Aptitude

NDA Exam | NDA syllabus | Agniveer | UPSC | NDA Paper Pattern | NDA notification

For free study material for nda maths : NDA maths free study material NDA maths Free mock test paper NDA Examination pattern In this examinaton , there are two papers. Paper I is 'Mathematics' and Paper II is 'General Ability Test'. Each paper duration is 2.5 hours. But paper I is 300 marks and Paper II is 600 marks. Subject Duration Maximum Marks Mathematics (Paper I) 2.5 hr 300 General Ability Test (Paper II) 2.5 hr 600 Note : 1. The Papers in all the subjects will consist of objective type qustions only .It means all the questions will be multiple choice question 2. There is also a minimum qualifying marks for each paper. 3.The Question papers(test booklets) of mathematics and part “B” of general ability test wil be set BILINGUALLY in Hindi as well as english NDA Examination Syllabus Paper I (Mathematics) 1. Algebra a) SET ( Concept of set, operations on sets, Venn di...

CBSE 10th Class Sample paper 2

General Instruction 1. All the questions are compulsory 2. The question paper consists of 40 question and it is divided into four sections A,B , C and D. SECTION A Comprises of 20 questions carrying 1 mark each. Section B comprises of 6 questions carrying 2 marks each, Second C comprises of 8 questions carrying 3 marks cach. Section D comprises of 6 questions carrying 4 marks each. 3. There is no overall choice 4. Use of calculator is not permitted. Section A 1. Find the LCM of 96 and 360 by using Fundamental Theorem of Arithmetic. 2. A line segment is of length 5 cm. If the coordinates of its one end are (2,2) and that of the other end are (-1, x), then find the value of x. 3. In figure, PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA is perpendicular to PB, then find the length of each tangents. 4. The first three terms of an A.P. respectively are 3y - 1, 3y +5 and 5y +1. Find the value of y....

Measurement of Angle ,Trigonometric Ratios and equation | free study Material for IIT-JEE , NDA and Airforce | SAT | CBSE

Measurement of Angle ,Trigonometric Ratios and equation ⚫Relation Between Degree and Radians ⚫ Relation Between Trigonometrical Ratios and Right Angled Triangle Side ⚫ Relation Between Trigonometrical Ratios sinθ.cosecθ = 1 tanθ.cotθ = 1 cosθ.secθ = 1 tanθ = sinθ/cosθ cotθ = cosθ/sinθ ⚫ Fundamental trigonometric Identities : sin 2 θ + cos 2 θ = 1 tan 2 θ + 1 = sec 2 θ 1 + cot 2 θ = cosec 2 θ ⚫ Trigonometrical ratios for various angles ⚫ Formula For the trigonometric ratios of sum and difference of two angles sin(A+B) = sinA cosB + cosA sinB sin(A-B) = sinA cosB - cosA sinB cos(A+B) = cosA cosB - sinA sinB cos(A-B) = cosA cosB + sinA sinB sin(A+B).sin(A-B) = sin 2 A - sin 2 B = cos 2 B - cos 2 A cos(A+B).cos(A-B) = cos 2 A - sin 2 B = cos 2 B - sin 2 A ⚫ Formulae to tran...

Learn New English words to improve your vocabulary | Vocabulary | daily vocabulary (new 5 words daily)

Learn New English words to improve your vocabulary Words for 7rd November 2023 Word Meaning Insouciant free from worry , anxiety Featly neatly Heartsease peace of mind Aliferous having wings Whelve to hide Words for 3rd November 2023 Word Meaning Affable Someone who is friendly , easily approachable and welcoming Palatable Pleasant and good Panache confidence or behavoiur that is very impressive Pizzazz Attractive and lively Splurge to spend money extravagantly Words for 1st November 2023 Word Meaning Oblivescene The process of forgetting Stolid Unemotional Busticate to break into pieces Luddite Someone who is opposed or ...

Start the test Question no. 1 Let z, w be complex numbers such that z + i w =0 and arg zw =π . Then arg z equals π/4 5π/4 3π/4 π/2 Question no. 2 If z and w are two non-zero complex number such that |zw|=1, and Arg (z)-Arg(w)=π/2 , then z¯w is equal to 1 -1 -i i Question no. 3 If |z+4|<= 3, then the maximum value of |z+1| is 4 10 6 0 Question no. 4 The conjugate of complex number is 1/(i-1), then that complex number is 1/(i+1) -1/(i+1) 1/(i-1) -1/(i-1) Question no. 5 What are the square roots of -2i ? ∓(1+i) ∓(1-i) ∓i ∓1 Question no. 6 What is the value of the sum of i 2i -2i 1+i Question no. 7 What is the number of distinct solution of the equation z 2 + |z| = 0 (where z i...

