Bright Zoom Maths

Logical Reasoning Logical Deductions 1. Statement: Raman is always successful. No fool is always successful. Conclusions: I. Raman is a fool II. Raman is not a fool A. Only I follows B. Only II follows C. Either I or II follows D. Both I and II follow Answer : B. Only II follows Explanation :  Since both the premises are universal and one premise is negative, the conclusion must be universal negative and should not contain the middle term. So, II follows.  2. Statement: All trucks fly. Some Scooters fly. Conclusions: I.All trucks are scooters II. Some scooters do not fly A. Only I follows B. Only II follows C. Neither I nor II follows D. Both I and II follow Answer : C. Neither I nor II follows  Explanation :  Since the middle term "fly" is not distributed even once in the premises, so no definition conclusion follows 3. Statement: All grasses are trees. No tree is shrub. Conclusions: I. No grasses are shrubs. II. Some shrubs are grasses. A. Only conclusion I follo...

Logical Reasoning skills  Logical Reasoning Essential Part 1 1. Choose the word that is necessary for the word given in the question: Antique A.prehistoric B. aged C. artifact D. rarity  Answer : B. aged Explanation :  An antique is something that belongs to, or was made in, an earlier period. It may or may not be a rarity, and it does not have to be an artifact, an object produced or shaped by human craft . An antique is old but does not have to be prehistoric. 2. Choose the word that is necessary for the word given in the question: Itinerary A. guidebook B. travel C. route D. map  Answer : C. route Explanation :  An itinerary is a proposed route of a journey. A map is not necessary to have a planned route. Travel is usually the outcome of an itinerary, but not always. A guidebook may be used to plan the journey but is not essential. 3. Choose the word that is necessary for the word given in the question: Dimension A. measure B. inch C. ruler D. compass Answer ...

Logical Reasoning skills  Find the missing letter  Logical Reasoning 1. Find the next term in this series : 11, 16, 23, 32, 43,...  Answer : 56 Explanation :  The pattern is + 5, + 7, + 9, + 11, + 13, ... Missing number = 43 + 13 = 56. 2. Find the missing letter : A, C, F, H, ____, M Answer : K Explanation :  The letters are alterntely moved two and three steps forward to obtain the successive terms. 3. Find the analogies pair:  RAIN : DRIZZLE A. run : jog B. juggle : bounce C. walk : run D. hop : shuffle Answer : A. run : jog Explanation :  To drizzle is to rain slowly; to jog is to run slowly. 4. Which of the following words will come fourth in the English dictionary? False, Follow, Faithfully, Fool, Fallible. Answer : Follow Explanation :  The given words can be arranged in the alphabetical order as: Faithfully, Fallible, False, Follow, Fool. Clearly, Follow comes fourth. 5. If SUCCESS is coded as VXFFHVV, how can VICTORY be coded ?  Ans...

Logical Reasoning skills  Logical Reasoning Seating Arrangements Read the following information carefully and answer the questions given below: (i) A, B, C, D, E and F are six students in a class. (ii) B and C are shorter than F but heavier than A. (iii) D is heavier than B and taller than C. (iv) E is shorter than D but taller than F. (v) F is heavier than D. (vi) A is shorter than E but taller than F. 1. Who among them is the tallest ? Answer : D is the tallest Explanation :  In terms of height, we have : B < F, C < F, C < D, E < D, F < E, A < E, F < A. So, C < F < E < D, B < F, F < A < E Thus, the sequence becomes : B < C < F < A < E < D or C < B < F < A < E < D. 2. Who is third from the top when they are arranged in descending order of heights ? Answer : A is third from the top when they are arranged in descending order of heights Explanation :  The descending order of height is : D > E > A ...

  Linear Algebra Symbols Symbol Symbol Name Meaning / definition Example · dot scalar product a  ·  b × cross vector product a  ×  b A ⊗ B tensor product tensor product of A and B A  ⊗  B inner product [ ] brackets matrix of numbers ( ) parentheses matrix of numbers |  A  | determinant determinant of matrix A det( A ) determinant determinant of matrix A ||  x  || double vertical bars norm A T transpose matrix transpose ( A T ) ij  = ( A ) ji A † Hermitian matrix matrix conjugate transpose ( A † ) ij  = ( A ) ji A * Hermitian matrix matrix conjugate transpose ( A * ) ij  = ( A ) ji A  -1 inverse matrix A A -1  =  I rank( A ) matrix rank rank of matrix A rank( A ) = 3 dim( U ) dimension dimension of matrix A rank( U ) = 3

  Algebra symbols Symbol Symbol Name Meaning / definition Example x x variable unknown value to find when 2 x  = 4, then  x  = 2 ≡ equivalence identical to ≜ equal by definition equal by definition := equal by definition equal by definition ~ approximately equal weak approximation 11 ~ 10 ≈ approximately equal approximation sin (0.01) ≈ 0.01 ∝ proportional to proportional to y  ∝  x  when  y  =  kx, k  constant ∞ lemniscate infinity symbol ≪ much less than much less than 1 ≪ 1000000 ≫ much greater than much greater than 1000000 ≫ 1 ( ) parentheses calculate expression inside first 2 * (3+5) = 16 [ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18 { } braces set ⌊ x ⌋ floor brackets rounds number to lower integer ⌊4.3⌋ = 4 ⌈ x ⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉ = 5 x ! exclamation mark factorial 4! = 1*2*3*4 = 24 |  x  | single vertical bar absolute value | -5 | = 5 f  ( x ) function ...

  Geometry symbols Symbol Symbol Name Meaning / definition Example ∠ angle formed by two rays ∠ABC = 30° measured angle ABC = 30° spherical angle AOB = 30° ∟ right angle = 90° α = 90° ° degree 1 turn = 360° α = 60° deg degree 1 turn = 360deg α = 60deg ′ prime arcminute, 1° = 60′ α = 60°59′ ″ double prime arcsecond, 1′ = 60″ α = 60°59′59″ line infinite line AB line segment line from point A to point B ray line that start from point A arc arc from point A to point B  = 60° ⊥ perpendicular perpendicular lines (90° angle) AC ⊥ BC | | parallel parallel lines AB | | CD ≅ congruent to equivalence of geometric shapes and size ∆ABC≅ ∆XYZ ~ similarity same shapes, not same size ∆ABC~ ∆XYZ Δ triangle triangle shape ΔABC≅ ΔBCD | x - y | distance distance between points x and y |  x - y  | = 5 π pi constant π  = 3.141592654... is the ratio between the circumference and diameter of a circle c  =  π · d  = 2· π · r rad radians radians angle unit 360° = 2π rad c ...