Register

Recent questions tagged geometry

1 1 vote
1 1 answer
764
764 views
ISI2015-DCG-39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b)$, $B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$b=\pm \sqrt{2}b$$b= – \sqrt{2}a$$b=a$
User Avatar
0 0 votes
0 0 answers
1.7k
1.7k views
ISI2015-DCG-40
The equations $x=a \cos \theta + b \sin \theta$ and $y=a \sin \theta + b \cos \theta$, $( 0 \leq \theta \leq 2 \pi$ and $a,b$ are arbitrary constants) representa circlea ...
User Avatar
0 0 votes
0 0 answers
406
406 views
ISI2015-DCG-41
A straight line touches the circle $x^2 +y^2=2a^2$ and also the parabola $y^2=8ax$. Then the equation of the straight line is$y=\pm x$$y=\pm (x+a)$$y=\pm (x+2a)$$y=\pm (x...
User Avatar
0 0 votes
1 answers 1 answer
642
642 views
ISI2015-DCG-42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8$. hen its eccentricity is$\frac{4}{5}$$\frac{1}{\sqrt{52}}$$\frac{3}{5}$$\frac{1}{2}$
User Avatar
0 0 votes
0 0 answers
587
587 views
ISI2015-DCG-43
Four tangents are drawn to the ellipse $\displaystyle{}\frac{x^2}{9} + \frac{y^2}{5} =1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\...
User Avatar
0 0 votes
1 1 answer
574
574 views
ISI2015-DCG-44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2}$, then the equation of the hyperbola is$y^2-x^2=32$$x^2-y^2=16$$y^2-x^2=16$$x^2-...
User Avatar
0 0 votes
1 1 answer
771
771 views
ISI2015-DCG-53
Four squares of sides $x$ cm each are cut off from the four corners of a square metal sheet having side $100$ cm. The residual sheet is then folded into an open box which...
User Avatar
0 0 votes
1 1 answer
1.1k
1.1k views
ISI2015-DCG-59
If in a $\Delta ABC$, $\angle B = \frac{2 \pi}{3}$, then $\cos A + \cos C$ lies in$[\:- \sqrt{3}, \sqrt{3}\:]$$(\: – \sqrt{3}, \sqrt{3}\:]$$(\:\frac{3}{2}, \sqrt{3}\:)$$(...
User Avatar
0 0 votes
0 0 answers
459
459 views
ISI2015-DCG-60
Which of the following relations is true for the following figure?$b^2 = c(c+a)$$c^2 = a(a+b)$$a^2=b(b+c)$All of these
User Avatar
0 0 votes
0 0 answers
505
505 views
ISI2016-DCG-51
Four squares of sides $x\: cm$ each are cut off from the four corners of a square metal sheet having side $10\: cm.$ The residual sheet is then folded into an open box w...
User Avatar
0 0 votes
0 0 answers
562
562 views
ISI2016-DCG-59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in$\left[\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:\frac{3}{...
User Avatar
0 0 votes
2 2 answers
757
757 views
ISI2017-DCG-2
The area of the shaded region in the following figure (all the arcs are circular) is$\pi$$2 \pi$$3 \pi$$\frac{9}{8} \pi$
User Avatar
0 0 votes
1 1 answer
681
681 views
ISI2017-DCG-14
If $a,b,c$ are the sides of a triangle such that $a:b:c=1: \sqrt{3}:2$, then $A:B:C$ (where $A,B,C$ are the angles opposite to the sides of $a,b,c$ respectively) is$3:2:1...
User Avatar
0 0 votes
1 1 answer
491
491 views
ISI2017-DCG-18
If $a,b,c$ are the sides of $\Delta ABC$, then $\tan \frac{B-C}{2} \tan \frac{A}{2}$ is equal to$\frac{b+c}{b-c}$$\frac{b-c}{b+c}$$\frac{c-b}{c+b}$none of these
User Avatar
0 0 votes
1 1 answer
669
669 views
ISI2017-DCG-19
The angle between the tangents drawn from the point $(-1, 7)$ to the circle $x^2+y^2=25$ is$\tan^{-1} (\frac{1}{2})$$\tan^{-1} (\frac{2}{3})$$\frac{\pi}{2}$$\frac{\pi}{3...
