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Find the D.E whose solution is a²y – ax + 8 = 0

(a) 8y12 + y + xy1 = 0 (b) 8y12 + y - xy1 = 0 (c) 8y12 - y - xy1 = 0 (d) 8y12 - y +xy1 = 0 Solution: Given a2y - ax + 8 = 0 …(i)... View Article

The D.E whose solution is x²/a² + y²/b² = 1 is

(a) xyy2 + xy12 = yy1 (b) xyy2 + y1 = y (c) x2y2 + xy1= y (d) x2y2 + 2xy1 = y12 Solution: Given x2/a2 + y2/b2 = 1 Differentiate with... View Article

The square root of 1- i is √(√2 + 1)/2 – i√(√2 – 1)/2. If this is true enter 1, else enter 0.

The square root of 1- i is . If this is true enter 1, else enter 0. Solution: Let √(1 - i) = ±(x - iy) …(i) Squaring... View Article

Which waterfall is known as Niagara Of Karnataka?

(A) Jog Falls (B) Gokak Falls (C) Magod Falls (D) Kalathgiri Falls Solution: Gokak falls is known as Niagara Of Karnataka. It is located on... View Article

Riaz takes 20 min to travel to his school with a speed of 3m/s. How far is the school.

(a) 2 km (b) 3.2 km (c) 3.6 km (d) 4.1 km Solution: Given speed = 3 m/s Time = 20 min = 20 × 60 = 1200 s Distance = speed ×... View Article

The lateral surface area of a cube is 100 m². The volume of the cube is

(a) 25 m3 (b) 125 m3 (c) 1000 m3 (d) 100 m3 Solution: Let a be the side of a cube. Then lateral surface area of a cube = 4a2 Given lateral... View Article

Fill in the blanks. A number which has only two factors is called a

(a) A number which has only two factors is called a _______. (b) A number which has more than two factors is called a _______. (c) 1 is... View Article

If one root of the quadratic equation 2x² + kx – 6 = 0 is 2, then the value of k is

(a) 1 (b) -1 (c) 0 (d) -2 Solution: Given one root of quadratic equation 2x2 + kx - 6 = 0 is 2. Put 2 in the equation, we get 2×22 +... View Article

While covering a distance of 30 km. Ajeet takes 2 hours more than Amit. If Ajeet doubles his speed, he would take 1 hour less than Amit. Find their speeds of walking.

Solution: Let the speed of Ajeet be x and Amit be y. We know speed = distance/time Time = distance/speed 30/x = 2 + (30/y) …(i)... View Article

A conical vessel, with a base radius of 5 cm and a height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel.

Solution: Given the radius of conical vessel = 5 cm Height of conical vessel = 24 cm The volume of conical vessel = (1/3) πr2h = ⅓... View Article

The difference in the measures of the two complementary angles is 12⁰. Find the measure of the angles.

Solution: Complementary angles are angles whose sum of measures is 900. Let x0 be one angle. Then the complementary angle = (90 - x)0... View Article

List five rational numbers between -2 and -1.

Answer: A rational number is a number that is in the form of p/q, where q is not equal to zero. Any fraction with a non-zero denominator is a... View Article

Write the multiplicative inverse of each of the following rational numbers. 7, -11, 2/5, -7/15.

Solution: The multiplicative inverse of a number is defined as a number which when multiplied by the original number gives the product as 1. The... View Article

If the perimeter of a rhombus is 4a and the lengths of the diagonals are x and y, then its area is

(a) a(x+y) (b) x2 + y2 (c) xy (d) xy/2 Solution: Given perimeter of a rhombus = 4a lengths of the diagonals are x and y. Area of rhombus =... View Article

Prove that (cos A – sin A + 1)/(cos A + sin A – 1) = cosec A + cot A.

Solution: LHS = (cos A - sin A + 1)/(cos A + sin A - 1) Divide numerator and denominator with sin A. = [(cos A/sin A - sin A/sin A +... View Article

Write 2 log 3 + 3 log 5 + 5 log 2 as a single logarithm.

Solution: We know log ab = b log a So 2 log 3 = log 32 = log 9 3 log 5 = log 53 = log 125 5 log 2 = log 25 = log 32 2 log 3 + 3 log 5 + 5... View Article

Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3.

Solution: log (1 + 2 + 3) = log 6 = log (1×2×3) log (ab) = log a + log b log (abc) = log a + log b + log c log... View Article

How many two-digit numbers are divisible by 4?

Answer: Two-digit numbers divisible by 4 are 12, 16, 20, … 96. This is an AP with a = 12 Common difference, d = 16-12 = 4 tn = a +... View Article

The sum of the first 50 natural numbers is

(a) 1175 (b) 1275 (c) 1257 (d) none of these Answer: The first 50 natural numbers are 1, 2,3….50 The sum of first n natural numbers... View Article

Prove that (cos A/(1 + sin A)) + ((1 + sin A)/cos A) = 2 sec A

Solution: LHS => (cos A/(1 + sin A)) + ((1 + sin A)/cos A) = [cos2 A + (1 + sin A)2]/cos A (1 + sin A) = [cos2A + 1 + 2 sin A + sin2 A]/cos... View Article