Mathematics and Ray optics | test no. 2

Start the test Question no. 1 If x = cost , y = sint , then what is equal to ? y -3 y 3 -y -3 -y 3 Question no. 2 What is the derivative of (log tanx cotx)(log cotx tanx) -1 at x = π/4 ? -1 0 1 1/2 Question no. 3 What is the derivative of log 10 (5x 2 + 3) with respect to x ? (xlog 10 e)/(5x 2 + 3) (2xlog 10 e)/(5x 2 + 3) (10xlog 10 e)/(5x 2 + 3) (10xlog e 10)/(5x 2 + 3) Question no. 4 Let f(x) = [|x| -|x-1|] 2 , What is f'(x) equal to when x > 1 ? 0 2x-1 4x - 2 8x - 4 Question no. 5 let f(x+y) = f(x)f(y) for all x and y . then what is f'(5) equal to ? f(5)f'(0) f(5) - f'(0) f(5)f(0) f(5) + f'(0) Question no. 6 y = ln(√tanx) , then what is the value of dy/dx at x = π/4 ? 0 -1 1/2 ...

Practice question On Eigen values and Eigen vectors Linear Algebra | Matrix algebra | GATE | UPSC | IES | Engineering

Linear Algebra Question no. 1 What are the eigen values of ? looks_one 1,4 looks_two 2,3 looks_3 0,5 looks_4 1,5 Answer Option looks_3 0,5 Solution Solution : ( 4 - λ)(1 - λ) - 4 = 0 λ 2 - 5λ + 4 - 4 = 0 λ 2 - 5λ = 0 λ(λ - 5) = 0 λ = 0 , 5 Question no. 2 What is the eigenvalues of the matrix ? looks_one 1, 4 ,4 looks_two 1 , 4 ,-4 looks_3 3 , 3 ,3 looks_4 1 , 2 ,6 Answer option looks_one 1, 4 ,4 Solution Solution : ( 3 - λ )[(3-λ) 2 -1] + 1(-3 + λ -1 ) - 1(1+3 -λ) = 0 ( 3 - λ )(9 + λ 2 - 6λ -1 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ 2 - 6λ + 8 ) + 2( λ - 4 ) = 0 ( 3 - λ )( λ - 4)( λ - 2) + 2( λ - 4 ) = 0 (λ - 4) [( 3 - λ )( λ - 2) + 2 ] = 0 (λ - 4) (λ 2 - 5λ + 4) = 0 (...

Previous Years Gate Question | Calculus | Engineering Question | Limit question

Calculus Question no. 1 If f(x) = , then will be [2006 , marks 2] looks_one -1/3 looks_two 5/18 looks_3 0 looks_4 2/5 Answer Option looks_two 5/18 Solution Solution : Question no. 2 [ 2007 , marks 1 ] looks_one 0.5 looks_two 1 looks_3 2 looks_4 undefined Answer option looks_one 0.5 solution Solution : Question no. 3 What is the value of [ 2007 , marks 2 ] looks_one 0 looks_two 1/6 looks_3 1/3 looks_4 1 Answer Option looks_two 1/6 Solution Solution : Question no. 4 The value of : [ 2008 , 1 Mark ] looks_one 1/16 looks_two 1/12 looks_3 1/8 looks_4 1/4 Answer option looks_two 1/12 Solution Solution : Question no. 5 The value of : [2008 , 1 Mark] looks_one 1 looks_two -1 looks_3 ∞ looks_4 -∞ Answer Option looks_one 1 Solution Solution : Question no. 6 ...

Magnetism Question for Class 10 | Class 10th Question

Physics Question for revision 1. State any two properties of magnetic field lines. 2. What is a magnetic field ? How can the direction of magnetic field lines at a place be determined ? 3. Explain why, two magnetic field lines do not intersect each other. 4. State and explain Maxwell’s right-hand thumb rule. 5. Draw the magnetic lines of force due to a circular wire carrying current. 6. In the straight wire A, current is flowing in the vertically downward direction whereas in wire B the current is flowing in the vertically upward direction. What is the direction of magnetic field : (a) in wire A ? (b) in wire B ? Name the rule which you have used to get the answer. 7. A thick wire is hanging from a wooden table. An anticlockwise magnetic field is to be produced around the wire by passing current through this wire by using a battery. Which terminal of the battery should be connected to the : (a) top end of wire ? (b) bottom end of wire ? Giv...

Complex Number | free study material for IIT-JEE , NDA and Airforce

Complex Number ⚫What is Complex number ? ⚪ Combination form of real and imaginary number z = a + ib where i(iota) = √ -1 ⚫ Integer power of i (√ -1 ) (a) i 4n = 1 (b) i 4n+1 = i (c) i 4n+2 = -1 (d) i 4n+3 = -i ⚫ Equality of two complex numbers ⚪ Two complex number z 1 = x 1 + iy 1 and z 2 = x 2 + iy 2 are said to be equal if and only if their real and imaginary parts are separately equal. z 1 = z 2 ⇔ x 1 + iy 1 = x 2 + iy 2 ⇔ x 1 = x 2 and y 1 = y 2 ⚫ Conjugate of a complex number : ⚪ For any complex number z = a + ib , then its conjugate is defined as z = a - ib ⚪ Geometrically , the conjugate of z is the reflection or point image of z in the real axis. ⚫ Properties of conjugate : ⚪ z̿ = z ⚪ ⚪ ⚪ ⚪ ⚪ ⚪ ⚪ z + z̅ = 2Re(z) = purely real ⚪ z - z̅ = ...

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