Q&A - Ask Doubts and Get Answers

Sort by :
Clear All
Q

Let \alpha and \beta   be the roots of equation

x^{2}-6x-2=0.\; if a_{n}=\alpha ^{n}-\beta ^{n},\; for\: n\geq 1,\; then\; the \: value\; of\; \frac{a_{10}-2a_{8}}{2a_{9}}

is equal to:

  • Option 1)

    6

  • Option 2)

    -6

  • Option 3)

    3

  • Option 4)

    -3

3

If in a parallelogram ABDC, the coordinates of A,B and C are respectively (1,2), (3,4) and (2,5) , then the equation of the diagonal AD is:

  • Option 1)

    5x-3y+1=0

  • Option 2)

    3x-5y+1=0

  • Option 3)

    5x+3y-11=0

  • Option 4)

    3x+5y-13=0

  Mid-point formula -   - wherein If the point P(x,y) is the mid point of line joining A(x1,y1) and B(x2,y2) .     Two – point form of a straight line -   - wherein The lines passes through    and    As BD and AC are parallel ..............................(1) As AB and CD are parallel ..............................(2) Solving (1) and (2) m=4 and n=7              Option 1)Option 2)Option...

In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is 10 and one of the foci is at \left ( 0,5\sqrt{3} \right ), then the length of its latus rectum is : 

 

 

 

  • Option 1)

    10

  • Option 2)

    5

  • Option 3)

    8

  • Option 4)

    6

  focus is at   given difference of major axis-minor axis  Length of LR = Option 1)Option 2)Option 3)Option 4)

Let f(x)=a^{x}(a>0) be written as f(x)=f_{1}(x)+f_{2}(x), where f_{1}(x) is an even function and f_{2}(x) is an odd function. Then f_{1}(x+y)+f_{1}(x-y) equals:

  • Option 1)

    2f_{1}(x)f_{1}(y)

  • Option 2)

    2f_{1}(x+y)f_{1}(x-y)

  • Option 3)

    2f_{1}(x)f_{2}(y)

  • Option 4)

    2f_{1}(x+y)f_{2}(x-y)

 
Now,     Option 1) Option 2) Option 3) Option 4)

If S_{1}\; and\; S_{2} are respectively the sets of local minimum and local maximum points of the function,f(x)=9x^{4}+12x^{3}-36x^{2}+25,x\: \epsilon \: \mathbb{R}, then :
 

  • Option 1)

    S_{1}=\left \{ -2 \right \};S_{2}=\left \{ 0,1 \right \}

  • Option 2)

    S_{1}=\left \{ -2 ,1\right \};S_{2}=\left \{ 0 \right \}

  • Option 3)

    S_{1}=\left \{ -2 ,0\right \};S_{2}=\left \{ 1 \right \}

     

  • Option 4)

    S_{1}=\left \{ -1\right \};S_{2}=\left \{ 0,2 \right \}

 
                                  Option 1) Option 2) Option 3)   Option 4)

A person throws two fair dice. He wins Rs. 15 for throwing a doublet 

( same numbers on the two dice), wins Rs. 12 when the throw results

in the sum of 9 , and loses Rs. 6 for any other outcome on the throw. 

Then the expected gain / loss (in Rs.) of the person is :

  • Option 1)

    \frac{1}{2}  gain 

  • Option 2)

    \frac{1}{4} loss

  • Option 3)

    \frac{1}{2} loss

  • Option 4)

    2 gain

 

Option 2) 1/4 loss

The Boolean expression \sim (p\Rightarrow (\sim q)) is equivalent to :

 

  • Option 1)

    p \wedge q

     

     

     

     

  • Option 2)

    q\Rightarrow \sim p

  • Option 3)

    p\vee q

  • Option 4)

    (\sim p)\Rightarrow q

 
The Boolean expression                                                                                 Option 1)         Option 2) Option 3) Option 4)

If the angle of intersection at a point where two circles with radii 5\: cm and 12\: cm intersects is 90^{\circ}, then the length (in cm) of their common chord is : 

 


 

  • Option 1)

    \frac{13}{2}

  • Option 2)

    \frac{13}{5}

  • Option 3)

    \frac{120}{13}

  • Option 4)

    \frac{60}{13}

Length of common chord =  Option 1)Option 2)Option 3)Option 4)

The value of \sin ^{-1}\left ( \frac{12}{13} \right )-\sin ^{-1}\left ( \frac{3}{5} \right )  is equal to : 
 

  • Option 1)

    \frac{\pi }{2}-\cos ^{-1}\left ( \frac{9}{65} \right )

  • Option 2)

    \pi -\sin ^{-1}\left ( \frac{63}{65} \right )

  • Option 3)

    \frac{\pi }{2}-\sin ^{-1}\left ( \frac{56}{65} \right )

     

  • Option 4)

    \pi -\cos ^{-1}\left ( \frac{33}{65} \right )

 
  Option 1) Option 2) Option 3)   Option 4)

The angles A,B and C of a triangle ABC are in A.P.  and a:b=1:\sqrt3.

