The number of distinct real values of λ for which the vectors λ^2 ı ˆ+ȷ ˆ+k ˆ,ı ˆ+λ^2 ȷ ˆ+k ˆ" Math Master - Impetus Gurukul 14,6 тыс. подписчиков Скачать
The number of distinct real values of λ for which the vectors λ^2 ı ˆ+ȷ ˆ+k ˆ,ı ˆ+λ^2 ȷ ˆ+k ˆ" Скачать
Out of 11 consecutive natural numbers if three numbers are selected at random - without repetition Скачать
Let a ⃗=3i ̂+j ̂ and b ⃗=i ̂+2j ̂+k ̂. Let c ⃗ be a vector satisfying a ⃗×(b ⃗×c ⃗ )=b ⃗+λc ⃗. Скачать
Let a function f:R→R be defined asf(x)={■(sin〖x-e^x 〗&if&x≤0@a+[-x]&if&0 x 1@2x-b&if&x≥1)┤where [x] Скачать
Let the system of linear equationsx+y+kz=22x+3y-z=13x+4y+2z=k, have infinitely many solutions Скачать
The maximum value off(x)=|■(sin^2x&1+cos^2x&cos2x@1+sin^2x&cos^2x&cos2x@sin^2x&cos^2x&sin2x Скачать
If α is the positive root of the equation p(x)=x^2-x-2=0, then lim┬(x→α^+)〖√(1-cos(p(x)) )/(x+α-4) Скачать
The line 12x cos〖θ+5y sinθ 〗=60 is tangent to which of the following curves? | Jee | Trignometry Скачать
tangent to the parabola y^2=4x at the point where it intersects the circle x^2+y^2=5 in the first Скачать
number of values of k, for which the system of equations (k+1)x+8y=4k,kx+(k+3)y=3k-1 has infinitely Скачать
letters of word OUGHT are written in all possible ways & these words are arranged as in a dictionary Скачать
The number of numbers, strictly between 5000 and 10000 can be formed using the digits 1, 3, 5, 7, 9 Скачать
Let S={θ∈[0,2π]:8^(2 sin^2θ )+8^(2 cos^2θ )=16}. Then n(S)+∑_(θ∈S)▒(sec(π/4+2θ)cosec (π/4+2θ)) Скачать
A function f(x) is given by f(x)=5^x/(5^x+5), then the sum of the series f(1/20)+f(2/20)+f(3/20)+⋯ Скачать
computer program generate only the digits 0 & 1 to form a string of binary numbers with probability Скачать
Two dice are rolled. If both dice have six faces numbered 1, 2, 3, 5, 7 and 11, then the probability Скачать
A fair die is tossed repeatedly until a six is obtained. Let X denote the number of tosses required Скачать
The solution curve of the differential equation, (1+e^(-x) )(1+y^2 ) dy/dx=y^2, which passes throug Скачать
Let f(x)=x/(1+x^n )^(1/n) for n≥2 and g(x)=⏟((f o f o…o f) )┬(f occurs n times) (x) | Function Скачать
Let f∶R→R be defined as f(x)={■(2 sin〖(-πx/2),〗&if&x-1@|ax^2+x+b|,&if&-1≤x≤1@sin〖(πx),〗&if&x1) Скачать
Let A=[█(1@1@1)] & B=[■(9^2&-10^2&11^2@12^2&13^2&〖-14〗^2@-15^2&16^2&17^2 )], then the value of A'BA Скачать
Let A={x∈R∶x is not a positive integer}. Define a function f∶A→R as f(x)=2x/(x-1), then f | function Скачать
If a hyperbola passes through the point P(10,16) and it has vertices at (±6,0),then the equation of Скачать
The line x=y touches a circle at the point (1, 1) If the circle also passes through the point (1,-3) Скачать
The number of values of c such that the straight line y=4x+c touches the curve x^2/4+y^2=1 is Скачать
1/(3^2-1)+1/(5^2-1)+1/(7^2-1)+⋯+1/((201)^2-1) is equal to #progression | #progressionpyq's 11 Math Скачать
If m is chosen in the quadratic equation (m^2+1) x^2-3x+(m^2+1)^2=0 such that the sum of its roots Скачать