User Avatar
0 0 votes
1 1 answer
501
501 views
ISI2017-DCG-20
If the coordinates of the middle point of the portion of a line intercepted between the coordinate axes are $(3,2)$, then the equation of the straight line is$2x+3y=12$$3...
User Avatar
0 0 votes
1 1 answer
523
523 views
ISI2017-DCG-21
If $a,b,c$ are in $A.P.$ , then the straight line $ax+by+c=0$ will always pass through the point whose coordinates are$(1,-2)$$(1,2)$$(-1,2)$$(-1,-2)$
User Avatar
0 0 votes
1 1 answer
744
744 views
ISI2017-DCG-29
The area (in square unit) of the portion enclosed by the curve $\sqrt{2x}+ \sqrt{2y} = 2 \sqrt{3}$ and the axes of reference is$2$$4$$6$$8$
User Avatar
1 1 vote
1 1 answer
858
858 views
ISI2018-DCG-15
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines is$6$$9$$12$$18$
User Avatar
0 0 votes
1 1 answer
377
377 views
KPGCET-CSE-2019-22
The scaling factors equals to $2$ in any directionRetains the distance of the defining point of the object from the origin, but doubles the size of the object in that dir...
User Avatar
0 0 votes
1 1 answer
403
403 views
KPGCET-CSE-2019-23
The normals to the plane surface $ax + by + cz+ d = 0$ is represented by$ai + bj + ck$$ai + bj +dk$$ai + cj + dk$$bi + cj + dk$where $(i, j, k)$ are unit normal respectiv...
User Avatar
1 1 vote
2 2 answers
1.9k
1.9k views
ISI2019-MMA-17
The reflection of the point $(1,2)$ with respect to the line $x + 2y =15$ is$(3,6)$$(6,3)$$(5,10)$$(10,5)$
User Avatar
1 1 vote
1 answers 1 answer
1.2k
1.2k views
ISI2019-MMA-16
If $S$ and $S’$ are the foci of the ellipse $3x^2 + 4y^2=12$ and $P$ is a point on the ellipse, then the perimeter of the triangle $PSS’$ is$4$$6$$8$dependent on the coor...
User Avatar
2 2 votes
1 answers 1 answer
682
682 views
UPPCL AE 2018:85
The set of equations $x^{2} + y^{2} = 1$ and $x + y = 0$ has how many real solutions?Infinite number of solutionsNo solution$2$ solutions$1$ solution
User Avatar
0 0 votes
1 1 answer
1.3k
1.3k views
MadeEasy Test Series: General Aptitude - Geometry
Triangles ABC and CDE have a common vertex C with the side AB of triangle ABC being parallel to side DE of triangle CDE. If the length of side AB=4 cm and length of side ...
User Avatar
1 1 vote
2 2 answers
2.7k
2.7k views
NIELIT 2018-8
Let us consider the length of the side of a square represented by $2y+3$. The length of the side of an equilateral triangle is $4y$. If the square and the equilateral tri...
User Avatar
1 1 vote
2 2 answers
991
991 views
Geometry
Which of the triangles is an isosceles triangle having the three angles :$40^{\circ},50^{\circ},90^{\circ}$$30^{\circ},60^{\circ},90^{\circ}$$45^{\circ},45^{\circ},90^{\c...
User Avatar
0 0 votes
1 1 answer
1.1k
1.1k views
Uttrakhand Asst. Professor Exam-90
If an image has a height of 4.5 inch and an aspect ration of 1.5, then what is its width?3 inches0.33 inches6.75 inchesNone of the above
User Avatar
44 44 votes
6 answers 6 answers
18.3k
18.3k views
GATE CSE 2018 | GA | Question: 9
In the figure below, $\angle DEC + \angle BFC$ is equal to _____$\angle BCD - \angle BAD$$\angle BAD + \angle BCF$$\angle BAD + \angle BCD$$\angle CBA + \angle ADC$
User Avatar
32 32 votes
3 answers 3 answers
11.3k
11.3k views
GATE CSE 2018 | GA | Question: 3
The area of a square is $d$. What is the area of the circle which has the diagonal of the square as its diameter?$\large{\pi} d$$\large{\pi} d^2$$\dfrac{1}{4}\large{\pi} ...
User Avatar
Page: