Question 1 : If <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bb2a6f3020298ca12b5c"> , then the points <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7bb2ac2a2ae2953d936a4"> and <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba54c2a2ae2953d9346c"> are
Question 2 :
For the Hyperbola {tex} \frac { x ^ { 2 } } { \cos ^ { 2 } \alpha } - \frac { y ^ { 2 } } { \sin ^ { 2 } \alpha } = 1 , {/tex} which of the following remains constant when {tex} \alpha {/tex} varies?
Question 3 : If the sum of the distance of a point <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> from two perpendicular lines in a plane is 1, then the locus of <img style='object-fit:contain' src="https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5ea7ba066f3020298ca1287d"> is a
Question 4 :
If one of the lines of {tex} m y ^ { 2 } + \left( 1 - m ^ { 2 } \right) x y - m x ^ { 2 } = 0 {/tex} is a bisector of the angle between the lines {tex} x y = {/tex} {tex} 0 , {/tex} then {tex} m {/tex} is
Question 5 :
If {tex} \left( a , a ^ { 2 } \right) {/tex} falls inside the angle made by the lines {tex} y = \frac { x } { 2 } , x > 0 {/tex} and {tex} y = 3 x , x > 0 , {/tex} then {tex} a {/tex} belongs to
Question 6 :
Let {tex} A ( h , k ) , B ( 1,1 ) {/tex} and {tex} C ( 2,1 ) {/tex} be the vertices of a right angled triangle with {tex} A C {/tex} as its hypotenuse. If the area of the triangle is 1 square unit, then the set of values which {tex} ^ { \prime } k ^ { \prime } {/tex} can take is given by
Question 7 :
A teacher takes 3 children from her class to the zoo at a time as often as she can, but she does not take the same three children to the zoo more than once. She finds that she goes to the zoo 84 times more than a particular child goes to the zoo. The number of children in her class is
Question 8 :
If A, B and C are any three sets, then A - (B∪C) is equal to
Question 9 :
Let {tex} y = f ( x ) {/tex} be a real-valued function with domain as all real numbers. If the graph of the function is symmetrical about the line {tex} x = 1 , {/tex} then {tex} \forall \alpha \in R , {/tex} which one is correct?
Question 10 :
The value of ${\cos ^2}{45^ \circ } - {\sin ^2}{15^ \circ }$ is
Question 11 :
If {tex} \sum \limits_ { i = 1 } ^ { 10 } \cos ^ { - 1 } x _ { i } = 0 , {/tex} then {tex} \sum \limits_ { i = 1 } ^ { 10 } x _ { i } {/tex} is
Question 12 :
The value of {tex} \sin \left[ \sin ^ { - 1 } ( \sqrt { 5 } / 4 ) + \tan ^ { - 1 } ( \sqrt { 5 } / 11 ) \right] {/tex} is
Question 13 :
If (cot<sup>-1</sup> x)<sup>2</sup> - 3 (cot<sup>-1</sup> x) + 2 > 0, then x lies in
Question 14 :
If circumradius and in radius of a triangle be 10 and 3 respectively then value of a cot A + b cot B + c cot C is equal to -
Question 15 :
Equation of the image of the line x + y = sin<sup>-1</sup>(a<sup>3</sup> + 1) + cos<sup>-1</sup>(a<sup>2</sup> + 1) - tan<sup>-1</sup>(a + 1), a ∈ R about y-axis is given by
Question 16 :
In $\sin \theta = \dfrac{{ - 1}}{{\sqrt 2 }}\& \;\tan \;\theta $ lies in which quadrant?
Question 17 :
In a triangle ABC the altitude from A is not less than BC and altitude from B is not less than AC. The triangle is
Question 18 :
If {tex} \cos ^ { - 1 } x - \sin ^ { - 1 } x = 0 , {/tex} then {tex} x {/tex} is equal to
Question 19 :
Range of ƒ(x) = sin<sup>-1</sup> x + tan<sup>-1</sup> x + sec<sup>-1</sup> x is-
Question 20 :
The middle term in ${\left( {{x^2} + \dfrac{1}{{{x^2}}} + 2} \right)^n}$ is
Question 21 :
The sum of the series <sup>10</sup>C<sub>1</sub>. 4 + <sup>10</sup>C<sub>2</sub> 4<sup>2</sup> + …… + <sup>10</sup>C<sub>10</sub> 4<sup>10</sup> is
Question 22 :
In the binomial expansion of $ (a-b)^n , n \geq{5} $, the sum of <br>5th and 6th terms is zero then a/b equal to<br><br>
Question 23 :
The term independent of {tex} a {/tex} in the expansion of {tex} \left( 1 + \sqrt { a } + \frac { 1 } { \sqrt { a } - 1 } \right) ^ { - 30 } {/tex} is
Question 24 :
If {tex} z = r e ^ { i \theta } , {/tex} then {tex} \left| e ^ { i z } \right| {/tex} is equal to
Question 25 :
If {tex} c > 0 {/tex} and {tex} 4 a + c < 2 b , {/tex} then {tex} a x ^ { 2 } - b x + c = 0 {/tex} has a root in the interval
Question 26 :
If a complex number {tex} x {/tex} satisfies {tex} \log _ { 1 / \sqrt { 2 } } \left( \frac { | z | ^ { 2 } + 2 | z | + 6 } { 2 | z | ^ { 2 } - 2 | z | + 1 } \right) < 0 , {/tex} then locus/region of the point represented by z is
Question 27 :
If {tex} k + \left| k + z ^ { 2 } \right| = | z | ^ { 2 } \left( k \in R ^ { - } \right) , {/tex} then possible argument of {tex} z {/tex} is
Question 28 :
For all x ∈ R, if mx<sup>2</sup> - 9mx + 5m + 1 > 0, then m lies in the interval -<br>
Question 29 :
For the equation {tex} 3 x ^ { 2 } + p x + 3 = 0 , p > 0 , {/tex} if one of the roots is the square of the other, then {tex} p {/tex} is equal to