Let f(x)={■(-1,&-2≤x lesTh0@x^2-1,&0≤x≤2)┤ and g(x)=|f(x)|+f(|x|).Then, in the interval (-2,2),g is Скачать
The domain of the derivative of the function f(x)={■(tan^(-1)〖x,〗&if&|x|≤1@1/2 (|x|-1),&if&|x|1)┤ Скачать
mean and variance of five observations are 4 and 5.20, respectively. If three of the observations Скачать
The centres of those circles which touch the circle, x^2+y^2-8x-8y-4=0, externally and also touch Скачать
A point on the straight line, 3x+5y=15, which is equidistant from coordinate axes will lie only in Скачать
number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining Скачать
How many ways are there to arrange letters in the word GARDEN with the vowels in alphabetical order Скачать
The number of natural numbers less than 7,000 which can be formed by using the digits 0, 1, 3, 7, 9 Скачать
Let α, β be real and z be a complex number. If z^2+αz+β=0 has two distinct roots on the line Re z=1 Скачать
If the equation cos^4〖θ+sin^4〖θ+ λ=0〗 〗 has real solutions for θ, then λ lies in the interval Скачать
If 0 lesTh x, y lesTh π and cos〖x+cos〖y-cos〖(x+y)=3/2,〗 〗 〗 then sin〖x+cosy 〗 is equal to Скачать
Let p ⃗,q ⃗,r ⃗ be three mutually perpendicular vectors of the same magnitude. If a vector x ⃗ satis Скачать
a ⃗=i ̂+j ̂+k ̂,b ⃗=4i ̂+3j ̂+4k ̂ and c ⃗=i ̂+αj ̂+βk ̂ are linearly dependent vectors & |c ⃗ |=√3 Скачать
angle betw pair of tangents drawn on P to the circle x^2+y^2+4x-6y+9 sin^2 α+13 cos^2 α=0 is 2α. Скачать
If A and B are two independent events such that P(A) gtr 0 and P(B)≠1 then P(A ̅/B ̅ ) is equal to Скачать
Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit Скачать
If a ⃗ and b ⃗ are vectors such that |a ⃗+b ⃗ |=√29 and a ⃗×(2i ̂+3j ̂+4k ̂ )=(2i ̂+3j ̂+4k ̂ )×b ⃗ Скачать
Let a ⃗ and b ⃗ be two unit vectors such that |a ⃗+b ⃗ |=√3. If c ⃗=a ⃗+2b ⃗+3(a ⃗×b ⃗ ), then 2|c ⃗ Скачать
Let a ⃗=2i ̂+j ̂-2k ̂ and b ⃗=i ̂+j ̂. Let c ⃗ be a vector such that |c ⃗-a ⃗ |=3,|(a ⃗×b ⃗ )×c ⃗ |= Скачать
a ⃗=3i ̂+2j ̂+2k ̂ and b ⃗=i ̂+2j ̂-2k ̂ be two vectors. If a vector perpendicular to both vectors Скачать
The integral ∫▒(x/(x sin〖x+cosx 〗 ))^2 dx is equal to(where C is a constant of integration) Скачать
If ∫▒sin^(-1)(√(x/(1+x))) dx=A(x) tan^(-1)〖(√x)+B(x)+C,〗 where C is constant of integration, Скачать
Let f(x)={■((x-1)^(1/(2-x)),&x gtr 1,x≠2@k,&x=2)┤The value of k for which f is continuous at x=2 is Скачать
If ∑_(i=1)^9 (x_i-5)=9 & ∑_(i=1)^9 (x_i-5) ^2=45 then standard deviation of the 9 term x_1 x_2 … x_9 Скачать
If lim┬(x→0)〖(((a-n)nx-tanx ) sinnx)/x^2 〗=0, where n is non zero real number then a is equal to Скачать
locus of the foot of the perpendicular drawn from the centre of the ellipse x^2+3y^2=6 on tangent Скачать
If the incentre of an equilateral triangle is (1, 1) and the equation of its one side is 3x+4y+3=0 Скачать
Fifth term of G.P. is 2 then the product of its 9 terms is || Value of 2^(1/4)∙4^(1/8)∙8^(1/16)…∞ is Скачать
The number of ways in which 5 boys and 3 girls can be seated on a round table if a particular boy B Скачать