If c = 4 cm , then the area ( in sq. cm) of this triangle is: 

  • Option 1)

    \frac{2}{\sqrt3}

  • Option 2)

    4\sqrt3

  • Option 3)

    2\sqrt3

  • Option 4)

    \frac{4}{\sqrt3}

 
In  , A,B,C are in A.P. =>  Now, it is given that a:b= Now, Area of                                                                                         Option 1) Option 2) Option 3) Option 4)

If \int \frac{dx}{(x^{2}-2x+10)^{2}}=A(\tan^{-1}(\frac{x-1}{3})+\frac{f(x)}{x^{2}-2x+10})+C

Where C is a constant of integration , then :

  • Option 1)

    A=\frac{1}{54}\: \: and\: \: f(x)=3(x-1)

  • Option 2)

    A=\frac{1}{81}\: \: and\: \: f(x)=3(x-1)

  • Option 3)

    A=\frac{1}{27}\: \: and\: \: f(x)=9(x-1)

  • Option 4)

    A=\frac{1}{54}\: \: and\: \: f(x)=9(x-1)^{2}

 
put              correct option is (1)    Option 1) Option 2) Option 3) Option 4)

All the pairs ( x, y ) that satisfy the inequality 

2^{\sqrt{sin^{2}x-2sinx+5}\cdot \frac{1}{4^{sin^{2}y}}}\leq 1  also satisfy the equation : 

  • Option 1)

    2|sinx|=3siny

  • Option 2)

    2 sinx=siny

  • Option 3)

    sinx=2siny

  • Option 4)

    sinx=|siny|

 
=>  &  So, correct option is (4). Option 1) Option 2) Option 3) Option 4)

If the line x-2y=12 is the tangent to the ellipse

 \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 at the point (3,\frac{-9}{2}) , then the length

of the latus rectum of the ellipse is : 

  • Option 1)

    9

  • Option 2)

    12\sqrt2

  • Option 3)

    5

  • Option 4)

    8\sqrt3

 
Tangent to a given ellipse at  Equation of tangent at  Now compare this equation with given equation of tangent  x - 2y = 12 Length of LR =  So, correct  option is (1). Option 1) 9 Option 2) Option 3) 5 Option 4)

If the circles x^{2}+y^{2}+5Kx+2y+K=0 and 

2(x^{2}+y^{2})+2Kx+3y-1=0 , (K\epsilon R) , intersect

at the points P and Q , then the line 4x+5y-K=0 passes

through P and Q , for :

  • Option 1)

    infinitely many values of K

  • Option 2)

    no value of K

  • Option 3)

    exactly two values of K

  • Option 4)

    exactly one value of K

 
Given two circles are      Equation of common chord  => ................(1) Given equation of chord is  ..................................(2) On Comparing (1) & (2) There is no value of k  So, option (2) is correct. Option 1) infinitely many values of  Option 2) no value of  Option 3) exactly two values of  Option 4) exactly one value of 

For any two statements p and q , the negation of the expression p\vee \left ( \sim p\wedge q \right ) is :

 

  • Option 1)

     \sim p\; \wedge \sim q     

  • Option 2)

    p\; \wedge q       

  • Option 3)

     p\; \leftrightarrow q

  • Option 4)

     \sim p\; \vee \sim q

Option 1)      Option 2)       Option 3) Option 4) 

If the line y=mx+7\sqrt{3} is normal to the hyperbola \frac{x^{2}}{24}-\frac{y^{2}}{18}=1   , then a value of m is :

  • Option 1)

    \frac{\sqrt{5}}{2}          

  • Option 2)

    \frac{\sqrt{15}}{2}

  • Option 3)

    \frac{2}{\sqrt{5}}

  • Option 4)

    \frac{3}{\sqrt{5}}

 
      given hyperbola       Normal to hyperbola is slope form            compare this                       Option 1)            Option 2) Option 3) Option 4)

The common tangent to the circle x^{2}+y^{2}=4\:\:and\:\:x^{2}+y^{2}+6x+8y-24=0  also passes through the point :

  • Option 1)

    (4,-2)

  • Option 2)

    (-6,4)

  • Option 3)

    (6,-2)

  • Option 4)

    (-4,6)

 
common tangent will  be   Option 1) Option 2) Option 3) Option 4)

Which one of the following statements is not a tautology?

  • Option 1)

    (p \vee q)\rightarrow (p\vee (-q))

  • Option 2)

    (p\wedge q)\rightarrow (\sim p)\vee q

  • Option 3)

    p\rightarrow (p\vee q)

  • Option 4)

    (p\wedge q)\rightarrow p

 
Option 1) Option 2) Option 3) Option 4)

The term independent of x in the expansion of 

(\frac{1}{60}-\frac{x^{8}}{81})\cdot (2x^{3}-\frac{3}{x^{2}})^{6} is equal to :

  • Option 1)

    -72

  • Option 2)

    36

  • Option 3)

    -36

  • Option 4)

    -108

 
The term independent of  in the expansion of  =>  =>  Option 1) Option 2) 36 Option 3) Option 4)

The length of the perpendicular drawn from the point (2,1,4) to the plane 

containing the lines \vec{r}=(\hat{i}+\hat{j})+\lambda (\hat{i}+2\hat{j}-\hat{k})  and 

\vec{r}=(\hat{i}+\hat{j})+\mu (-\hat{i}+\hat{j}-2\hat{k}) is : 

 

  • Option 1)

    3

  • Option 2)

    \frac{1}{3}

  • Option 3)

    \sqrt{3}

  • Option 4)

    \frac{1}{\sqrt{3}}

 
Perpendicula vector to the plane   Equation of the plane  Equation =>    Option 1) 3 Option 2) Option 3) Option 4)
Exams
Articles
Questions