Question 30 :
If {tex} f ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x } + \left( \frac { 4 } { 5 } \right) ^ { x } - 1 , {/tex} where {tex} x \in R , {/tex} then the equation {tex} f ( x ) {/tex} {tex} = 0 {/tex} has
Question 31 :
If α, β are the roots of equation x<sup>2</sup> + px + q = 0 and γ, δ are roots of equation x<sup>2</sup> + rx + s = 0 then the value of (α - γ)<sup>2</sup> + (β - γ)<sup>2</sup> +(α - δ)<sup>2 </sup>+ (β - δ)<sup>2 </sup>is -<br>
Question 32 :
The number of complex numbers {tex} z {/tex} satisfying {tex} | z - 3 - i | = | z - 9 - i | {/tex} and {tex} | z - 3 + 3 i | = 3 {/tex} are
Question 33 :
If {tex} \frac { \left( x ^ { 2 } - 1 \right) ( x + 2 ) ( x + 1 ) ^ { 2 } } { ( x - 2 ) } < 0 , {/tex} then {tex} x {/tex} lies in the interval
Question 34 :
If one end of a diameter of the circle x<sup>2</sup> + y<sup>2</sup> - 4x - 6y + 11 = 0 is (3, 4), then its other end is
Question 35 :
P is a variable point on the parabola x<sup>2</sup> + 44x = y + 88 and Q is a point on the plane not lying on the parabola. If PQ<sup>2</sup> is minimum, then the angle between the tangent at P and PQ is-
Question 36 :
If 2x + y + 1 = 0 is a tangent to the parabola y<sup>2</sup> = 8x, the point of contact is
Question 37 :
The number of distinct tangents that can be drawn from the origin to the circle x<sup>2</sup> + y<sup>2</sup> = 2(x + y) is
Question 38 : For hyperbola <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e749c08f511820358e67ea1' height='47' width='123' > which of the following remains constant with change in 'α':
Question 39 :
One focus and the corresponding directrix of an ellipse are (1, 2) and x - y = 5. Its eccentricity is ½. Then centre is
Question 40 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cfbe6d3604eaa92eea7' height='68' width='91' >
is continuous " x ∈ R then (A, B) is-
Question 41 : If x is real number in [0, 1], then the value of <br><img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cf275ed294f2c7c42ed' height='27' width='55' >[1 + cos<sup>2m</sup> (n!πx)] is given by
Question 42 : <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870cec75ed294f2c7c42db' height='27' width='57' >, where [.] is GIF, is
Question 43 : Let f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d0719f8d44d3a17fc80' height='89' width='124' ><br>Then f(x) is continuous at x = 4 when
Question 44 : If f(x) = <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e870d0319f8d44d3a17fc72' height='55' width='96' >
then f(x) is -
Question 45 :
If A and B are square Matrices of order 3 such that |A| = -1 , |B| = 3 then |3AB| = ---------
Question 46 :
If {tex} a , b , {/tex} and {tex} c {/tex} are in G.P., then {tex} a + b , 2 b , {/tex} and {tex} b + c {/tex} are in
Question 47 : The numbers <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e87288019f8d44d3a1805c9' height='23' width='97' > will be in
Question 49 :
In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression is equals
Question 50 :
The coefficient of {tex} x ^ { 19 } {/tex} in the product {tex} ( x - 1 ) ( x - 3 ) \cdots ( x - 99 ) {/tex} is
Question 51 :
The equation of the line passing through point P(3, 5) and having slope $m = 2$ is<br/>
Question 52 :
Find the equation of perpendicular bisector of the line joining the points $(2,-3)$ and $(-1,5)$.
Question 53 :
The equation of line with slope $1$ and passing through origin
Question 54 :
The equation of line with slope $4$ and point passing through $(2,5)$ is
Question 55 :
If $m$ and $b$ are real numbers and $mb > 0$, then the line whose equation is $y = mx + b$ cannot contain the point-
Question 56 :
Point (-4, 6) divide the line segment joining the points A (-6, 10) and B (3, -8) in the ratio
Question 57 :
Find the distance between the points $P(3, 2)$ and $Q(-2, -1).$
Question 58 :
If the distance between the points $(8, 7)$ and $(3, y)$ is 13 what is the value of y?
Question 59 :
A triangle has vertices A(1,-1) B(2,4) and C(6,0) The length of the median from A is
Question 60 :
Harmonic conjugate of the point $C(5, 1)$ with respect to the point $A(2, 10)$ and $B(6, -2)$ is?
Question 62 :
The ratio in which the line joining the points $(3, 4)$ and $(5, 6)$ is divided by $x-$axis :
Question 63 :
The coordinates of $A$ and $B$ are $(1, 2) $ and $(2, 3)$. Find the coordinates of $R $, so that $A-R-B$ and $\displaystyle \frac{AR}{RB} = \frac{4}{3}$.<br/>
Question 64 :
What is the equation of $X$-axis? Hence, find the point of intersection of the graph of the equation $x\, +\, y\, =\, 3$ with the $X$-axis.
Question 65 :
A line segment of $8$ cm can be divided into ......... many equal parts.
Question 66 :
If $O(0,4)$ and $P(0,-4)$, are the co-ordinates of the line segment $OP$ then co-ordinate of its midpoint are