If the difference between the roots of the equation x^2+ax+1=0 is less than √5, then the set of Скачать
The quadratic equation x^2-6x+a=0 and x^2-cx+6=0 have one root in common. The other roots of the Скачать
sides of a triangle are sin α, cos α and √(1+sin α cos α) for some 0 α π/2. greatest angle of Скачать
number of integral values of m so that abscissa of point of intersection of lines 3x+4y=9 and y=mx+1 Скачать
If the length of the chord of the circle, x^2+y^2=r^2 (rgtr0) along the line, y-2x=3 is r, then r^2 Скачать
Let the tangents drawn from the origin to the circle, x^2+y^2-8x-4y+16=0 touch it at the points Скачать
((x^2+5x+3)/(x^2+x+3))^(1/x) =? | If (((a-n)nx-□tan tan x ) □sin sin nx )/x^2 =0, n is non zero a= Скачать
If ∫ dx/(x^2-2x+10)^2 =A(((x-1)/3)+(f(x))/(x^2-2x+10) )+C, where C is a constant of integration Скачать
If ∫ x^5 e^(-x^2 ) dx=g(x) e^(-x^2 )+c, where c is a constant of integration, then g(-1) is equal to Скачать
curve satisfying the differential equation, (x^2-y^2 )dx+2xydy=0 & passing through the point (1, 1) Скачать
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are Скачать
Let ω be a complex cube root of unity with ω≠1. A fair die is thrown three times. If r_1,r_2 and r_3 Скачать
length of latus rectum of a hyperbola is 8 and its eccentricity is 3/√5 Equation of the hyperbola is Скачать
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probabili Скачать
The equation of the hyperbola whose foci are (8, 3) and (0, 3) and whose eccentricity is (4/3) is Скачать
If three distinct numbers are chosen randomly from the first 100 natural numbers, then the probabili Скачать
If a=i ̂+j ̂+k ̂,b=4i ̂+3j ̂+4k ̂ and c=i ̂+αj ̂+βk ̂ are linearly dependent vectors and |c|=√3 then Скачать
If a b c are noncoplanar vectors and λ is real number, then the vectors a+2b+3c, λb +4c and (2λ-1) c Скачать
Let a ⃗=i ̂-k ̂,b ⃗=xi ̂+j ̂+(1-x) k ̂ and c ⃗=yi ̂+xj ̂+(1+x-y) k ̂. Then [a ⃗b ⃗c ⃗ ] depends on Скачать
If a ,b ,c are non-coplanar vectors and λ is a real number then [λ(a +b) λ^2 b λc ]=[a b +c b ] for Скачать
distinct real values of λ, for which the vectors -λ^2 i ̂+j ̂+k ̂,i ̂-λ^2 j ̂+k ̂ and i ̂+j ̂-λ^2 k Скачать
Let k be a non-zero real number. Iff(x)={(e^x-1)^2/(□sin sin (x/k) □log log (1+x/4) ),x≠0 12,x=0 Скачать
If the 10th term of an AP is 1/20 and its 20th term is 1/10, then the sum of its first 200 terms is Скачать
Difference between the corresponding roots of x^2+ax+b=0 and x^2+bx+a=0 is same and a≠b, then Скачать
If the angles of a triangle are in the ratio 4 : 1 : 1 then the ratio of longest side to perimeter Скачать
Four fair dice D1 D2 D3 & D4 each having six faces numbered 1 2 3 4 5 & 6 are rolled simultaneously Скачать
Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random Скачать
If a ⃗,b ⃗ and c ⃗ are three non coplanar vectors then (a ⃗+b ⃗+c ⃗ )∙[(a ⃗+b ⃗ )×(a ⃗+c ⃗ )] equals Скачать
If a b c are non coplanar unit vectors such that a×(b ×c )=((b+c))/√2 then the angle between a and b Скачать
If y=y(x) is the solution of the differential equation, x dy/dx+2y=x^2 satisfying y(1)=1 then y(1/2) Скачать
