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Let Alpha And Beta Are The Roots Of The Equation Px2 Plus Qx Plus R Equal 0 P Not Eq 0 If P Q And R Are In Ap Then The Value Of

(1) v61/9 (2) 2v17/9 (3) v34/9 (4) 2v13/9 Solution: Given a and ß be the roots of the equation px2 + qx + r = 0. Sum of roots, a... View Article

The Sequence Log A Log A2 By B Log A3 By B2 Is

(1) GP (2) AP (3) HP (4) GP and HP Solution: log a, log a2/b, log a3/b2,... Let x = log a y = log a2/b = 2 log a - log b z =... View Article

The Four Arithmetic Means Between 3 And 23 Are

(1) 5,9,11,13 (2) 7,11,15,19 (3) 5,11,15,22 (4) 7,15,19,21 Solution: Let a+d, a+2d, a+3d and a+4d be the four arithmetic means... View Article

If A B C D E F Are In Ap Then The Value Of E C Will Be

(1) 2(c - a) (2) 2(f - d) (3) 2(d - c) (4) d - c Solution: Given a, b, c, d, e, f are in A.P. Let p be the common difference. b... View Article

Three Numbers Are In Ap Whose Sum Is 33 And Product Is 792 Then The Smallest Number From These Numbers Is

(1) 4 (2) 8 (3) 11 (4) 14 Solution: Let a-d, a, a+d be the 3 numbers in AP. Sum = a-d+a+a+d = 33 3a = 33 a = 11 Product,... View Article

If The Sides Of A Right Angled Triangle Are In Ap Then The Sides Are Proportional To

(1) 1 : 2 : 3 (2) 2 : 3 : 4 (3) 3 : 4 : 5 (4) 4 : 5 : 6 Solution: Let a-d, a, a+d be the 3 sides of the right triangle. Let a+d... View Article

If Log 2 Log 2n 1 And Log 2n Plus 3 Are In Ap Then N Equal

(1) 5/2 (2) log2 5 (3) log3 5 (4) 3/2 Solution: Given log 2, log(2n - 1) and log(2n + 3) are in A.P. 2 log(2n - 1) = log 2 + log... View Article

If F X Plus Y X Y Equal Xy Then The Arithmetic Mean Of F X Y And F Y X Is

(1) x (2) y (3) 0 (4) 1 Solution: f (x + y, x - y) = xy Let x+y = x …(i) x-y = y….(ii) Add (i) and (ii) 2x = x+y x = (x+y)/2... View Article

The Mean Of The Series A A Plus Nd A Plus 2nd Is

(1) a + (n - 1) d (2) a + nd (3) a + (n + 1)d (4) None of these Solution: Mean of the series = (a+a+nd+a+2nd )/3 = (3a+3nd)/3 =... View Article

If A Be An Arithmetic Mean Between Two Numbers And S Be The Sum Of N Arithmetic Means Between The Same Numbers Then

(1) S = nA (2) A = nS (3) A = S (4) None of these Solution: Let a and b be the two numbers Then arithmetic mean, A = (a+b)/2 Sum of n... View Article

If The Sum Of The 10 Terms Of An Ap Is 4 Times To The Sum Of Its 5 Terms Then The Ratio Of First Term And Common Difference Is

(1) 1 : 2 (2) 2 : 1 (3) 2 : 3 (4) 3 : 2 Solution: Sn= (n/2)(2a+(n-1)d) Given S10 = 4S5 (10/2)(2a+(10-1)d) = 4(5/2)(2a+(5-1)d)... View Article

There Are 15 Terms In An Arithmetic Progression Its First Term Is 5 And Their Sum Is 390 The Middle Term Is

(1) 23 (2) 26 (3) 29 (4) 32 Solution: Given n = 15 a = 5 Sum, Sn = 390 (n/2)(2a+(n-1)d) = 390 (15/2)(2×5+(15-1)d) = 390... View Article

The Number Of Terms Of The Ap 3 7 11 15 To Be Taken So That The Sum Is 406 Is

(1) 5 (2) 10 (3) 12 (4) 14 Solution: Given AP is 3,7,11,15.. Here a = 3 d = 7-3 = 4 Sum, Sn = (n/2)(2a+(n-1)d) 406 =... View Article

If Sum Of N Terms Of An Ap Is 3n2 Plus 5n And Tm Equal 164 Then M Is Equal To

(1) 26 (2) 27 (3) 28 (4) None of these Solution: Given Sn = 3n2 + 5n S1 = 3 + 5 = 8 a = 8 S2 = 3×22 + 5×2 = 12+10 = 22 Second term =... View Article

7th Term Of An Ap Is 40 Then The Sum Of First 13 Terms Is

(1) 53 (2) 520 (3) 1040 (4) 2080 Solution: Given a7 = 40 a+6d = 40 Sum of first 13 terms = a+ a+d + a+2d +.... +a+12d =... View Article

The Sum Of Numbers From 250 To 1000 Which Are Divisible By 3 Is

The sum of numbers from 250 to 1000 which are divisible by 3 is (1) 135657 (2) 136557 (3) 161575 (4) 156375 Solution: Sum = 252 +... View Article

If The Sum Of The First 2n Terms Of Ap 2 5 8 Is Equal To The Sum Of The First N Terms Of Ap 57 59 61 Then N Is Equal To

If the sum of the first 2n terms of A.P 2,5,8,... is equal to the sum of the first n terms of A.P 57,59,61,...., then n is equal to (1) 10... View Article

The Sum Of The First And Third Term Of An Arithmetic Progression Is 12 And The Product Of First And Second Term Is 24 Then First Term Is

(1) 1 (2) 8 (3) 4 (4) 6 Solution: Let a-d, a , a+d be the 3 terms of AP. a-d+a+d = 12 2a = 12 a = 6 (a-d)a = 24 (6-d)= 24/6... View Article

The Sum Of The Integers From 1 To 100 Which Are Not Divisible By 3 Or 5 Is

(1) 2489 (2) 4735 (3) 2317 (4) 2632 Solution: Sum of integers which are not divisible by 3 or 5 = sum of first 100 natural numbers... View Article

What Is H In Magnetic Field

H is the magnetic field produced by the flow of current through the wire. The expression for H can be written as H = (B/µ) - M. B is the... View Article