) 14.25 m Solution: Height of the cone, h = 13... View Article