If ∫▒e^secx (sec〖x tan〖x f(x)〗 〗+(sec〖x tan〖x+sec^2x 〗 〗 ))dx=e^secx f(x)+C, then f(x) is Скачать
Let f(x)=(1+b^2 ) x^2+2bx+1 and let m(b) be the minimum value of f(x).Asb varies, range of m(b) is Скачать
a,b∈R,(a≠0). If the function f defined as f(x)={((2x^2)/a, a, (2b^2-4b)/x^3 is conti in inter [0,∞) Скачать
Let tan^(-1) y=tan^(-1) x+tan^(-1)(2x/(1-x^2 )) , where |x| lessTh 1/√3. Then a value of y is Скачать
Let S_n denote the sum of the first n terms of an A.P. If S_4=16 and S_6=-48, then S_10 is equal to Скачать
If a_1,a_2,a_3,…,a_n are in A.P. and a_1+a_4+a_7+⋯+a_16=114, then a_1+a_6+a_11+a_16 is equal to Скачать
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected Скачать
Total number of ways in which 5 balls of different colours can be distributed among 3 persons Скачать
number of integers greater than 6000 can be formed, using digits 3, 5, 6, 7 and 8 without repetition Скачать
If sum of the roots of the quadratic equation ax^2+bx+c=0 = sum of the squares of their reciprocals Скачать
value of a for which one root of quadratic equation (a^2-5a+3) x^2+(3a-1)x+2=0 is twice as large as Скачать
If sum of all the sol of the equ 8 cosx∙(cos(π/6+x)∙cos(π/6-x)-1/2)=1 in [0,π] is kπ, then k is Скачать
Let X be a random vari binomial distribution B(7,p). If P(X=3)=5P(X=4) then the sum of the mean Скачать
If u ̂ and v ̂ are unit vectors and θ is the acute angle between them then 2u ̂×3v ̂ is unit vector Скачать
f be a diff function such that f(1)=2 and f^' (x)=f(x) for all x∈R. If h(x)=f(f(x)), then h^' (1) is Скачать
total number of local max and local min of the function f(x)={((2+x)^3,&-3 x -1x^(2/3),&-1 x 2) is Скачать
3 randomly non-negative integers x,y and z are satisfy eq x+y+z=10 Then probability that z is even Скачать
The value of k for functionf(x)={((4/5)^(tan4x/tan5x )0 x π/2@k+2/5,&x=π/2) is continuous at x=π/2 Скачать
Let A=(■(cosα&-sinα@sinα&cosα )),(α∈R) such that A^32=(■(0&-1@1&0)). Then a value of α is Скачать
mean & SD of 5obs are 9 & 0 If one of obs is changed such that mean of new set of 5obs be 10 then SD Скачать
The integer n for which lim┬(x→0) (cos x-1 )(cos x-e^x )/x^n is a finite non-zero number is Скачать
The circle passing through (1,-2) and touching the axis of x at (3, 0) also passes through the point Скачать
If the sum and product of first 3 terms in an AP are 33 and 1155 respectively then value of 11 term Скачать
common difference of the A.P. b_1,b_2,…,b_m is 2 more than common difference of A.P. a_1,a_2,…,a_n Скачать
class of 5 girls & 7 boys number of different teams consisting of 2 girls & 3 boys can be formed Скачать
four letter words formed from the word MEDITERRANEAN first letter is R and the fourth letters is E Скачать
Let two numbers have arithmetic mean 9 and geometric mean 4. Then roots of the quadratic equation Скачать
The second degree polynomial f(x), satisfying f(0)=0,f(1)=1,f^' (x)(greThan)0 for all x∈[0,1] is Скачать
If the expansion in powers of x of the function 1/(1-ax)(1-bx) a_0+a_1 x+a_2 x^2+a_3 x^3+ then a_n Скачать